Global Analysis of Parton Distributions

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					Current Issues and Challenges in Global Analysis of
                Parton Distributions




          DIS06       Tsukuba       Tung
                          Outline

• Challenges for Global QCD Analysis in the era of HERA II,
  Tevatron Run II, and LHC
• New Experimental Input to Current Global Analysis of PDFs
• More Precise Theoretical Calculations needed to meet these
  challenges
• Recent Results and Work in Progress (CTEQ):
   Implications of PDF uncertainties on Physical Applications;
   A new implementation of the general PQCD formalism with
    quark mass effects. This is applied to a comprehensive
    global analysis, including the full HERA I total and semi-
    inclusive cross section data sets with correlated errors;
   Close examination of new fixed-target experimental data
    (NuTev, E866) and large-x behavior of PDFs;
• Summary and Outlook
           Challenges for Global QCD Analysis
                   —from here to LHC

In spite of steady progress in over 20 years of global
analysis of PDFs, it is surprising how much knowledge is
still missing on the parton structure of the nucleon !

     • Gluon Distribution;
     • Small-x and Large-x behavior of all
       distributions;
     • Strange distribution;
     • Charm and bottom distributions;
     • Quantifying uncertainties of all PDFs.

  A successful LHC program depends on making
  substantial improvement on most of these fronts.
           Some recent ―CTEQ‖ work (2005–)

• NLO PQCD is stable for Collider phenomenology
  (Huston, Pumplin, Stump, wkt. JHEP 0506:080,2005);

• LHC phenomenology: Uncertainties of the inclusive
  Higgs production cross section at the Tevatron and
  the LHC (Belyaev, Pumplin, Yuan, wkt. JHEP 0601:069,2006);
 (PDF uncertainties can be larger than commonly estimated
 ―theoretical uncertainties‖, depending on the Higgs mass.)

• CTEQ6A,B series of PDFs: for physical applications
  that are sensitive to as.
  (Pumplin, Belyaev, Huston, Stump, wkt. JHEP 0602:032,2006 );
    Uncertainties of the inclusive Higgs production
     cross section at the Tevatron and the LHC
       (Belyaev, Pumplin, Yuan, wkt. JHEP 0601:069,2006)

T                                                          vs.

               Enhanced bbA-coupling in MSSM
              CTEQ6A,B PDFs for a series of as
        (Pumplin, Belyaev, Huston, Stump, wkt: JHEP 0602:032,2006 )

               Many applications. One example:




* Curves: as = 0.110 – 0.126 ; (Realistic range: between blue lines.)
* Shaded areas: uncertainty band based on CTEQ6 error analysis
for fixed as = 0.118 .
    New Experimental Input to Current Global Analysis

• Extensive HERA I data sets (complete?) on
    total inclusive NC and CC cross sections, covering a
     wide range of kinematic phase space;
    semi-inclusive (tagged heavy flavor) cross sections:
     charm and bottom;
    semi-inclusive jet cross sections.
• (Note: out go the SFs, F1,2,3; in come the xSec’s!)

• Fixed-target Experiments (Last of the kind?)
    NuTeV n DIS S.F.s and cross sections;
    E866 DY pp and pd cross sections (finally?).
• New Tevatron Data on W/Z production, jet
  production, … etc.
  Available HERA Data Sets for Current Global Analysis
                    (by our reckoning)
• H1                             • ZEUS
   CCe+9497X                        CCe+9497X
   CCe+9900X                        CCe+9900X
   CCe-9899X                        CCe-9899X
   (NCe+9497X ?)                    NCe+9697X
   NCe+9697X                        NCe+9900X
   NCe+9900X                        NCe-9899X
   NCe-9899X                        NCe+9697F2c
   NCe-9900X                        NCe+9890F2c
   NCe+9697F2c
   NCe+9900Xc       Wow!                  Just wait until
   NCe+9900Xb       (both in coverage     HERA II data
                     and in accuracy.)     come along!
              ―New‖ Precision Global Analysis
      (S. Belyaev, H.L. Lai, J. Pumplin, D. Stump, wkt, C.P. Yuan)
―New‖ Phenomenology work always trail frontier Theory and
Experimental advances (examplified by the plenary talks), by yeas!

• Data: Full HERA I total-inclusive and semi-inclusive
  heavy flavor cross sections with correlated errors + F.T.
  DIS + DY + Tevatron Jet;
• Theoretical tool: New implementation of General Mass
  Variable-Flavor-Number-Scheme factorization
  formalism of Collins for consistency + recent SAcot,
  Acot-c, … practical prescriptions for efficiency.
                      (cf. talk in the joint HQ/SF session, wkt).
———————————
• Sorry! DIS jet inclusive not yet implemented. ( Jon Pumplin)
• NLO for now. Extension to order as2 is ―straightforward‖, given
  the perturbative approach.
                          Results


• Excellent fit to 32 sets of data—CTEQ6C0:
  Details in the c2 analysis are dependent on: (i) using
  the xSec data (vs. SFs); and (ii) using CorSysErr’s.
  (representative plots.)

• Comparison of CTEQ6.1M and CTEQ6C0 PDFs;
  (representative plots)

• Where do mass effects matter?
  (H1NCe+9697X, ZeusNCe+9697X)
  —low Q2 data.
     NC e+ 96-97 X
H1                   ZEUS
     NC e+ 99-00 X




H1                   Zeus
                                Pull Plots: NC e+ 99-00 X

                                   • N.B. This is after correlated
                                     SysErr’s have been taken into
                                     account!
                                   • The shifts for individual
                                     SysErr’s are generally ~ 1.

                                                            Zeus




  H1




Close to normal distribution.
Comparison to
CC data




Lines:
theory (fits);
Red points:
raw data points;
Blue points:
data points shifted
by optimal
correlated SysErr.       H1 CC
(usually within 1s)   e+ 99-00 X
 ZEUS

CC e+ 99-00X
       Where does the General Mass Formalism make
        a difference? Compare with CTEQ6.1M (ZM)
Low Q2 bins, of course.


                                                       GM




H1 96-97




                                                       ZM




               ZEUS 96-97 data show the same effects
               Charm Production S.F. and xSec.



Only show comparison
with 1 (out of 4) data
set—will re-visit this
comparison in Talk in
joint SF & HQ session,
which concerns the
theoretical basis, and
heavy flavor physics.




                                                 Zeus NC
                                                 e+ 98-00 F2C
     An interesting application of the GM formalism
            and the precision global analysis:



The first phenomenological study of

―Is there room in the nucleon for intrinsic charm?‖

or
―How well can available data constrain the charm
content of the nucleon?‖


                  Talk in the joint HQ/SF session, wkt
           Comparison of New PDF (CTEQ6C0) with
       previous PDFs (CTEQ6.1 and its uncertainty band)
• Space only permit a very brief comparison: Gluon at two scales




• New PDFs lie within the previously estimated uncertainty bands.
• After a new round of careful study, the new uncertainty bands should
  be narrower, due to improvements on both theory and experiment.
     ―New‖ Fixed Target Data for Global Analysis

• E866:
    Measurement of pp and pd DY cross sections;
    Interest: Preliminary results (hep-ex/0302019)
     indicated discrepancies with existing PDFs;

• NuTeV:
   extensive n and anti-n F2,3 & cross section data;
   Interest:
     • Experimental: extracted F2,3 data indicates
       discrepancies with CCFR results at large x;
     • Theoretical: new data pull the PDFs in the opposite
       direction compared to the E866 results!
         Study of Large-x Behavior of PDFs
          (Kuhlmann, Morfin, Olness, Owens, Stump)


• E866 pp and pd cross sections
    Preliminary results (hep-ex/0302019)
    CTEQ studies (deuteron corr. + other effects)
    Final results ??
• NuTeV n and anti-n scattering data
    Comparison of F2 vs. theory
    • NuTeV (Tzanov)
    • CTEQ study (nuclear corr., quark mass effects)
   Comparison of cross section data vs. theory
     • Petti & Kulagin (emphasizes nuclear correction)
     • CTEQ study (nuclear corr., quark mass effects)
     E866




• ― The results imply that the u quark distributions in CTEQ6 and
  MRST2001 are overestimated as x 1.               —hep-ex/0302019
• These .. discrepancies .. imply that future PDF fits will see a
  substantial correction to the u and d quark distributions at large x.‖

•CTEQ group have studied possible sources for this discrepancy,
 particularly deuteron target corrections. Results were inclusive.

Reports by E866 in subsequent conferences indicate that improved
radiative corrections seem to reduce the discrepancy, but it has not
completely gone away.                            … stay tuned.
Notable NuTeV Results                          Tzanov, DIS2005
                  F2 Measurement


                         • Isoscalar ν-Fe F2

                         • NuTeV F2 is compared with CCFR and
                           CDHSW results
                            - the line is a fit to NuTeV data

                         • All systematic uncertainties are included

                         • All data sets agree for x<0.4.

                         • At x>0.4 NuTeV agrees with CDHSW

                         • At x>0.4 NuTeV is systematically above CCFR
    Our Attempts to Incorporate the NuTeV Structure
       Function, F2,3, data in the Global Analysis

Find this data set ―incompatible‖ with the other data
  sets in the global analysis—with our usual assumptions;
• Total c2 of the NuTeV data set unacceptably high;
  shape discrepancy clearly seen;
• Tried to: (i) vary nuclear target corrections; (ii)
  include target and heavy quark mass effects, …
• None of these help; some make things worse.




     However, it is more preferable to directly compare
     theory with the cross section data !
Kulagin and Petti   Caution: 2, out of many, energy bins (total
                    # data points > 1000); details impossible
                    to see in these plots.
 NuTeV xSec.
 data compared to
 a typical fit:

•This is only an impression
 plot;
•Data with different E are
 superimposed;
•Error bars are shown only
 for two bins;
•Overall c2 is
 1140 / 1170 pts.
•However,
 •CorSysErr not yet
  included;
 •the devil may be in the
  details.
                Can Nuclear Corrections Help?




•For each x, data are
 combined and errors
 are weighted;
•See a systematic x-
 dependent deviation
 that cannot be
 reduced
 substantially by
 nuclear correction
 models.
    Our Attempts to Incorporate the Full NuTeV
     Cross section data in the Global Analysis

The situation improves!
• Total c2 of the NuTeV data set becomes acceptable—
  not too different from 1 /dof ;
However, upon closer examination, a clear shape
  discrepancy persists;
• Tried to: (i) vary nuclear target corrections; (ii)
  include target and heavy quark mass effects, …
• None of these help; some make things worse.
Therefore, we believe the compatibility of this
  measurement with the other data sets in the global
  analysis within the conventional PQCD framework
  remains an open question.
                  Summary and Outlook

• The impressive consistency between the improved theoretical
  calculation and much improved HERA input on DIS NC, CC &
  heavy flavor production (and other F.T. and hadron collider
  processes) provides a new basis for performing precision
  phenomenology within and beyond the SM.
• A lot of work remains to be done to pin down the full parton
  structure of the nucleon (particularly gluon, s, c, b);
• HERA II and Tevatron Run II data can contribute
  substantially to fill the gaps. More specifically,
• With more accurate data on CC cross sections, we gain
  additional (clean) handles for differentiating up and down
  types of quarks;
• Direct FLong measurement in the cards?
• With W/Z/g + tagged heavy flavor events at the hadron
  colliders, we can get direct information on s/c/b quark
  distributions;
• ….
               LHC physics is waiting for these advances …
?
Reserve Slides
                Comments on NNLO

• In the perturbative approach, for the total inclusive S.F.s
  and cross sections, once a comprehensive NLO calculation
  is in place, it is ―straightforward‖ to include known NNLO
  corrections additively.
• Extending global analysis to NNLO is certainly desirable,
  but not necessarily urgent for current applications, since
  experimental errors for most measured quantities, as well
  as other sources of uncertainties (such as
  parametrization, power-law corrections …), largely
  outweigh the NNLO corrections.
• Additional note: unlike total inclusive F2,L, quantities such
  as ‖F2c‖ are not well defined theoretically at NNLO and
  beyond. (It is not infra-red safe!) It is rather misleading
  to talk about a true ―NNLO theory‖ of F2c (except within
  the 3-flv scheme, which has a very limited range of
  applicability).

				
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