Top quark physics Future Measurements - Fermilab

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					         Fermi National Accelerator Laboratory

                                                                                                   FERMILAB-Conf-97/085




                         Top Quark Physics: Future Measurements


     R. Frey, D. Gerdes, J. Jaros, S. Vejcik, E. Berger, R.S. Chivukula, F. Cuypers, P. Drell, M. Fero,
     N. Hadley, T. Han, A. Heinson, B. Knuteson, F. Larios, H. Miettinen, L. Orr, M. Peskin, R. Raja,
                        T. Rizzo, U. Sarid, C. Schmidt, T. Stelzer, and Z. Sullivan



                                         Fermi National Accelerator Laboratory
                                          P.O. Box 500, Batavia, Illinois 60510




                                                            April 1997



Published Proceedings of the Workshop on New Directions for High Energy Physics (Snowmass ’96),
Snowmass, Colorado, June 25-July 12, 1996




Operated by Universities Research Association Inc. under Contract No. DE-AC02-76CH03000 with the United States Department of Energy
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                                 Top Quark Physics: Future Measurements
             R. Frey, D. Gerdes, J. Jaros, S. Vejcik, E. Berger, R. S. Chivukula, F. Cuypers, P. Drell,
                 M. Fero, N. Hadley, T. Han, A. Heinson, B. Knuteson, F. Larios, H. Miettinen,
                L. Orr, M. Peskin, R. Raja, T. Rizzo, U. Sarid, C. Schmidt, T. Stelzer, Z. Sullivan
                        ABSTRACT                                                         II. TOP QUARK YIELDS
  We discuss the study of the top quark at future experiments              At both hadron colliders and lepton colliders, most top quarks
and machines. Top’s large mass makes it a unique probe of                are produced in pairs. Each t quark decays immediately to Wb,
physics at the natural electroweak scale. We emphasize mea-              and the observed event topology depends on the decay mode of
surements of the top quark’s mass, width, and couplings, as well                                        
                                                                         the two W ’s. About 5% of tt decays are to the “dilepton” fi-
as searches for rare or nonstandard decays, and discuss the com-         nal state, which occurs when both W ’s decay to e or  . The
plementary roles played by hadron and lepton colliders.                  “lepton+jets” final state occurs in the 30% of tt decays where
                                                                                                                           
                                                                         one W decays into e or  and the other decays into quarks.
                                                                         The remaining 65% of the decays are to final states containing 
                   I. INTRODUCTION                                       leptons or hadronic jets. In this section we discuss the yields in
                                                                         these channels at future colliders.
   The recent observation of the top quark by the CDF and D0
collaborations[1, 2] has opened up the new field of top physics.
The top quark’s measured mass of approximately 175 GeV[3]                           A. Top Yields at Hadron Colliders
is nearly twice the mass of the next most massive particle, the             The dominant top quark production mechanism at hadron col-
Z boson. It is also tantalizingly close to the natural electroweak       liders is pair production through qq or gg annihilation. The rela-
                                                                                                              
scale, set by vHiggs = 246 GeV. While the Standard Model pro-            tive contribution of these two processes at the Tevatron is about
vides a theoretical context in which the top mass can be com-            90%–10%, while at the LHC these percentages are reversed.
pared to (and found consistent with) other electroweak data, it          The cross section for top pair production has been calculated by
offers no fundamental explanation for the top quark’s large mass,        several authors[7]. For pp collisions at the planned Tevatron en-
                                                                                  p                 
which arises from its large coupling to the symmetry-breaking            ergy of s = 2:0 TeV, the cross section for mt = 175 GeV is
sector of the theory. Precision measurements of the top mass,            calculated to be 7.5 pb, with an uncertainty estimated by various
width, and couplings at future experiments may therefore lead            groups to be 10-30%. This is a 40% increase over the cross sec-
to a deeper understanding of electroweak symmetry-breaking.              tion at 1.8 TeV, and underscores the importance of even modest
Such measurements are possible in part because the top quark’s           upgrades to the Tevatron energy. Thus a 30 fb 1 Tevatron run
natural width of 1.4 GeV is much greater than the hadronization                                                        
                                                                         would resultp about 225,000 produced tt pairs. The LHC (pp
                                                                                        in
timescale set by QCD , so that top is completely described by           collisions at s = 14 TeV) is a veritable top factory, with a cal-
perturbative QCD. Thus nature has presented us with the unique           culated tt production cross section of about 760 pb. This would
                                                                                   
opportunity to study the weak interactions of a bare quark. It is        result in about 7.6 million produced tt pairs per experiment in
                                                                                                                   
the conclusion of this subgroup that precision studies of the top        one year of low-luminosity LHC running.
quark should be a high priority at future machines.                         In addition, single top quarks can be produced through elec-
   We have concentrated our attention on top physics at the fol-         troweak processes such as W -gluon fusion or the production of
lowing machines. The first is the so-called “TeV-33,” defined              an off-shell W that decays to t[8]. The single-top production
                                                                                                            b
                                                                                                         
                                                                         cross section is about 1/3 the tt cross section at both the Tevatron
                                     p
as a luminosity upgrade to the Fermilab Tevatron that would
result in datasets of 30 fb 1 at s = 2:0 TeV. For com-                  and the LHC. The single-top channels are of particular interest
parison, the goal for Tevatron Run II, scheduled to begin in             for measurements of the top quark width and Vtb as described
1999, is 2 fb 1 at the same energy. We have also considered              below.
the top physics capabilities of the LHC, which will initially de-           Studies of the top quark at hadron colliders emphasize the
liver 10 fb 1/year and evolve to 100 fb 1/year during high-              dilepton and lepton+jets decay modes. Because these final states
luminosity running. Finally, we have considered an e+ e lin-             contain isolated high-PT lepton(s) and missing energy, they are
ear collider operating at or above the tt threshold and deliver-
                                                                        relatively easy to trigger on and reconstruct. The dilepton mode
ing approximately 50 fb 1/year. We have not explicitly consid-           has low backgrounds to begin with, while backgrounds in the
ered a muon collider, although its top physics capabilities ap-          lepton+jets channel can be reduced to an acceptable level by a
pear qualitatively similar to those of e+ e machines provided            combination of kinematic cuts and b-tagging. Recently CDF has
that detector backgrounds can be controlled. We did not study a          demonstrated that top signals can be identified in the  and all-
“super pp collider” in the 60–200 TeV range. Other recent stud-          hadronic decay modes as well, but to establish benchmark yields
ies of top physics at the Tevatron can be found in the TeV2000           for future experiments it is useful to focus on the dilepton and
report[4] and references therein, while top physics at e+ e ma-          lepton+jets final states. These yields are obtained from current
chines has recently been reviewed by Murayama and Peskin[5]              CDF and D0 acceptances by including the effects of planned up-
and Frey[6].                                                             grades such as full geometrical coverage for secondary-vertex

                                                                     1
b-tagging and improved lepton-ID in the region 1 < jj <                            
                                                                              The tt are produced polarized and, due to initial-state brem-
2:5[4]. These acceptances are believed to be representative                sstrahlung and gluon radiation, are not always back to back. Ac-
of any hadron collider detector with charged particle tracking             cording to expectations, the weak decay t ! bW proceeds be-
in a magnetic field, good lepton identification, and secondary-              fore hadronization can occur. This allows the possibility to per-
vertexing capability. The assumptions include:                             form, in principle, a complete reconstruction in an environment
                                                                           with little additional hadronic activity. The rapid top decay also
     High-PT charged lepton identifiction with good efficiency              ensures that its spin is transferred to the bW system, which opens
      for jj < 2                                                          up unique opportunities to probe new physics, as will be ex-
                                                                           plored in Section VII.
     Secondary-vertex b-tagging with an efficiency of 50-60%                  The emphasis of most simulations to date has been to perform
      per b-jet for jj < 2                                                a largely topological event selection, taking advantage of the
                                                                                                                         
                                                                           multi-jet topology of the roughly 90 of tt events with 4 or 6 jets
     Ability to tag “soft leptons” from b   ! lX with an effi-            in the final state. Therefore, cuts on thrust or number of jets dras-
      ciency of about 15% per b jet                                        tically reduces the light fermion pair background. In addition,
                                                                           one can use the multi-jet mass constraints M jet-jet  MW
                                                
      Double b-tag efficiency of about 40% per tt event. Double-            and M 3-jet  mt for the cases involving t ! bqq0 . Simula-
      tagged events are a particularly clean sample with low com-          tion studies[10] have shown that multi-jet resolutions of 5 GeV
      binatoric background and are well-suited for measurement             and 15 GeV for the 2-jet and 3-jet masses, respectively, are ade-
      of the top mass.                                                     quate and readily achievable with standard detector resolutions.
                                                                           A detection efficiency of about 70% with a signal to background
Table I shows the expected yields and signal/background at the             ratio of 10 was attained in selecting 6-jet final states just above
Tevatron. The acceptance of the LHC detectors is expected to be            threshold. These numbers are typical also for studies which se-
comparable to that of the Tevatron experiments, so to first order           lect the 4-jet+` decay mode.
the yields at the LHC will be greater by a factor equal to the ratio          Another important technique is that of precision vertex detec-
of the cross sections, approximately 100.                                  tion. The present experience with SLC/SLD can be used as a
                                                                           rather good model of what is possible at NLC. The small and sta-
                                                                           ble interaction point, along with the small beam sizes and bunch
          Table I: Expected top yields at the Tevatron.                    timing, make the NLC ideal for pushing the techniques of ver-
                                                                           tex detection. At this meeting, Jackson presented[11] simulation
              Mode            2 fb 1    30 fb 1      S/B                   results indicating that b-jets can be identified with an efficiency
             Dilepton           80       1200       5:1                    of 60% with about 97% purity. This has important implications
         l+  3 jets / 1 b     1300     20,000      3:1                    for top physics. Rather loose b-tagging, applied in conjunction
         l+  4 jets / 2 b     600       9000       12 : 1                 with the standard topological and mass cuts mentioned above,
          Single top (all)     170       2500       1:2.2                  imply excellent prospects for an efficient and pure top event se-
         Single top (W  )      20        300       1:1.3                  lection. Detailed studies employing such a combination of tech-
                                                                           niques have not yet been performed, however, and it will be in-
                                                                           teresting to see what can be achieved.
                                                                              The background due to W -pair production is the most difficult
                                                                           to eliminate. However, in the limit that the electron beam is fully
                B.    Top Yields at the NLC                                right-hand polarized, the W + W cross section is dramatically
   The tt cross section due to s-channel e+ e annihilation me-
                                                                          reduced. This allows for experimental control and measurement
diated by 
; Z bosons increases abruptly at threshold, reaches a           of the background. On the other hand, the signal is also reduced,
maximum roughly 50 GeV above threshold, then falls roughly                 albeit to a much smaller degree, by running with right-polarized
as the point cross section (pt = 87fb=sTeV) at higher en-
         p                                                                 beam. A possible strategy might be to run with right-hand polar-
ergy. At s = 500 GeV the lowest-order total cross section for              ized beam only long enough to make a significant check of the
unpolarized beams with mt = 180 GeV is 0:54 pb. The elec-                  component of background due to W pairs.
tron beam will be highly polarized ( 90), and this has a sig-
nificant effect on tt production. The lowest-order cross section
                                                                              III. MASS MEASUREMENT AT HADRON
becomes 0:74 pb (0:34 pb) for a fully left-hand (right-hand) po-                             COLLIDERS
              p
larized electron beam. A design year of integrated luminosity
(50 fb 1) at s = 500 GeV corresponds to roughly 25  103                      The precision with which the top quark mass, mt , can be mea-
 
tt events. The cross sections for t-channel processes, resulting,          sured is an interesting and important benchmark of proposed
for example, in final states such as e+ e tt or  tt, increase with
                                                                        future experiments. Within the Standard Model and its exten-
energy, but are still relatively small. If it turns out that elec-         sions mt is a fundamental parameter whose value is related to
troweak symmetry breaking is strongly coupled, this latter proc-           the Higgs sector of the electroweak interaction[12]. As such, it
ess then turns out to be of particular interest, as emphasized by          is desirable to have a measurement with a precision comparable
Barklow[9].                                                                to that of other electroweak parameters, typically of the order of

                                                                       2
< 1. This would correspond to an uncertainty of about 2 GeV               the resolution for the cases where the incorrect parton-jet assign-
in mt . Extensions to the Standard Model often predict the value           ment is made. The relative contribution of each of these sources
of mt , and a sufficiently precise measurement of mt could also             varies according to the tagging information available. Using no
help distinguish between different models. For this purpose, it            tagging information results in a resolution dominated by the mis-
would be of interest to measure the top quark mass with a preci-           assigned component but also results in the largest number of top
sion of about 1 GeV[13].                                                   events. Requiring two tagged jets results in the smallest resolu-
   The measurements provided by contemporary experiments at                tion because of the much higher fraction of events with correctly
CDF and at D0[14, 15] have been studied in sufficient detail that           assigned jets but has a corresponding loss of efficiency. Table II
the expected precision at hadron colliders can be conservatively           summarizes the tradeoff in the tagging requirements with the ex-
extrapolated with some confidence[4, 16, 17]. Issues relevant to            pected statistical uncertainty for a luminosity of 2 fb 1 at the
this extrapolation are presented below as understood from stud-            Tevatron or LHC. As shown, the ultimate statistical uncertainty
ies of the TeV2000 work but are believed to be a fair representa-          is a fraction of a GeV for any of the three samples.
tion of the challenges for experiments at the LHC as well. Other
mass-measurement techniques also exist but have not been ex-
plored at the same level of detail. Control of systematic uncer-           Table II: Expected statistical precision for measurement of top
tainties is likely to be the critical issue in the measurement of mt       quark mass for differently b-tagged subsamples.
in any method.
                                                                             Tags                
                                                                                      Number of tt Events      Background      mt (GeV)
                                                                             0             20000                 40000             0.3
     A. Constrained Fits in Lepton+jets Decays
                                                                             1             12000                  3000             0.3
   The most precise direct determination of the top mass cur-                2              4000                   100             0.3
rently comes from reconstructing candidate top events with a
l + jets topology. Assuming that the momenta of all final-state
partons except the one neutrino are measured, that the transverse             The second source of uncertainty in the top mass measurement
                                                    
energy of the system is conserved, that the t and t quarks have            is systematic. The largest sources of systematic uncertainty arise
a common mass, and that there are two real W bosons results                from differences between the observed mass distribution and the
in an overconstrained system from which the event kinematics               prediction from Monte Carlo and detector simulations. Such dif-
can be obtained. The method is of additional interest because it           ferences arise, for instance, in the jet-parton ET scale and in
provides a means of determining other kinematic features of the                               
                                                                           the modeling of tt production and decay. Table III shows the
 
tt decay such as their transverse momentum or total invariant              expected systematic uncertainties for the constrained fit tech-
mass.                                                                      nique at future hadron colliders with an integrated luminosity of
   The accuracy with which the technique can reconstruct the               2 fb 1.
kinematics is limited by the ambiguity in making the correspon-
dence between observed jets and underlying quarks. Without re-
lying on b-tagging, there are 12 different ways to label the jets          Table III: Expected systematic uncertainties in the measurement
as either a b-quark or a light quark from a W and to associate             of mt for an integrated luminosity of 10 fb-1 at a hadron collider.
them with either the t or  quark. If one jet is b-tagged, there
                            t
are six such combinations and if two jets are tagged then there                           Systematic              mt (GeV)
are two possibilities. Additionally, by requiring the  lepton                            Jet-Parton ET Scale          2.0
invariant mass to equal MW , the component of the  momen-                                Event Modeling               2.0
tum along the direction of the beam axis can be determined up                             Background Shape             0.3
to a quadratic ambiguity. Thus, there are twice as many kine-
matically consistent solutions for each event. By selecting the
single solution which best fits the tt hypothesis according to a
                                                                                                                    
  2 test, the reconstruction of the kinematics results in an esti-           Based on present understanding of tt event reconstruction,
                                                                          systematic uncertainties are expected to limit the ultimate pre-
mated top mass for each event. The measured top mass is ob-                cision with which the top mass can be measured. The most im-
tained by comparing the event mass distributionto that predicted           portant of these are the precision with which the jet ET scale can
by Monte Carlo models for different top masses using a maxi-               be determined and understanding the multijet environment of tt   
mum likelihood method.
                                                                           production.
   Two sources of uncertainty limit the precision with which this
technique can be used to measure mt . The first is the statistical
uncertainty which arises from the finite detector resolution and
                                                                                                 B.    Jet ET Scale
                                              p
the limited number of events. Monte Carlo studies indicate that               Jets are typically identified using fixed-cone clustering algo-
this source of uncertainty decreases like = N . The intrinsic             rithms. Monte Carlo models are used to derive a correspondence
resolution,  is itself composed of two pieces. The first piece             between observed jet energies and the momenta of the under-
is the resolution for those events where the correct assignment            lying partons. An understanding of the ET scale therefore in-
is made between the partons and jets and the second piece is               volves both theoretical uncertainties in the model of parton frag-

                                                                       3
                                                    W+jets F=(1.0-0.4)/0.4 ET1,ET2 < 8 GeV                                   No W Constraint (320 top, 80 bkg)
                                10                                                                               120
                                                                                                                                          Entries      1000
                                                                                                                                          Mean       0.8592
                                                   ET(2) < 8 GeV                                                                          RMS         2.334
                                          8                                                                      105                      Constant    83.73         3.590
                                                                                                                                          Mean       0.6071    0.5135E-01
                                                                                                                                          Sigma       1.461    0.4004E-01
      F = (PT(1.0)-PT(0.4))/PT(0.4) (%)

                                          6
                                                                                                                  90

                                          4
                                                                                                                  75
                                          2

                                          0                                                                       60


                                    -2
                                                                                                                  45

                                    -4
                                                                                                                  30
                                    -6

                                                                                                                  15
                                    -8

                         -10                                                                                       0
                                              20         40        60        80        100   120                       -15   -10     -5       0      5        10            15

                                                       Corrected PT of Jet1(0.4) GeV



Figure 1: Energy flow in annular region around single jets pro-                                         Figure 2: Estimated jet-parton ET scale extracted from toy
duced in association with W bosons.                                                                    Monte Carlo experiments. Each entry is the measured jet-parton
                                                                                                       ET scale obtained from the reconstructed W ! qq0 decay in top
                                                                                                                                                       
                                                                                                       events. Simulated experiments consisted of samples of top and
                                                                                                       background typical for Tevatron Run II data samples.
mentation to a jet, and experimental uncertainties in the detec-
tor’s measurement of the jet energy.
  Figure 1 shows a comparison of energy flow in an annulus
about single jets produced in association with W decays. Com-                                          trolled to the 1% level, implying a corresponding uncertainty
parison of jet anatomies with this technique between data and                                          in the top quark mass of about the same size.
Monte Carlo can be used to quantify theoretical uncertainties in
the jet-parton ET scale. Such studies will likely improve with
the size of the control samples and indicate that theoretical un-                                             C. Uncertainties in Kinematic Modeling
certainties in the jet-parton ET scale can be managed to better
than 1 GeV in future experiments.                                                                        In addition to the jet-parton ET scale, uncertainties in the top
  It is more difficult to reduce the detector effects below the                                         quark mass can arise from the uncertainty in modeling the jet
present typical value of 3-4 GeV, and this source of uncertainty                                       environment of top decays. Constrained fitting techniques typ-
could limit the ultimate precision of the top mass measurement.                                        ically associate the leading four jets with the two b jets and
New possibilities for understanding the jet-parton ET scale are                                        two jets from hadronic W decay; however, initial- or final-state
offered by control samples that will be available in future high-                                      gluon emission may contaminate the leading four jets with jets
statistics data sets. One example is to use the W ! qq0 decay in
                                                                                                                                          
                                                                                                       that do not arise directly from tt decay, resulting in a more
the top-quark events themselves to calibrate the scale. The di-                                        confused event kinematics. This effect is modelled by parton
jet mass distribution for W ! qq0 candidates in top events can
                                                                                                      shower Monte Carlo programs, such as Herwig. Figure 3 shows
be compared to a model where the jet ET scale is varied and                                            the invariant mass distribution for top events for those events
used to fit the scale. A toy Monte Carlo can be used to simu-                                           where extra gluon radiation results in a leading jet not associ-
late many such experiments with the appropriate combinations                                                                                      
                                                                                                       ated with the partons directly from the tt decay. Conservatively
of signal and background. Relying on the CDF detector as a                                             assuming no information is available on the rate of such events
model, Fig. 2 shows the distributionof extracted Jet ET scale us-                                      implies a corresponding uncertainty on the top quark mass of
ing the technique on experiments of varying signal-background                                          3 GeV. This uncertainty is currently limited by the lack of a large
composition. Each entry in the histogram is the extracted ET                                           sample of top quarks with which the modeling of jet kinemat-
scale obtained by the method for a single toy experiment where                                         ics can be tested. At the same time, significant theoretical and
the true ET scale was perfect. The width of the distribution is                                        phenomenological work has proceeded towards an understand-
the expected precision with which the Jet ET scale can be esti-                                        ing of gluon radiation in tt events[19]. In datasets with large
                                                                                                                                    
mated and is seen to be typically of order 1%, or a factor of 3-                                       number of top events, it is evident that the understanding of this
4 better than currently derived from sample of about 100pb 1.                                          and other related theoretical issues will improve and indeed will
We therefore conclude that the jet-parton ET scale can be con-                                         be a source of interesting physics as well.

                                                                                                   4
                                                                                                resolution can be substantially improved, it appears that a pro-
                                           Top 175 Monte Carlo
                                                                                                gram that relies on control samples in the data can manage the
                                                                                                leading systematic uncertainties to the 1% level. The ultimate
                        400                                                                     resolution as represented by the statistical uncertainty will be on
                                                                                                the order of a few hundred MeV. The issues of the modeling of
                        350
                                                                                                the top kinematics will be crucial but at the same time will be
     Entries/5 GeV/c2




                                                                                                very interesting tests in and of themselves. In short, our present
                        300
                                                                                                                    
                                                                                                understanding of tt reconstruction at hadron colliders supports
                        250
                                                At least 1 gluon jet among 4 leading Jets       the expectation that the measurement of mt at either the LHC or
                                                                                                at an upgraded Tevatron can be made with the precision thought
                        200                                  Lowest χ2 and Tagged               to be needed to provide insights into the Electroweak and Higgs
                                                                                                sector of the Standard Model.
                        150
                                                        Right Jets and Assignments

                        100
                                                                                                          IV. MEASUREMENTS AT THE tt
                                                                                                                                   
                         50
                                                                                                                   THRESHOLD

                          0
                                                                                                  Production of tt near threshold in e+ e (or +  ) annihi-
                                                                                                                   
                              100    150         200       250        300        350
                                    Reconstructed Top Mass (GeV/c )   2                         lation offers qualitatively unique opportunities for top physics
                                                                                                studies. In addition, in many cases, it promises to allow the most
                                                                                                precise measurements of key parameters. The cross section in
                                                                                                the tt threshold region depends sensitively on mt , s, and t ,
                                                                                                     
Figure 3: Reconstructed mass spectra from tt Monte Carlo
                                                                                               and interestingly, also depends on the top-Higgs Yukawa cou-
(mt = 175 GeV) with and without the presence of hard gluon                                      pling, t , and mH . In this section we briefly discuss the phe-
radiation.                                                                                      nomenology and prospects for these measurements near thresh-
                                                                                                old. The +  case is not expected to differ significantly from
                                                                                                e+ e except for radiative and accelerator effects, and is not oth-
                                                                                                erwise specifically discussed.
              D. Other Mass Measurement Techniques
  While the constrained fit technique provides the most precise                                                      A. Threshold Shape
determination available, other techniques exist, although they
                                                                                                                                                 
                                                                                                   In Fig. 4 we show the cross section for tt production as a
have not been explored in the same depth. As described above,
                                                                                                function of nominal center-of-mass energy Ecm =
                                                                                                                                                            ps for
the measurement of the top quark mass can be viewed as sim-
ply comparing a kinematic feature (such as the reconstructed                                    mt = 175 GeV. The theoretical cross section, indicated as
mass) with that predicted by models for different top masses.                                   curve (a), is based on the results of Strassler and Peskin[20]
                                                                                                             2
                                                                                                with sMZ  = 0:120, infinite Higgs mass, and nominal Stan-
The same philosophy can be applied, for instance, to under-
constrained topologies such as events where the tt decay in the
                                                                                               dard Model couplings. The characterization of the top thresh-
dilepton mode[18]. This technique is statistically less powerful                                old is an interesting theoretical issue, and the theoretical cross
than the lepton + jets method and suffers from similar systemat-                                section and its associated phenomenology have been extensively
ics due to the jet energy scale; however the method may comple-                                 studied[21, 20, 22, 23, 24, 10]. The energy redistributionmecha-
ment the more conventional analysis. Another intriguing possi-                                  nisms of initial-state radiation, beamstrahlung, and single-beam
bilityis to measure the decay length of B mesons associated with                                energy spread, have been successively applied to the theoretical
the b-jets in top decays. The decay length is correlated with the                               curve of Fig. 4. Hence, curve (d) includes all effects. We begin
b-jet boost and hence the mass. It has the additional attractive                                the discussion of top threshold physics with a brief overview of
feature of being a mostly tracking-based measurement, and is                                    these radiative and accelerator effects, which are especially im-
therefore much less dependent on the jet-parton ET scale. The                                   portant at tt threshold because of the relatively sharp features in
                                                                                                            
systematics in this technique, which include uncertainty in the                                 the cross section.
top quark transverse momentum distribution, need further study.                                    The effects of initial-state radiation (ISR) are appreciable for
                                                                                                high energy electron colliders, where the effective perturbative
                                                                                                expansion parameter for real photon emission, rather than =,
                                                                                                                                         p
                                           E.     Outlook                                                
                                                                                                is  = 2 lns=m2  1  1=8 for s = 500 GeV. We use a
                                                                                                                    e
  It appears that with available technology, the top quark mass                                 standard calculation[25] of ISR, which sums the real soft-photon
can be measured to a precision of about 1%, with the caveat that                                emission to all orders and calculates the initial state virtual cor-
the understanding of theoretical issues dealing with the jet envi-                              rections to second order. An analytic calculation[26] provides a
ronment in top decays is thought to be limited primarily by the                                 good approximation for the effects of beamstrahlung at the NLC.
small number of events presently available. It is hoped that sys-                               The figure of merit in the calculation is  = 
 B=Bc , where
tematic effects from these sources can be brought under control                                 
 = Ebeam=me c2 , B is the effective magnetic field strength of
with larger samples of data. While it is not clear that detector                                the beam, and Bc = m2 c3 =e  4  109 T. When   1
                                                                                                                           e      h

                                                                                            5
                                                                            rameter  decreases from 0:12 to 0:07. On the other hand, the
             0.8
                                                                                                                                  p
                                                                            accelerator design will have some effect on the resulting beam-
                                                                            strahlung spectrum. For example, in changing s from 500
                                                                            GeV to tt threshold, one might choose to keep the collision point
                                                                                      
                                        a                                   angular divergences constant, in which case the spot sizes would
             0.6                                                            increase roughly as 500=350, resulting in lower luminosity and
                                                                            decreased beamstrahlung. Alternatively, scaling the energy at
                                                                                                                                     p
                                            b                               constant beta would result in decreases only by  500=350.
                                                                            So one can expect for the SLAC design to have the fraction of lu-
  σtt (pb)




             0.4                                c                           minosity unaffected by beamstrahlung (the delta-function frac-
                                                                            tion) to be  50 at tt threshold.
                                                                                                     
                                                d                              An additional accelerator effect on the threshold shape results
                                                                            from the energy spread of each beam in its respective linac. This
             0.2                                                            is the additional effect included in curve (d) of Fig. 4, and is char-
                                                                            acterized by the FWHM of the energy spread for a single beam,
                                                                            E=E , which is a symmetric, non-centrally peaked distribution
                                                                            about the nominal beam energy. The calculation of Fig. 4 used
                                                                            E=E = 0:6. This quantity can be adjusted during opera-
                                                                            tion, typically by 50, within some bounds set by the acceler-
             0.0
                    340           345               350       355

                              Ecm (GeV)                                     ator design. In Section IV.E we discuss the measurement of the
                                                                            luminosity spectrum resulting from these effects.
Figure 4: Production cross section for top-quark pairs near
threshold for mt = 175 GeV. The theoretical cross section is                                B. Sensitivity to mt and s
given by curve (a). The following energy redistribution effects
have been applied to the theory for the remaining curves: (b)                  The threshold enhancement given by the predicted cross sec-
initial-state radiation (ISR); (c): ISR and beamstrahlung; (d):             tion curve (a) of Fig. 4 reflects the Coulomb-like attraction of the
ISR, beamstrahlung, and single-beam energy spread.                          produced top pair due to the short-distance QCD potential

                                                                                                  VQCD  CF sr ;
                                                                                                              
                                                                                                                                              (1)

the beamstrahlung is in the classical regime and is readily cal-            where CF = 4=3 and  is evaluated roughly at the scale of
culated analytically. For example, in the case of the SLAC X-               the Bohr radius of this t-t bound system:   smt . This
                                                                                                        
band NLC design, we have B  6  102 T and   0:08 at
ps = 500 GeV. In this case, there is an appreciable probabil-               bound state exists, on average, for approximately one classical
                                                                            revolution before one of the top quarks undergoes weak decay.
ity for a beam electron (or positron) to emit no photons. So the            The level spacings of the QCD potential, approximately given
spectrum is well-approximated as a delta function at E = Ecm                by the Rydberg energy,  2mt , turn out to be comparable to
                                                                                                           s
with a bremsstrahlung-like tail extending to lower energies. The            the widths of the resonance states, which are  2 t . There-
fraction of luminosity within the “delta function piece” of the             fore the various bound states become smeared together, where
                           
spectrum resolves the tt threshold structure, while the remain-             only the bump at the position of the 1S resonance (at about 347:5
ing luminosity is, for the most part, shifted in energy well away           GeV in Fig. 4) is distinguishable. The infrared cutoff imposed
from threshold. Hence, the primary effect of beamstrahlung is               by the large top width also implies[21] that the physics is in-
to reduce the useful luminosity at threshold. The delta-function            dependent of the long-distance behavior of the QCD potential.
fraction of luminosity for the nominal SLAC X-band NLC de-                  The assumed intermediate-distance potential is also found[10]
sign at 500 GeV, for example, is 43. The energy loss spectrum              to have a negligible impact. Hence, the threshold physics mea-
for initial-state radiation, like beamstrahlung, has a long tail, and       surements depend on the short-distance potential (Eq. 1) of per-
is also qualitatively similar to beamstrahlung in that it is rather         turbative QCD.
likely to have negligiblysmall energy loss. For example,  50                 An increase of s deepens the QCD potential, thereby increas-
of the total luminosity resultsp a center of mass collision energy
                                 in                                         ing the wave function at the origin and producing an enhanced
within 0:1 of the nominal s [27].                                          1S resonance bump. In addition, the binding energy of the state
   Hence, to good approximation the combined effect of these                varies roughly as the Rydberg energy  2 mt . So the larger s
                                                                                                                        s
    p
processes is an effective reduction of luminosity at the nomi-
nal s due to beam particles which have undergone energy loss
                                                                            has the combined effect of increasing the cross section as well as
                                                                            shifting the curve to lower energy. The latter effect would also
> t . We see this in Fig. 4, although there is clearly also some            occur, of course, for a smaller mt . Therefore, measurements of
smearing out of the threshold shape due to small energy loss. Of            s and mt extracted solely from a fit to the threshold cross sec-
course, there is no control of ISR, except for the choice of beam           tion will be partially correlated, but separable.
energy and accelerated particle—here a muon collider would                     In addition to the measurement of the threshold excitation
benefit from the decreased radiation, where the expansion pa-                curve, an interesting and potentially quite useful measurement

                                                                        6
near threshold is based upon the observation that the lifetime of                           C.       The Top Yukawa Potential
the bound state is determined by the first top quark to undergo
                                                                           In addition to the QCD potential, the Standard Model predicts
weak decay, rather than by annihilation. This implies that the                     
                                                                         that the tt pair is also subject to the Yukawa potential associated
reconstructed kinetic energy (or momentum) of the top decay
                                                                         with Higgs exchange:
products reflect the potential energy of the QCD interaction be-
fore decay. Hence, a measurement of the momentum distribu-                                          2 mH r
                                                                                            VY = 4 e r ;
                                                                                                     t
tion will be sensitive to VQCD and s . A larger s produces a                                                                   (2)
deeper VQCD , hence increasing the kinetic energy given to the
top decay products when the “spring” breaks upon decay of the            where mH is the Higgs mass and t is the Yukawa coupling,
first of either t or . The theory[22, 24] and phenomenology[10,
                    t                                                                             p
                                                                                                      2GF 1=2 H mt = H mt =vHiggs
                                                                                                        
28] of this physics have been extensively studied. The observ-
                                                                                       t =                                               (3)
able used to characterize the distribution is the peak of the mo-        The dimensionless parameter H is discussed below. Because
mentum distribution, p0 , which shifts to larger values for larger
                p                                                        of the extremely short range of the Yukawa potential, its effect
s. The best s to run the accelerator for this measurement is            is only on the wave function at the origin, and hence provides
about 2 GeV above the 1S peak. The studies show that p0 is in-           a shift of the cross section across the threshold region with a
deed sensitive to s . The measurement also has useful sensitiv-         slight energy dependence. Fig. 5 gives a calculation[31] of this
ity to the top width, which arises because a variation in t moves        effect. It is quite interesting that because of the large top mass,
                
the average t–t separation rd at the time of decay, and hence the        the Yukawa potential may indeed be observable in this system.
average potential energy VQCD rd .                                     From the various mH curves given in this calculation, we clearly
                                                                         see the exponential cutoff of the Yukawa potential for large mH .


   A number of studies have been carried out to simulate mea-
                
surements at tt threshold. Typically one fixes the width and
fits the threshold shape for the correlated quantities mt and                          1.0
       2
sMZ . For example, a simulation[10] assuming mt = 150
GeV used 1 fb 1 for each of 11 scan points. If mt and sMZ    2                     0.8
are left as free parameters, then a simultaneous 2-parameter fit
results in errors of 200 MeV and 0:005, respectively. If one per-
                                                                             σ (pb)




                                                                                      0.6
forms a single-parameter fit, holding the other quantity to a fixed
value, the resulting sensitivities approach 100 MeV and 0:0025.                                                                   MH
An update[29] of the 2-parameter fit for mt = 170 GeV gives                            0.4
                                                                                                                                ∞
errors of 350 MeV and 0:007 for the same 11-point scan. A sim-                                                                100 GeV
ilar simulated scan[30] assuming mt = 180 GeV and 5 fb 1 for                          0.2                                      60 GeV
each of 10 scan points resulted in single-parameter errors of 120
MeV and 0:0025 for mt and s, respectively. We see that while                          0
                                                         2
the error on mt is remarkably good, the error on sMZ  is less
                                                                                       –6              –4       –2      0             2       4
                                                                              12-95                               E (GeV)                 8100A1
impressive relative to current measurements. Of course, it will
be very interesting at the outset to compare the threshold exci-         Figure 5: Cross section near threshold for different Higgs
tation curve with expectations to see, for example, that the R          masses due to the Yukawa potential. mt = 180 GeV/c2 was as-
increase is consistent with the charge and spin of the top quark.        sumed. The abscissa center-of-mass energy is relative to 2mt .
But if the threshold curve can indeed be fit by QCD, then a rea-
                                                          2
sonable strategy for extracting mt might be to fix sMZ  at the
World average value and perform the single-parameter fit of the             It is assumed here, of course, that the Higgs bosons(s) will
threshold to extract mt . The studies cited above have also exam-        have already been discovered when such a measurement is un-
ined the use of the top momentum (p0) technique. It improves             dertaken. However, the Yukawa coupling to fermions is a fun-
somewhat the precision of the fitted parameters, typically im-            damental element of electroweak theory, and very likely can
proving both the mt and s MZ  errors by  20. The p0 mea-
                                 2                                       only be tested with top quarks. The factor H in Eq. 3 is used
surement also has different correlation between mass and strong          to parameterize the strength of the Yukawa coupling and pos-
coupling than the cross section, hence providing a useful cross-         sible deviations from the Standard Model, in which H = 1.
check. In fact, Fujii, et al. have emphasized that if the scan en-       For example, in two-Higgs-doublet models H is complex with
                                p
ergy is referenced to the measured position of the 1S peak, rather       real (imaginary) part proportional to 1= sin  (1= tan  ), where
than with respect to 2mt or s, then the p0 measurement be-               tan  is the usual ratio of Higgs vacuum expectation values.
comes independent of mt . Carried out in this way, the top mo-           Hence, these measurements can also be used to help distin-
mentum measurement would indeed be invaluable as a cross-                guish between different models of the Higgs sector. In Section
check. Systematic errors associated with the threshold measure-          VIII we review the prospects for the measurement of t in open
ments and scan strategies are discussed briefly in Section IV.E.          top production. However, the effect of the Higgs field on the tt 

                                                                     7
state at threshold is unique and it is interesting to see how sensi-                    1.25
tive a threshold scan might be. Figure 6 shows a calculation of                                                                a
the cross section across threshold for different values of H . The                     1.00
values mt = 175 GeV and mH = 300 GeV were used and all ra-
                                                                                                                               b
                                                                                                                               c
diative and accelerator effects are included. (Hence, the H = 1
                                                                                        0.75                                       de
curve corresponds to curve (d) of Fig. 4.) So one would have a                          0.50
reasonable sensitivity to this physics with some dedicated run-
                                                                                        0.25
ning just above threshold. Fujii[29] also applied the previously
mentioned 11 point scan of 1 fb 1 per point to the measurement




                                                                             σtt (pb)
                                                                                        0.00
of H . For larger mt the accuracy improves, as expected, and at                               340    342     344        346        348   350   352
mt = 170 GeV he finds that H can be measured to 25.                                     0.5

                                                                                         0.4
                0.6
                                                                                         0.3

                                                                                         0.2
                0.5                                                                                            e dc
                                                      1.5 1.0                                                       ba
                                                                                         0.1
                                                                 0.5
                0.4                                                                      0.0
                                                                                               340    342     344        346        348   350   352
     σtt (pb)




                0.3                                                                                         Ecm (GeV)
                                                                            Figure 7: Threshold shape for various values of t . The upper
                0.2                                                         plot is the theoretical prediction, while the lower plot includes
                                                                            all radiative and beam effects. The different curves corresond
                                                                            to t = SM = (a) 0:5, (b) 0:8, (c) 1:0, (d) 1:2, and (e) 1:5. We
                                                                                     t
                                                                            assumed mt = 175 GeV, where the Standard Model width is
                0.1

                                                                              SM = 1:42 GeV.
                                                                              t
                0.0
                      340   342.5      345   347.5   350        352.5       355

                               cm
                                       E (GeV)
Figure 6: Threshold shape for various (real) values of the
Yukawa coupling strength H . All radiative and beam effects                                                                             
                                                                            follows. The vector coupling present with Z -t-t and 
 -t-t can
are included, and mt = 175 GeV, mH = 300 GeV are used.                      proceed to S and D-wave bound states. On the other hand, the
The different curves corresond to H = 1:5, 1:0, and 0:5, as                                                           
                                                                            axial-vector coupling present with Z -t-t gives rise to P-wave
indicated.                                                                  states. Hence, it is possible to produce interference between S
                                                                            and P-waves which gives rise to a forward-backward asymmetry
                                                                            (AFB ) proportional to v=c cos , where  is the usual produc-
                                                                                                     
                                                                            tion polar angle in the tt rest system. Because of the large width
                                                                            of these states, due to the large t, they do overlap to a signif-
                            D.      The Top Width
                                                                            icant extent, and a sizeable AFB develops. The value of AFB
                 
  Running at tt threshold allows a direct measurement of the top            varies from about 5% to 12% across the threshold, with the min-
quark width, t , without making any assumptions about top de-               imum value near the 1S resonance. Since the top width controls
cay modes. As discussed below in Section V, this is especially              the amount of S-P overlap, we expect the forward-backward
important for non-standard decays in which top does not decay               asymmetry to be a sensitive method for measuring t . In fact,
to W . On general grounds, we expect the peak cross section of a            this has been studied, again by the same groups as above. Al-
1S quarkonium bound state to vary with the total width as t 1,              though considerably less sensitive to t than the threshold cross
independent of decay modes. This is shown by the theoretical                section (about a factor ten in terms of luminosity), this technique
curves given in the upper plot of Fig. 7. After applying ISR and            again provides a useful crosscheck of the threshold physics.
beam effects, the width is affected as shown in the lower plot of
Fig. 7. In this case, we see that the cross section just below the 1S
                                                                                        E.      Systematic Effects and Scan Strategies
threshold is also quite sensitive to the width. The studies cited
above indicate sensitivity to t at the level of 10% for 50 fb 1               As indicated in Section II.B, an efficient and pure event se-
of data. However, as discussed in the next section, any estimate            lection with good experimental controls appears to be possible.
will depend crucially on the scan strategy employed.                        So we expect the outstanding systematic issue to be the char-
  Yet another, quite different observable which is particularly             acterization of the redistribution of collision energy due to ra-
sensitive to t has been studied[32, 10] to help further pin down            diation and beam effects, as discussed in Section IV.A. This
the physics parameters at threshold. The idea is summarized as              can be quantified by a differential luminosity spectrum dL=dE

                                                                        8
which describes how the nominal center-of-mass energy s is
                                                             p               Of course, one would really like to directly measure t given
distributed to e+ e collision energies E . Of course, this must            this opportunity. From Fig. 7 we see that measuring the slope of
be determined in order to unfold the physics parameters from the           the threshold rise is required to measure the width. So one would
experiemental scan points. One would hope to measure the lu-               want to expend luminosity at about 344 and 348 GeV, as well.
minosity expended at each scan point to  1. Fortunately, it              Fujii[29] finds that fixing s and performing a 2-parameter fit to
is not necessary to know the radiative and accelerator effects a           mt and t, the usual 11  1 fb 1 scan gives (statistical) errors
priori at this level of precision. One can, in fact, make an inde-         of 100 MeV for mt and  t= t = 16. If t looked interest-
pendent measurement of the luminosity spectrum. As proposed                ing one could go after the especially sensitive scan energies. Ap-
by Frary and Miller[33], the idea is to measure the acollinearity          parently, the error could be pushed by statistical scaling until the
distribution of final state particles in a 2 ! 2 process. Bhabha            luminosity systematics become important, at the level of  1.
scattering turns out to be ideal. At intermediate scattering an-           Hence, a scan chosen in this way would push the measurement
gles (about  = 20 to  = 40), Bhabha scattering has a rate              of t to about 5% in 50 fb 1 .
 100 times that of top production, the acollinearity can be mea-
sured with the requisite accuracy (< 1 mrad), and it is theoret-
ically well known at the 1% level. The acollinearity angle A
                                                                              Observing the effect of the Yukawa potential would be unique,
for a final-state e+ e pair produced at scattering angle  is re-
                                                                           and checking the Yukawa coupling would be a fundamental test.
lated to the energy difference E of the initial-state e+ e by
                                                                           First of all, one would want to check that the cross section at the
                                                                           1S (about 347:5 GeV for mt = 175 GeV) is as expected given
E=E = A = sin , where E  Ebeam is their average energy.                the value of mH taken from other measurements (see Fig. 5).
So starting with the theoretical distribution in A , one applies
                                                                           This would establish whether the strength of the Yukawa poten-
contributions due to ISR and beamstrahlung (and single-beam
                                                                           tial is as expected. Then, from Fig. 6 we see that one or two
energy spread), whose functional forms are known, until the re-
                                                                           scan points above the 1S would establish the slope and provide a
                                                                           measurement of H . Again, if the physics demands it, this mea-
sulting distribution agrees with the measured one. One then ap-
plies this luminosity spectrum to the top scan data taken over the
                                                                           surement could be pushed statistically, eventually to the level of
same running period.
   The other related issue is the determination of the absolute en-
                                                                            1.
ergy scale, that is, the energy of the beams. This is presently
               p
done at the SLC using a spectrometer for each spent beam. The
accuracy for s is 25 MeV (0:03). Scaling this same error
                                                                              In all cases, a reasonable fraction of the luminosity will have
                                                                           to be expended just below threshold to measure the background.
to top threshold gives 100 MeV accuracy, which is at or below              This fraction would depend, of course, on the ultimate purity of
the level of error quoted above for a high statistics measurement          the event selection, but 10 to 20% is a reasonable guess. Since
of mt . To measure the beam energy, the beams will be briefly               W + W production is expected to be the largest background,
taken out of collision, which eliminates beamstrahlung. (The               an important experimental control is provided by the electron-
beamstrahlung-reduced beam energy measured by the spectrom-                beam polarization. Flipping between left and right-handed po-
eter is not equivalent to that seen by collisions since the two sam-       larizations would give a huge change in this background (since
ple the beam populations differently.)                                     the cross section for right-handed production is tiny) by a pre-
                                                                           dictable amount. So one should expect that the background frac-
   Most of the sensitivity to the threshold physics measurements
of mt , s, t, and H comes from the cross section scan across
                                                                           tion can be accurately determined.
threshold, although as we have seen, the measurements of top
momentum and the forward-backward asymmetry also provide                     In summary, the physics quantities of interest at threshold each
useful input. These latter two techniques also are more diffi-              have different effects on the shape of the threshold curve, and
cult and demand more study to determine limiting systematics.              can be optimally extracted with a cross section scan employ-
Therefore, it is useful to consider how to extract the measure-            ing carefully chosen scan points. In addition, measurements of
ments solely from the cross section scan. From the discussions             the top momentum and forward-backward asymmetry at thresh-
above we have seen that each physics quantity has a different ef-          old provide useful crosschecks of the same quantities. A mod-
fect on the threshold shape. So the physics goals will certainly           est data set of 10 fb 1 would provide a check of the overall
define the scan strategy.                                                   phenomenology and would allow a measurement of mt with an
   Expending even a modest fraction of a standard year of lumi-            error of 100 MeV to 350 MeV, depending upon the scan and
nosity (50 fb 1) at threshold would check the overall physics of           whether s is fixed or allowed to be a free parameter. This lumi-
the threshold system and would give an excellent measurement                                                                    2
                                                                           nosity would allow initial measurements of sMZ , t, and the
of the top mass at the level of  200 MeV. To concentrate on               Yukawa coupling H with errors at the level of 0:005, 16%, and
the mass measurement, one would choose to expend luminos-                  25%, respectively. Physics priorities would push optimization
ity where the cross section changes most rapidly, at about 346 to          of the scan strategy to concentrate on a subset of these quantities,
347 GeV for mt = 175 GeV. Assuming a standard model width                  so that with 50 fb 1 one could attain errors of 100 MeV (mt ),
and fixing s from external measurements, in only  10 fb 1                                 2
                                                                           0.0025 (sMZ ), 5% ( t ), or 10% (H ). At the current level
one would reach the level of 100 MeV error, which is where the             of understanding, the measurements become systematics limited
systematics of the absolute energy scale would be expected to              near these errors for mt and s, but the width and Yukawa cou-
become important.                                                          pling measurements could be pushed to the level of  1.

                                                                       9
    V. THE TOP QUARK WIDTH AND Vtb AT                                       the Tevatron, an 8% measurement of this partial width should
             HADRON COLLIDERS                                               be achievable, where the uncertainty is likely to be dominated
                                                                            by the 5% uncertainty on the integrated luminosity. To convert
   In the Standard Model, the top quark decays essentially 100%             this measurement into a measurement of the total width, it is nec-
of the time to Wb, and the rate for this process leads to a firm pre-        essary also to know the branching ratio B t ! Wb. This can
diction for the top width of t = 1:4 GeV (for mt = 175 GeV),                be extracted, albeit in a model-dependent way, from measuring
corresponding to a lifetime of < 10 25s. A measurement of t                 the ratios of branching ratios B t ! Wb=B t ! Wq and
is of great interest because t is affected by any nonstandard de-           B t ! Wq=B t ! non W + X . The first of these can be
cay modes of the top, whether visible or invisible. Future exper-           measured in tt events using the ratio of single to double b-tags
                                                                                            
iments must therefore address the related questions “Does top               in the lepton + jets sample. The requirement of one b-tagged jet
always decay to Wb?” and “Is Vtb equal to 1?”. That these ques-             leaves the second b-jet unbiased, so that with a known tagging
tions are not equivalent can be seen by considering the situation           efficiency the branching ratio can be measured from the number
with b decays, in which the b quark decays essentially 100% of              of additional tags. A similar technique can be used in the dilep-
the time to Wc despite the fact that Vcb  0:04. The relatively             ton sample. Because b-tagging is not required to select high-
narrow width of the b is a consequence of the fact that the quark           purity dilepton events, the ratio of non-tagged to single-tagged
to which it has a large coupling, the top quark, is kinematically           events can be used as well. Finally, one can compare the ratio of
inaccessible. Similarly, a heavy fourth generation quark with a             double tags in the same jet with two different tagging techniques
large CKM coupling to top could allow for a small values of Vtb             (i.e. secondary vertex tags and soft lepton tags) to double tags in
while keeping a large value of B t ! Wb. Thus it is important             different jets. Small values of B t ! Wb=B t ! Wq would
to measure B t ! Wb), Vtb, and t directly.                                 result in large values of this “same to different jet” ratio. Mea-
   The best measurement of Vtb at hadron colliders will come                surements of B t ! Wb=B t ! Wq using these techniques
from the s-channel single-top process qq ! W  ! t[34].
                                                             b             have already been performed by CDF[3], although the current
These events are detected by requiring a W + 2-jet topology                 statistical power is limited. In a 10 fb 1 data set, a 1% measure-
where one or both of the jets are b-tagged. The largest back-               ment of this ratio appears achievable[4].
                            
ground, as in the case of tt events, comes from the QCD pro-                   This analysis depends on the model-dependent assumption
duction of a W in association with one or more b-jets. How-                 that the branching ratio of top to non-W final states is small.
ever, since the single top signal peaks in the 2-jet bin instead            For example, if top has a significant branching ratio to H + b,
of the 3- and 4-jet bins, this QCD background is considerably               there will be additional sources of b-tags from the decays to
higher. Nevertheless, Monte Carlo studies of the signal com-                the charged Higgs, and the above-mentioned analysis becomes
bined with the observed tagging rate at CDF in W +2-jet events              problematic. This is particularly true in the unlucky situation
indicate that the signal can be isolated with a combination of b-           where mH +  80 GeV, which would give lepton + jets events
tagging and kinematic cuts. The expected yield for this process             kinematically identical to those arising from Standard Model de-
is shown in Table I. The advantage of the s-channel single-top                             
                                                                            cays of the tt pair. In the case of a significant branching ratio
process over the higher-rate t-channel Wg fusion process is that            to H  + b, however, we would expect to under-produce dilepton
the cross section can be more reliably calculated (the uncertainty          events, which result from two leptonically-decaying W ’s, rela-
on the Q2-dependence is only 4%, as opposed to 30% for the t-               tive to lepton + jets events. This possibility is discussed next.
channel process). The disadvantage of this mode is that has only               The ratio B t ! Wq=B t ! non W + X  can be mea-
half the rate of the Wg single-top process, and therefore requires
greater luminosity. The cross section is proportional to jVtbj2:
                                                                            sured by examining the ratio of single-lepton to dilepton events,
                                                                            since number of high-PT , isolated charged leptons in the final
                                                                            state counts the number of leptonically-decaying W ’s. If all tt  
                   SM / jVtbj2B t ! Wb:                      (4)
                                                                            decays contain two W , the ratio of (produced) single- to dilep-
Since the branching ratio must be 1, a lower limit on jVtbj is             ton events is 6:1. If top can decay to a non-W final state (such as
readily obtained from                                                       a charged Higgs, or a stop quark plus a gaugino) with different
                                                                            branching ratios to leptons, this ratio will be modified. Experi-
                     jVtbj2  meas=SM ;                       (5)         mentally, top decays to non-W final states would be indicated by
                                                                            a departure of DIL=L+J from unity, where DIL and L+J
where meas is the measured cross section. In 3 fb 1 at the                 are the cross sections measured in the dilepton and lepton+jets
Tevatron, a lower limit of jVtbj > 0:9 can be obtained, while               modes. Assuming that top always decays to Wb, measurement
in a “TeV33”-sized sample of 30 fb 1 the limit can be extended              of this ratio will give a 2% measurement of B t ! Wq=B t !
to 0.97[35]. This measurement will be extremely difficult at the             Xb in 30 fb 1. However, if a departure from the expected value
LHC because the qq initial state is swamped by gg contributions.
                                                                           is observed, the interpretation of the results is model-dependent.
                              
Furthermore the enormous tt cross section at the LHC leads to               For example, the above-mentioned case of a large branching ra-
significant “feed-down” of the tt signal into the 2-jet signal re-
                                                                           tion to H + b, with mH +  80 GeV, would increase L+J at
gion.                                                                       the expense of DIL . Of course, such a departure would be ev-
   From Eqn. 4, it is clear that the measurement of the single-             idence for new physics and would arguably be even more inter-
top production rate via qq ! W  ! t is directly propor-
                                          b                                esting than a measurement of the width.
tional to the partial decay width t ! Wb. In 30 fb 1 at                      Combining the measurements of t ! Wb from the single

                                                                       10
top production cross section, B t ! Wb=B t ! Wq from                                                                 
                                                                         estimate its expected precision. The rate of tt production above
the ratios of tags, and B t ! Wq=B t ! Xb from the ratio             threshold is well understood theoretically given the standard
of the dilepton to lepton+jets cross section, a 9% measurement           model assumptions for top’s neutral current couplings. If one
of the total width appears achievable with 30 fb 1.                      requires six-jet final states, two b jets in the event, dijet masses
   This somewhat indirect method of obtaining t may be con-              consistent with the W mass, and Wb masses consistent with the
trasted with the direct measurement that is possible from a tt                                                      
                                                                         top mass, one obtains a clean sample of tt events where both t’s
threshold scan at the NLC. Though the two measurements have              have decayed to Wb[10]. Assuming a net efficiency of 20% for
comparable precision, the approaches are quite different and             event selection and 25 fb 1 of data above tt threshold, there will
                                                                                                                       
illustrate the complementary nature of the two environments.             be about 2000 tt events selected. The measured cross-section is
                                                                                          
The pp measurement of t relies on collecting data from many
                                                                        thus determined to better than 3% accuracy, as long as the lumi-
                                 
different channels (single top, tt, with different numbers of b-         nosity is known to the 2% level or better. The branching fraction
tags) that span much of the hadron collider top program; it is           is then given in terms of the theoretical cross section and detec-
sensitive to a variety of possible sources of new physics. But           tion efficiency  as
model-dependence may be involved in the interpretation of the
result, especially the measurement of B t ! Wq=B t !                                B t ! Wb = meas =SM 1=2:                  (7)
non W + X . Because the model-dependence and sensitivity
to new physics are two sides of the same coin, this may actually The error is most likely dominated by the error in the efficiency.
be a virtue. The NLC offers a clean and well-controlled environ- Assuming it to be 5% leads to an uncertainty in the branching
ment where a single measurement can be performed with high       fraction of 2.5%.
precision and easily interpreted. Since t will be measured first     It is likely that a clean and efficient method for tagging a single
at hadron colliders, the t measurement at the NLC will cross-    top decay in a tt event is possible in the e+ e environment. For
                                                                                    
check many aspects of the hadron collider program, not just the  example, one could demand a b jet opposite a hard lepton from
  t measurement itself.                                          a W decay, and use the measured lepton momentum to test the
                                                                 consistency of the hypothesis that the W and b jet are back-to-
                    VI.  V   tb AT THE NLC                       back, as they must be for top decay near threshold. Such a sin-
                                                                 gle tag lets one measure the branching fraction directly without
   The NLC provides a well-understood environment for mea- assumptions about top quark couplings, simply by finding the
suring the CKM parameter Vtb. To date, nearly all our knowl- fraction of the remaining top quarks which decay to Wb. Monte
edge of this parameter is inferred from measurements of bot- Carlo studies are needed to quantify the precision of this tech-
tom and strange decays along with the assumption of the uni- nique.
tarity of the CKM matrix. Top decays provide the opportunity        The error in the partial width is simply the sum in quadra-
to determine Vtb directly; with the advent of very large data ture of the errors in the total width and branching fraction, i.e.
sets, they may also allow the measurement of Vts . If the mea- 5.6%. Errors in the phase space factors and QCD factors are
sured values differ significantly from present expectations, i.e. likely small compared to the error in the partial width, so the er-
         6
if jVtbj = 1 for example, new physics is indicated, perhaps the ror in V is about 2.8%.
                                                                            tb
existence of a new generation or the violation of weak univer-      Can one hope to measure Vts or Vtd at the NLC? If jVtsj =
sality. These CKM parameters are also essential for checking :04, as expected from unitarity constraints on the CKM matrix,
the phenomenology of B mixing and the assumptions underly- B t ! Ws = 1:6  10 3, leaving a sample of tens of events
ing CP violation studies in the the B sector.                    from the a 50 fb 1 data set. Preliminary studies show that re-
   Just as the b lifetime and the knowledge that b ! c transi- quiring a hard kaon in the quark jet, and the absence of secondary
tions dominate b decays determine Vbc , so the top width and the b decay vertices, provides strong rejection against b decay back-
branching fraction for t ! Wb fix the partial width t ! Wb, grounds. Even so, substantially more than 50 fb 1 is needed for
and hence Vtb. Explicitly,                                       such a measurement. The measurement of Vtd is much further
                 jVtbj 2 GF m3 QCD       MW 2 
2       2MW2 
 out of reach.
 t ! Wb =             p     t       1              1+
                      8 2                 m2
                                            t              m2
                                                            t
                                                              (6)            VII. COUPLINGS AND FORM FACTORS
where Vtb scales the universal weak decay rate given by the
Fermi coupling constant, phase space terms, and a QCD correc-              Due to its rapid weak decay, the top spin is transfered directly
tion factor. To measure the partial width requires that the total        to the final state with no hadronization uncertainties, therefore
width and the branching fraction to Wb final states be measured.          allowing the helicity dependent information contained in the La-
The measurement of the total width has been discussed in Sec-            grangian to be propagated to the final state. To the extent that the
tions IV.D and V. Studies indicate, for example, that the total          final state, expected to be dominated by bW +  bW , can be fully
width will be measured with an error of 5% given a 50 fb 1 scan          reconstructed, then a helicity analysis can be performed. At the
of the tt threshold.
                                                                        NLC or at a muon collider, the top neutral-current couplings are
   What remains is the measurement of the branching fraction,            accessible via the top production vertex. The charged-current
B t ! Wb. Although this measurement has not been simu-                 couplings are accessible to both lepton and hadron colliders via
lated with full Monte Carlo, simple arguments can be used to             top decay.

                                                                    11
   The study of top couplings, or more generally the interaction                        A. Helicity Analysis at NLC
form factors, is broadly speaking an exploration of new physics
which is at a very high energy scale or is otherwise inaccessi-              Top pair production above threshold at NLC (or a muon col-
ble directly. For example, some models for physics beyond the             lider) will provide a unique opportunity to measure simultane-
Standard Model predict new contributions to dipole moments in             ously all of the top charged and neutral-current couplings. In
top couplings. However, we also know that the Standard Model              terms of helicity amplitudes, the form factors obey distinct de-
itself predicts interesting new behavior for top couplings and he-        pendences on the helicity state of e , e+ , t, and , which can
                                                                                                                                t
licity properties. This is due to the very large top mass, making         be accessed experimentally by beam polarization and the mea-
it the only known fermion with mass near that of vHiggs = 246             surement of the decay angles in the final state. These helicity
GeV. The large top Yukawa coupling is an important implica-               angles can be defined as shown in Fig. 8. The angle W is de-
tion of its unique connection to electroweak physics. The phe-            fined in the W proper frame, where the W direction represents its
nomenology of the top Yukawa coupling is discussed separately             momentum vector in the limit of zero magnitude. The analgous
in Sections VIII and IV.C. Given the important role of longitu-           statement holds for the definition of t . As mentioned earlier,
dinally polarized W bosons (Wlong ) in electroweak symmetry               the case where the W is longitudinally polarized is particularly
breaking, it is interesting that the Standard Model (SM) predicts         relevant for heavy top, and the t and W distributions are sen-
the fraction of Wlong in top decay to be m2 =m2 + 2MW  =
                                              t     t
                                                            2
                                                                          sitive to this behavior. Experimentally, all such angles, includ-
70, with the remainder being left-hand polarized. Measuring              ing the angles corresponding to t and W for the t hemisphere,
                                                                                                                               
this should be a rather straightforward test.                             are accessible. Given the large number of constraints available
   The top neutral-current coupling can be generalized to the fol-        in these events, full event reconstruction is entirely feasible. To
                                   
lowing form for the Z-t-t or 
 -t-t vertex factor:                        reconstruct  one must also take into account photon and gluon
                         h                             i
                                                                          radiation. Photon radiation from the initial state is an important
  M
;Z  =      e
  Q
;Z F1
;Z + Q
;Z F1
;Z 
5
                         V     V     A      A
                                                                          effect, which, however, represents a purely longitudinal boost
                        h                          i                      which can be handled[40] within the framework of final-state
               ie  k Q
;Z F 
;Z + Q
;Z F 
;Z 
5 ;
            + 2mt                                                         mass constraints. Gluon radiation can be more subtle. Jets re-
                           V 2V         A 2A                  (8)
                                                                          maining after reconstruction of t and  can be due to gluon ra-
                                                                                                                  t
                                                                          diation from t or b, and the correct assignment must be decided
which reduces to the familiar SM tree level expression when the
                     
         Z        Z
form factors are F1V = F1V = F1A = 1, with all others
                                                                          based on the kinematic constraints and the expectations of QCD.
                        
;Z are the usual SM coupling constants:
zero. The quantities QA;V
Q
 = Q
 = 2 , QZ = 1 8 sin2 W =4 sin W cos W ,
  V        A      3 V              3
and QZ = 1=4 sin W cos W . The non-standard couplings
       A 
;Z
F2
;Z and F2A correspond to electroweak magnetic and electric
   V
                                                                                                                      t
dipole moments, respectively. While these couplings are zero                                                       θ
at tree level in the SM, the analog of the magnetic dipole cou-                               e+                          e-
pling is expected to attain a value  s= due to corrections be-
yond leading order. On the other hand, the electric dipole term                                    t
violates CP and is expected to be zero in the SM through two
                                                                                                       W                            l
loops [36]. Such a non-standard coupling necessarily involves a
top spin flip, hence is proportional to mt . In fact, many exten-                                       χ
                                                                                                       t
                                                                                                                                    χ
                                                                                                                                      W
sions of the Standard Model[37, 38] involve CP violating phases                                            t                              W
which give rise to a top dipole moment of O10 21 e-m at one
loop, which is about ten orders of magnitude greater than the SM                b
                                                                                                                  ν
expectation, and may be within the reach of future experiments,
as discussed below. A study of anomalous chromomagnetic mo-
ments was presented[39] at this meeting using the gluon energy            Figure 8: Definitions of helicity angles. (a) Production angle 
                  
distribution in ttg events, which was also found to be sensitive
                                                                              
                                                                          in tt proper frame; (b) t measured in the top proper frame as
to the electroweak neutral-current couplings.                             shown; and (c) W in the W proper frame.
  For the top charged-current coupling we can write the W -t-b
vertex factor as
                                                                            The distributions of the production angle  for the SM in terms
                      g                          
      M;W =                    W        W
                     p2 
  PL F1L + PR F1R                               of the various helicity states are given[41] in Fig. 9 for left and
                              
                                            W
               + 2pigmt  k PLF2L + PR F2R ;
                                   W                          (9)
                                                                          right-hand polarized electron beam. We see, for example, that
                   2                                                      for left-hand polarized electron beam, top quarks produced at
                                                                          forward angles are predominantly left handed, while forward-
where the quantities PL;R are the left-right projectors. In the SM        produced top quarks are predominantly right handed when the
            W                                               W
we have F1L = 1 and all others zero. The form factor F1R rep-             electron beam is right-hand polarized. These helicity amplitudes
resents a right-handed, or V + A, charged current component.              combine to produce the following general form for the angular

                                                                     12
                                                                                       Table IV: Subset of results from the global form factor analysis de-
                                                                                       scribed in the text. The upper and lower limits of the couplings in their
                      0.8                                                              departures from the SM values are given at 68% and 90% CL. All cou-
                                   –
                              (a) eL Beam
                                                                                       plings, each with real and imaginary parts, can be determined in this
                                  mt = 150 GeV                                         way. The right-handed charged-current coupling is shown both for un-
                      0.6          s = 400 GeV                                         polarized and 80% left-polarized electron beam, whereas the other re-
                                                                     tLtR              sults assume 80% left-polarized beam only. = is the imaginary part,
                                                                                       otherwise the results listed here are for the real parts.
                      0.4

                                                                                            Form Factor          SM Value             Limit        Limit
                      0.2                                                                                      (Lowest Order)        68% CL       90% CL
                                  tRtL              tLtL+ tRtR                             F1W P = 0)
                                                                                              R                      0                0:13 0:18
                                                                                          F1W P = 80)                               0:06 0:10
         dσ/dΩ (pb)




                                                                                            R Z                      0
                       0                                                                        F1A                  1               1  0:08 1  0:13
                                   –
                              (b) eR Beam                                                      F1ZV                  1               1  0:10 1  0:16
                                                                                                F2
A                 0                0:05 0:08
                                                                                               F2
V                                   0:07     +0:13
                      0.3
                                                                                                                     0                           0:11
                                                                     tRtL                       F2ZA                 0                0:09 0:15
                      0.2                                                                      F2ZV                  0                0:07 0:10
                                                                                             =F2ZA                 0                0:06 0:09
                      0.1
                                                        tLtL+ tRtR
                                  tLtR

                        0                                             where ` = e; . The branching fraction for this decay chain is
                                                                      8=27.
                       –1.0       –0.5            0            0.5          1.0
           12-95                                 cosθ 8100A3
                                                                         Now, since the top production and decay information is cor-
Figure 9: Production angle for tt for the possible final-state he-
                                                                     related, it is possible to combine all relevant observables to en-
                                                                      sure maximum sensitivity to the couplings. In this study, a like-
licity combinations, as indicated, for (a) left-polarized electrons,
                                                                      lihood function is used to combine the observables. We use
and (b) right-polarized electrons. The complete cross sections
                                                                      the Monte Carlo generator developed by Schmidt[42], which in-
                                                                      cludes ttg production to Os . Most significantly, the Monte
                                                                               
are the solid curves.
                                                                      Carlo correctly includes the helicity information at all stages.
                                                                      The top decay products, including any jets due to hard gluon ra-
distribution [40]:                                                    diation, must be correctly assigned with good probability. The
   d          t       2                     2                  2  correct assignments are rather easily arbitrated using the W and
d cos  = 32s c0 sin  + c+ 1 + cos  + c 1 cos  top mass constraints. When the effects been shown[40] that the
                                                                      and beamstrahlung are included, it has
                                                                                                                 of initial-state radiation
                                                                (10)
where c0 and c are functions of the form factors of Eq. 8, in- correct event reconstruction can be performed with an efficiency
cluding any non-standard couplings. The helicity structure of of about 70%. The overall efficiency of the analysis, including
the event is highly constrained by the measurements of beam po- branching fractions, reconstruction efficiency, and acceptance,
larization and production angle. An alternative analysis frame- is about 18%.
work has been proposed[43] involving a beam-axis system,                 After simple, phenomenological detection resolution and ac-
which might provide higher purity if the final states can be only ceptance functions are applied, the resulting helicity angles (see
partially reconstructed.                                              Fig. 8) are then used to form a likelihood which is the square
   We now outline an analysis[6, 44] to measure or set limits on of the theoretical amplitude for these angles given an assumed
the complete set of form factors defined in Eqs. 8 and 9. We con- set of form factors. Table IV summarizes some of the results
sider a modest integrated luminosity of 10 fb 1, mt = 180 GeV, of this analysis. We seep even with a modest integrated lu-
     p                                                                                            that
and s = 500 GeV. Electron beam polarization is assumed to minosity of 10 fb 1 at s = 500 GeV, the sensitivity to the
be 80. The decays are assumed to be t ! bW . In gen- form factors is quite good, at the level of 5–10% relative to SM
eral, one needs to distinguish t from . The most straightforward couplings. In terms of real units, the 90% CL limits for F2A of
                                      t                                                                                               Z
method for this is to demand that at least one of the W decays 0:15, for example, correspond to a t-Z electric dipole moment
be leptonic, and to use the charge of the lepton as the tag. (One of  8  10 20 e-m. Other studies[45, 40, 46] have found simi-
might imagine using other techniques, for example with topo- lar sensitivities. As discussed above, this limit is in the range of
logical secondary vertex detection one could perhaps distinguish interest for probing new physics. Therefore it is interesting for
b from .) So we assume the following decay chain:
        b                                                             future studies to quantify the experimental errors which would
                                                                      result from larger data samples than the modest one assumed
                       bWW ! b q0`;
                     tt ! b            bq                     (11) above.

                                                                                  13
      B.    Helicity Analysis at Hadron Colliders
   As discussed above, the Standard Model makes the firm pre-
diction that the W polarization in top decays depends only on
mt and MW . For mt = 175 GeV, the fraction of longitudinally                          9000


polarized W ’s in top decay is roughly 70%, with the remaining
W ’s being left-hand polarized. This prediction, which is a direct
                                                                                      8000



consequence of the Lorentz structure of the t-W -b vertex, can be                     7000

tested in the large tt samples expected at the Tevatron and LHC.
                     
Non-universal top couplings may manifest themselves in a de-                          6000


parture of B t ! bWlong from its expected value.
   The W polarization can be measured in lepton + jets final
                                                                                      5000



states by analyzing the angular distribution of the charged lepton
from the decay t ! Wb followed by W ! l . The polarization
                                                                                      4000



                                                           
of the W is related to the charged lepton helicity angle l , which                   3000


is defined to be the emission angle of the lepton in the rest frame
of the W , with respect to the direction of the W in the rest frame
                                                                                      2000


of the top. (It is equivalent to the angle W of Fig. 8.) This an-                    1000
gle can be expressed in terms of quantities measured in the lab
frame via[47]                                                                            0
                                                                                             -1   -0.8   -0.6   -0.4   -0.2        0       0.2     0.4      0.6     0.8        1


                                 2m2
                                                                                                                               Cosθ*

                  cos l         lb
                                                                                                                                   e

                                              1:                                                               
                                                                           Figure 10: The parton-level cos l distribution for mt =
                              m2 MW
                               lb
                                      2                       (12)
                                                                           170 GeV. The contributions from left-handed and longitudinally
Here mlb is the invariant mass of the charged lepton and the b,            polarized W ’s are shown as the dotted and dashed lines respec-
and Mlb is the invariant mass of the lepton, the b, and the neu-          tively.
trino, nominally equal to mt .
   The experimental strategy is to use the constrained fit de-
scribed in Section III to obtain the jet-parton correspondence,
which allows one to evaluate the invariant mass combinations.
                      
The resulting cos l distribution is then fitted to a superposi-
tion of W helicity amplitudes in order to extract the fractions
                                                             
of Wleft , Wlong, and Wright , which contribute to cos l like
1 1 cos  2 , 1 sin2  , and 1 1 + cos  2 respectively. A
4             l     2      l       4           l                                                                              P1
                                                                                                                                           17.65    / 19
                                                                                                                                                   0.7082         0.3030E-01
model analysis of this type at the Tevatron has been performed
                         
by Winn[4]. The cos l distribution at the parton level, assum-                        250

ing perfect resolution and no combinatoric misassignments, is
shown in Fig. 10. Note that a right-handed component would
                  
peak near cos l = 1, where the Standard Model predicts few                            200


events. To determine best-case statistical precision of this mea-
surement, Monte Carlo[48] pseudo-experiments are performed
                                                                                       150
with top samples of various sizes, still assuming perfect reso-
lution and jet-parton assignment, but correcting the acceptance
              
with a cos l -dependent factor. A fit to a sample of 1000 events                       100

is shown in Fig. 11. The fit accurately returns the input longitu-
dinal W fraction of 69% to within a 3% statistical uncertainty.
The statistical puncertainty in this best-case scenario is found to                     50

behave like 1= N .
   In a real experiment the precision will be lower due to the
                                                                                         0
same effects that complicate the mass measurement: combina-                                  -1   -0.8   -0.6   -0.4   -0.2        0       0.2     0.4      0.6     0.8        1
                                                                                                                                       *
toric misassignment of the top decay products, detector resolu-                                                                Cosθe

tion, and backgrounds. The impact of these effects on the helic-                                                                
                                                                           Figure 11: Parton-level, acceptance-corrected cos l distribu-
ity analysis has not yet been evaluated in detail. However, since
                                                                           tion for 1000 events, together with a fit to the Standard Model
this analysis uses the same constrained fit as the mass measure-
                                                                           hypothesis.
ment, it is reasonable to assume that these effects would be of the
same order of magnitude in both analyses. In the mass analysis,
these effects lead to a degradation in resolution that is approxi-
mately equivalent to a reduction in statistics by a factor of two,

                                                                      14
                                           p
i.e. a reduction in precision by a factor of 2. If this holds true                                           p
                                                                          mass reach improve at higher energies. For example, Fujii finds
for the helicity analysis as well, then with a 10 fb 1 sample at          a 10% measurement is possible at s = 700 GeV with the same
the Tevatron it would be possible to measure the branching frac-
tion to Wlong to approximately 2%, and to have sensitivity to a
                                                                                                                           p
                                                                          integrated luminosity. Studies are needed to quantify sensitivity
                                                                          to intermediate and high mass Higgs at higher s.
right-handed component at the 1% level.                                                                     
                                                                             The Higgs-strahlung process (ttH ) is also sensitive to effects
   Neutral-current electroweak couplings of the top quark are not         that might arise from extended Higgs sectors. The interference
accessible at hadron colliders due to the dominance of strong             between Higgs emission from a virtual Z and Higgs-strahlung
production mechanisms (or, in the case of single top, produc-             from the final t quark gives rise to CP-violating effects in two
tion through the weak charged current). Final-state couplings of          Higgs doublet models. This was studied in Ref. [50] where it
the top to the photon and Z are extremely small. A study of the           was found that CP-violation effects could be seen at 3 level
neutral-current couplings is therefore the domain of l+ l collid-                                 
                                                                          with several hundred ttH events and the most favorable param-
ers.                                                                      eter choices. Such studies will require center of mass energies
                                                                          above 800 GeV and integrated luminosities of 300 fb 1 or more.
              VIII. THE ttH COUPLING                                      Gunion and He presented[51] an analysis to discriminate be-
                                                                          tween different models of the Higgs sector, using two-Higgs-
   The role that the large top mass plays in electroweak sym-             doublet models to exemplify the technique, which consists of
metry breaking can be directly explored by measuring the top-             measurements of the tth differential cross section together with
                                                                                                  
Higgs Yukawa coupling. In the Standard Model, thisp      coupling                            section, where h is a neutral Higgs boson. For
                                                                          the Zh total cross p
strength t is proportional to the top mass: t = 21=4 GF mt .            mh = 100 GeV, s = 1000 GeV, and an integrated luminos-
The top-Higgs coupling is consequently large and can be directly          ity of 500 fb 1, they find that the Yukawa couplings and Higgs
measured. Such measurements are possible at both the LHC and              model can be accurately determined.
the NLC. The measurements are challenging in both environ-                   Measuring the coupling of the top quark to a heavy Higgs
ments, requiring design-level luminosities for adequate statis-           (mH > 2mt ) requires high center of mass energies and high in-
tics.                                                                     tergrated luminosity. Three processes are of interest: e+ e !
   The process pp ! ttH + X has been studied at the LHC
                                                                         ttH ; e+ e ! ttZ ; and e+ e !  tt. Only the latter two have
                                                                                                             
for Higgs masses up to 120 GeV[17]. The process relies on the             been studied.
availability of good vertex detection even at the highest LHC lu-            The cross-section for e+ e ! ttZ is about 5 fb between 500
                                                                                                              
minosities for efficient b-tagging. The Higgs is identified as a            and 1000 GeV. It is enhanced by the process e+ e ! ZH when
bump over a large background in the bb invariant mass distri-             the Higgs subsequently decays to tt. For mH = 500 GeV, the
                                                                                                         ps =1000 GeV. Fujii et al.[29],
bution in events with a trigger lepton and at least three b jets.         enhancement is about 2 fb at
                                         
The dominant backgrounds are due to tt and W production with              have studied this process. They enrich their Higgs sample by
additional jets, some of which are misidentified as b jets. With                              
                                                                          first requiring a ttZ final state, and then cutting on the p appro-
100 fb 1, signals of more than 3 significance are expected for                     invariant mass. Extrapolating their results to s =
                                                                          priate tt
mH < 115 GeV. In principle this signal could yield a mea-                 1000 GeV and assuming mH = 500 GeV, leads to an estimated
surement of the top-Higgs coupling, but no such analysis is dis-          precision in the top-Higgs coupling of 20% for a 100 fb 1 data
cussed.                                                                   set.

                                                                          e+ e !  tt. At ps = 1500 GeV, the cross-section for
   Several techniques can be applied at the NLC. The top cou-                Higgs enhancements are more dramatic in the reaction
pling to a light Higgs (mH < 2MW ) can be measured at a                                 
tt threshold or by measuring the rate of ttH events at ps =
500 GeV collider with accurate cross-section measurements at              this process is about 2 fb in the absence of a Higgs, but will
 
500 GeV. Higher energies (
                              ps = 1 or 1.5TeV) are needed to            be enhanced by more than a factor of two for Higgs masses
                                                                          in the range 400 to 850 GeV. Peak sensitivities, which occur
study the coupling for intermediate or high Higgs mass (mH >              when mH = 500 GeV, are nearly 10 times the nominal rate.
2mt).                                                                     Preliminary studies by Fujii[29] show that care is required to
   The presence of an additional attractive force arising from            eliminate radiative tt, e+ e tt, and ttZ backgrounds. They find
                                                                                                              
Higgs exchange produces a distinctive distortion in the cross             that the p Higgs coupling can be measured to 10% with 300
                                                                                   top
section for tt production near the 1S resonance. This was dis-
                                                                         fb 1 at s of 1000 GeV for mH = 600 GeV.
cussed in the Section IV.C above. The size of the distortion is
proportional to 2 =mH . The coupling could be measured to at
                   t                                                         IX. RARE AND NONSTANDARD DECAYS
least 10% for mH = 100 GeV with a 100 fb 1 threshold scan.
                  
   The yield of ttH events is proportional to the square of the              The search for and discovery of the top quark at Fermilab has
top-Higgs coupling. The cross section for the process is small,           relied on the assumption that the standard model decay t !
of order 1 fb at a 500 GeV NLC for mH = 100 GeV; it grows                 Wb dominates. This fact is far from established, of course. In
to a few fb by 1 TeV[49]. The final state typically contains               fact, the interesting speculation[52] that a conspiracy of SUSY-
eight jets, including four b jets. Preliminary studies[10, 30] in-        enhanced production balancing SUSY-depleted decays explains
                    
dicate that ttZ and ttjj events are significant backgrounds. The                           
                                                                          the observed tt signal has not been excluded as yet. The top
top-Higgs coupling could be measured to 25% with 100 fb 1 if
mH = 100 GeV at ps = 500 GeV. The accuracy and Higgs
                                                                          width is unknown, and present estimates of the branching ra-
                                                                          tio t ! Wb are model dependent; so there are only weak ex-

                                                                     15
perimental constraints on non-standard top decays. The high                 ety. Measurements of the top couplings and form factors directly
top mass opens the kinematic window for decays to new, mas-                 probe the weak interactions of a bare quark at their natural scale,
sive states, such as those inspired by supersymmetric models,               and anomalies in these couplings could signal the presence of
t ! ~+ neutralino (0) and t ! H + b. The high top mass also
      t                                                                     new physics at the TeV scale or higher. Direct measurements
encourages speculation that neutral-current decays, like t ! c
             of the top width and Vtb could reveal the existence of nonstan-
or t ! cZ , may be large enough to be interesting experimen-                dard decay modes or additional quark generations. And the top-
tally. If the stop and neutralino masses are low enough, the decay          Higgs Yukawa coupling can be probed directly, particularly if
t ! t0 can occur with a sizable branching fraction. Typically,
      ~                                                                     the Higgs is light. Each of these measurements is of great inter-
one imagines that the neutralino escapes undetected and that the            est and should play an important role in planning future experi-
subsequent decay, t ! c0 , leaves a lone remnant hadronic
                      ~                                                     ments.
jet and missing energy. It is reasonable to expect that this is-               The Fermilab Tevatron will be the only facility capable of
sue will be addressed with present and future Fermilab data by              studying the top quark until the LHC turns on in 2005. With
searching for events with an identified t, a charm jet, and miss-            30 fb 1 delivered in “Run III” following the initial Main Injector
ing energy. Venturi[53] has studied how to detect this decay at             collider run, a top mass uncertainty of <2 GeV appears feasible.
                                                                                                                     
an NLC, which is done by looking for an event where the invari-             This measurement would be sufficiently accurate that uncertain-
ant mass of one hemisphere is near the top mass, and the other is           ties in other quantities (MW , sin2 W ,s MZ ) would dominate
                                                                                                                           2
substantially below. He finds that a 10 fb 1 data set is sufficient           the precision electroweak fits. The Tevatron can measure t and
to establish a 3 discovery, provided the branching fraction is             Vtb to better than 10%, albeit with some model-dependent as-
> 2 (for mt = 80 GeV and m0 = 55 GeV).
                ~                                                           sumptions. The Tevatron will also test the charged-current form-
   Top decays to a charged Higgs, t ! H + b, are also expected              factors and search for rare and nonstandard decays. Its main
in supersymmetric models when the decay is kinematically al-                advantage, of course, is that it exists and has a monopoly on
lowed. The charged Higgs is expected to decay predominantly                 the subject for roughly the next decade. The Tevatron program
to  when tan  > 1, so the appropriate signature is an ap-               should take full advantage of this situation and maximize the in-
parent violation of lepton universality in top decays, leading to           tegrated luminosity before the LHC turn-on.
an excess of taus in the top decay products. Run 2 at the Teva-                The LHC, with its enormous top production cross section, is a
tron will be sensitive to branching fractions B t ! H + b >               veritable top factory. In particular, its sensitivity to rare decays
11[4]. At LHC, the decay is detectable if mH < 130 GeV for                 is unlikely to be matched by other machines. As is the case for
most values of tan  with 10 fb 1[17]. At NLC a study[53] has               the Tevatron, many measurements will be systematics-limited.
shown that the decay is observable if mH < 125 GeV, essen-                  Neither LHC experiment, for example, is currently willing to
tially independent of the value of tan  , with 100 fb 1.                   claim a mass measurement better than 2 GeV. However, the very
   The FCNC decays t ! c
 and t ! cZ are tremendously sup-                  large control samples that will be available at the LHC suggest
pressed in the Standard Model, with branching fractions of order            that these systematics might be better controlled, or that preci-
10 12. Consequently their observation at detectable levels is a             sion measurements could be performed using small, very clean
robust indication of new physics. Models with singlet quarks or             subsamples. The measurement of the top-Higgs coupling at the
compositeness could have branching ratios for these decays as               LHC will be extremely challenging due to the low cross section
large as 1%[54]. The signature for these decays, a very high PT             and difficult backgrounds. In general, top physics at the LHC
photon or a high energy lepton pair with an invariant mass con-             has not been studied in the same level of detail as, say, Higgs and
sistent with the Z mass, are distinctive enough to permit sensi-            SUSY searches. It could benefit from additional study since its
tive searches in the hadronic environment. Run 2 at the Tevatron            potential has not been fully explored.
will probe to branching fractions of about 3  10 3 (2  10 2)                 An e+ e linear collider offers the greatest potential for high-
for t ! c
 (t ! cZ )[4]. At the LHC with its very large top sam-            precision top physics in the LHC era. If the beam energy spec-
ples, branching fractions as small as 5  10 5 could be measured            trum can be understood to the level expected, the top mass can
for t ! cZ , assuming an integrated luminosity of 100 fb 1[17].             be measured to better than 200 MeV. A number of fundamen-
At NLC, the sensitivity is limited by the available statistics to of        tal parameters can be measured at the tt threshold, including
                                                                                                                         
order 10 4 for t ! c
 and 10 3 for t ! cZ , assuming an inte-                 t, Vtb , s, the charge and spin of the top quark, and the top-
grated luminosity of 50 fb 1. Similar limits could be established           Higgs Yukawa coupling if the Higgs is sufficiently light. The
by looking directly for e+ e ! tc events[54].
                                                                           full array of top gauge couplings can be measured, including the
                                                                            neutral-current couplings, which are inaccessible at hadron col-
                   X. CONCLUSIONS                                           liders. The top-Higgs coupling can be measured in the open top
                                                                            region as well, though this will require extended running at de-
   The systematic study of the top quark offers many possibili-             sign luminosity. If the Higgs (or a Higgs) is light enough for this
ties for exploring physics beyond the standard model. Because               measurement to be made, it will also be light enough to have
the top quark mass enters quadratically into the -parameter, a             been directly observed at the NLC, LHC, or even perhaps the
precision measurement of mt can be used together with MW to                 Tevatron. The Yukawa coupling of this particle to the top quark
constrain the Higgs mass. In the exciting event that a Higgs par-           may depend on whether it is a standard model Higgs, a SUSY
ticle is observed, knowledge of mt will help determine whether              Higgs, or some other thing entirely. A direct measurement of
it is a standard model Higgs or some other, more exotic vari-               this coupling will thus address head-on the question of how the

                                                                       16
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