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Factorization and factorization breaking in non-diffractive

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Factorization and factorization breaking in non-diffractive Powered By Docstoc
					  Factorization and factorization breaking in non-diffractive
                     scattering at HERA
                                     Bruce Straub, University of Oxford
                              Representing the ZEUS and H1 Collaborations
                          XXXV International Symposium on Multiparticle Dynamics
                                     ˇ rı ˇ
                               Kromeˇ´z, Czech Republic, 9-15 August 2005

• When Should Factorization Apply?
• Tests of Factorization
  • Parton Densities: Can NLO QCD fits describe ep, γp and p¯ ?
                                                           p
  • Fragmentation Functions: Compare NC DIS (Breit frame) and e+e−
• Factorization Breaking
  • Underlying event studies in tagged photoproduction
  • Forward Neutron Production
• Sketch of the Dipole Model of DIS
• Conclusions



Factorization and factorization breaking in non-diffractive scattering at HERA/ Bruce Straub/ ISMD 2005   1
                             When Should Factorization Apply?


• Incident particles have high momentum
    • Hadrons are Lorentz contracted along the direction of flight, so the
      interaction time is decreased.
    • Interactions internal to hadrons are time dilated, so the lifetime of the
      partonic state is increased.
    • Long distance interactions of partons within the hadron can be neglected
      during the (short-distance) hard interaction, so the partons can be
      treated as free particles.
    • The partons can be assigned a fraction x of the hadron’s longitudinal
      momentum. The momentum distribution of parton species i within
      hadron H in x can be described by a universal parton density fi/H(x)
      with 0 < x < 1.

• The density of partons should not be too high, so that the collision can be
  described by a single hard scattering


Factorization and factorization breaking in non-diffractive scattering at HERA/ Bruce Straub/ ISMD 2005   2
                                       Factorized Cross Sections

• The Neutral Current DIS cross section can be factored into a sum over
  quark densities and a hard scattering cross section

                               d2σ(ep) 2πα2
                                      =     (1 + (1 − y)2)                                   e2fi/p(x, Q2)
                                                                                              i
                               dxdQ2    Q4                                              i


• The direct γp cross section can be written

       σdir (ep → e + N jets + X) =                               fγ/e (y, Q2)              fi/p(x, µ2)dˆ (γi → N jets)
                                                                                                        σ
                                                              Ω                         i


• The resolved γp cross section can be written

    σres (ep → e+N jets+X) =                               fγ/e (y, Q2)               fi/p(x, µ2)fj/γ (xγ , µ2 )dˆ (ij → N jets)
                                                                                               p             γ σ
                                                       Ω                        ij




Factorization and factorization breaking in non-diffractive scattering at HERA/ Bruce Straub/ ISMD 2005                   3
                                  Factorization in the Final State


• After the hard scatter, hadron formation occurs over a much longer time
  scale, so it can be described independently of the hard process, again by
  a universal function gH/i(z) which gives the density in z, the fraction of the
  parton momentum carried by the hadron for hadrons of species H produced
  in the fragmentation of parton species i.




Factorization and factorization breaking in non-diffractive scattering at HERA/ Bruce Straub/ ISMD 2005   4
                               ZEUS NLO QCD Fit Compared to ZEUS NC DIS Data

                                              ZEUS                                                                                                                          ZEUS




                                                                                                                            σNC
σNC

              2
            Q = 2.7 GeV 2              3.5 GeV2                   4.5 GeV2                          6.5 GeV 2
                                                                                                                                  1.5    2
                                                                                                                                        Q = 200 GeV 2           250 GeV2           350 GeV 2          450 GeV 2




                                                                                                                            ~
~



      1.5

       1                                                                                                                           1

      0.5
                                                                                                                                  0.5
       0
                  8.5 GeV2             10 GeV2                    12 GeV2                           15 GeV2
      1.5                                                                                                                          0
                                                                                                                                             650 GeV2           800 GeV2           1200 GeV2          1500 GeV2
       1                                                                                                                           1
                                                                                                                                  0.8
      0.5
                                                                                                                                  0.6
       0
                                                                                                                                  0.4
                  18 GeV2              22 GeV2                    27 GeV2                           35 GeV2
      1.5                                                                                                                         0.2

       1                                                                                                                           0
                                                                                                                                             2000 GeV2          3000 GeV2          5000 GeV2          8000 GeV2
      0.5                                                                                                                         0.8

       0                                                                                                                          0.6
                           2                    2                            2                                 2
                  45 GeV               60 GeV                     70 GeV                            90 GeV
      1.5                                                                                                                         0.4

       1                                                                                                                          0.2

      0.5                                                                                                                          0
                                                                                                                                             12000 GeV2         20000 GeV2         30000 GeV2       10-2   10-1       1
       0                                                                                                                          0.6
                                                             -3        -2        -1            -3        -2        -1                                                                                  ZEUS-JETS
                  120 GeV2             150 GeV2         10        10        10        1   10        10        10        1
      1.5                                                                                                                                                                                              tot. uncert.
                                                                                                                                  0.4
       1                                                               ZEUS-JETS
                                                                       tot. uncert.                                                                                                                   ZEUS NC e+p 99-00
                                                                                                                                  0.2
      0.5                                                                                                                                                                                             ZEUS NC e-p 98-99
                                                                       ZEUS NC e+p 96-97                                                                                                              ZEUS NC e+p 96-97
       0                                                                                                                           0
            10-3 10-2 10-1     1   10-3 10-2 10-1   1                                                                                   10-2    10-1      1   10-2   10-1    1   10-2   10-1    1
                                                    x                                                                                                                                           x
DESY-05-71, submitted to European Physical Journal C


Factorization and factorization breaking in non-diffractive scattering at HERA/ Bruce Straub/ ISMD 2005                                                                                                                   5
                                              CTEQ61 Compared to CDF Jet Data

                      2
                 10                                                                          2.5
  [nb/(GeV/c)]




                                                                             Data / Theory
                                            KT D=0.7 0.1<|Y|<0.7                                    KT D=0.7 0.1<|Y|<0.7
                  10                             Data
                                                 Systematic errors                                       Data
                      1
                                                 NLO: JETRAD CTEQ61                           2          Systematic errors
                      -1
                 10                              corrected to hadron level
                                                                                                         NLO uncertainties
JET




                   -2                            µ R = µ F = max PJET / 2
d σ / dY dPT




                                                                  T
                 10
                                                   NLO uncertainties
                   -3                                                                        1.5    CDF Run II Preliminary
                 10

                 10-4
2




                   -5
                 10                                                                            1
                   -6
                 10
                              CDF Run II Preliminary
                   -7
                 10                               -1
                               s =1.96 TeV L=385 pb
                   -8                                                                        0.5
                 10
                          0   100   200   300    400    500    600     700
                                                                                                0    100 200 300 400 500 600 700
                                                               JET                                                            JET
                                                              PT [GeV/c]                                                     PT [GeV/c]
CTEQ61 also gives an excellent description of the HERA DIS data


Factorization and factorization breaking in non-diffractive scattering at HERA/ Bruce Straub/ ISMD 2005                              6
                  ZEUS NLO QCD Fit Compared to Direct Photoproduction Data
                                                                                               e+
dσ/dET (pb/GeV)                                    ZEUS
                                                                                                    γ
                  10   6    xobs > 0.75
                             γ                               ZEUS-JETS
                                                             tot. uncert.
                  105                                        ZEUS dijet γ p 96-97
     jet1




                                                             Jet energy scale uncert.
                  104                                                                          p


                  103                                                                          e+

                  102                                                       1<ηjet1,2<2.4           γ
                                                                            (× 20000)

                   10

                    1                                             1<ηjet1<2.4                  p
                                                                  0<ηjet2<1
                                               1<ηjet1<2.4        (× 100)
                  10-1                         -1<ηjet2<0
                                               (× 20)
                                                                                               e+
                  10-2
                                                                                                    γ
                  10-3                                        0<ηjet1,2<1
                                          0<ηjet1<1           (× 0.01)
                                          -1<ηjet2<0
                  10-4                    (× 0.0005)
                                                                                               p
                                -1<ηjet1,2<0
                                (× 0.00001)
                  10-5
                           20          30          40        50             60          70

                                                                                 Ejet1 (GeV)
                                                                                  T




Factorization and factorization breaking in non-diffractive scattering at HERA/ Bruce Straub/ ISMD 2005   7
                 ZEUS NLO QCD Fit Compared to Resolved Photoproduction Data
                                                            ZEUS                                                          γ
 d σ /dE T (pb/GeV)                                                                                                           xγ
                            6
                      10              x OBS < 0.75
                                        γ                                         ZEUS 96-97 ( γ p data)
                                                                                  Jet Energy Scale Uncertainty
                            5
                      10                                                          NLO QCD (AFG-PH) × δhad:
                                                                                  ZEUS-JETS (prel.) 94-00
                            4                                                     total uncertainty                       p
  jet1




                      10
                            3
                      10
                            2
                                                                                                                          γ
                      10
                                                                                                 1< η jet1,2<2.4
                      10                                                                         ( × 5000)


                       1
                                                                                       1< η <2.4,0< η
                                                                                          jet1             jet2
                                                                                                               <1         p
                                                                                       ( × 100)
                           -1
                                                 1< η <2.4,-1< η
                                                    jet1               jet2
                      10                                                  <0
                                                 ( × 20)
                           -2
                      10
                                                                     0< η
                                                                         jet1,2
                                                                               <1
                                                                                                                          γ
                           -3
                      10                                             ( × 0.01)

                           -4
                      10
                                -1< η jet1,2<0
                                                           0< η <1,-1< η
                           -5                                 jet1            jet2
                                ( × 0.00001)                                      <0
                      10
                                                           ( × 0.0005)
                           -6                                                                                             p
                      10
                                      20           30                   40                50                      60
                                                                                                        jet1
                                                                                                     ET           (GeV)

The data lies above the NLO QCD calculations, especially at high E T

Factorization and factorization breaking in non-diffractive scattering at HERA/ Bruce Straub/ ISMD 2005                            8
                             Resolved Photoproduction Data Compared to NLO Predictions
Cross section/theory                               ZEUS
                        2           1<η        < 2.4
                                          jet1,2




                        1                                                                        CTEQ5M1 parton densities for the proton
                        2
                                                                            1<η       < 2.4
                                                                                  jet1

                       1.5                                                                       The hatched theory error band includes:
                                                                            0<η       <1
                                                                                  jet2


                        1
                                                                                                 · Renormalization and factorization
                                                                                                 scales µ varying between ET /4 and ET
                        3                                                    1<η
                                                                                   jet1
                                                                                         < 2.4   · Hadronization uncertainty
                                                                            -1 < η        <0
                                                                                   jet2
                        2
                                                                                                 · αs(Mz ) = 0.116 ± 0.003
                        1
                        2
                                                                            0<η
                                                                                  jet1,2
                                                                                          <1
                                                                                                 High ET excess especially pronounced
                                                                                                 for forward jets
                        1

                        4
                                                                             0 < ηjet1< 1
                                                                            -1 < ηjet2< 0
                        2


                       1.5
                                    -1 < ηjet1,2< 0         ZEUS 1996-97 xγ < 0.75
                                                                              obs

                        1                                   NLO (GRV) ⊗ HAD
                                                            NLO (AFG) ⊗ HAD
                       0.5                                  Jet energy scale uncertainty

                               20        30            40             50             60
                                                                               jet1
                                                                              ET (GeV)
European Physic. Journal C23 (2002) 4, 615-631


Factorization and factorization breaking in non-diffractive scattering at HERA/ Bruce Straub/ ISMD 2005                               9
            NC DIS Breit Frame Current Region Scaled Momentum Spectra
European Physical Journal C 11 (1999) 2, 251-270

                                            ZEUS 1994-7

                                                                     2


                                                                     0
                                                                                                    q = (0, 0, 0, −Q) is the
                                                                     2                              virtual photon momentum.
                                                                     0
                                                                         0     5
                                                     2                                              Max      momentum     of
                                                     0
                                                                                                    particles in the current
                                                     2                                              region is Q/2
                                                     0

                                    2                                                               For    particle     with
                                    0
                                                                                                    momentum p,
                                                         0       5
                                    2                                                               xp = 2p/Q
                                    0

                    2


                    0

                    2


                    0
                                        0      2.5   5
    2


    0
        0     2.5   50      2.5     5




Factorization and factorization breaking in non-diffractive scattering at HERA/ Bruce Straub/ ISMD 2005                    10
Breit Frame Current Region Multiplicity in Bands of Scaled Momentum


                                                                                            Open Symbols are e+e−
                                                                                            multiplicities (divided by 2)
                                                                                            plotted at Q2 = s

                                                                                            Q2 variation = scaling violation


                                                                                            e+ e− and NC DIS data agree
                                                                                            well




Factorization and factorization breaking in non-diffractive scattering at HERA/ Bruce Straub/ ISMD 2005                        11
     Compare Shape of the NC DIS Scaled Momentum Spectra to e+e−



                                                                                Parameterize the ln(1/xp ) distribution with
                                                                                mean l and width w as a distorted Gaussian
                                                                                in δ = (ln(1/xp ) − l)/w:
                                                                                                                       (2+k)δ 2       sδ 3        kδ 4
                                                                                            “                            ”
                                                                                                      k       sδ
                                                                                f (δ) = exp           8   −   2    −      4       +    6     +     24


                                                                                     e+e− and NC DIS data agree well




Factorization and factorization breaking in non-diffractive scattering at HERA/ Bruce Straub/ ISMD 2005                                      12
                                   Event Characteristics for Tagged Photoproduction
Z. Phys. C70 (1996) 17
                                                                                     Q2 < 0.01 GeV2
dσ/dET [nb/GeV]


             10
                                                                                     Tagged electron with 8 < E     e   <
                  1                                                                  20 GeV

          10
                      -1                                                             0.25 < y < 0.7


          10
                      -2                                                             150 < W < 251 GeV
                       20     25       30        35          40       45     50
                                                                      ET [GeV]       Better description using simulations
             12                                                                      with multiple interactions (PHOJET,
<dET/dη > [GeV]




             10                                                                      PYTHIA mia)
*




                  8

                  6

                  4

                  2

                  0
                      -2.5   -2     -1.5    -1        -0.5        0   0.5       1
                                                                            η
                                                                                *




  Factorization and factorization breaking in non-diffractive scattering at HERA/ Bruce Straub/ ISMD 2005               13
                                  Tagged Photoproduction Underlying Event ET density vs. xγ

                                                                                                           jet
                                                                                      Require 2 jets with ET > 7 GeV and
                                                                                      −2.5 < η ∗ < 0.5

                        1.4                                                           xjets is the fraction of the photon’s
<ET>/(∆η∆φ) [GeV/rad]




                                                                                        γ
                                                                                      longitudinal momentum carried by
                        1.2                                                           the dijet system

                         1
                                                                                        jets       (E − Pz )jet1 + (E − Pz )jet2
                                                                                      xγ       =
                        0.8                                                                                (E − Pz )γ

                        0.6
                                                                                      Plot shows the (η, φ) ET density in
                                                                                      the central region |η ∗| < 1 excluding
                        0.4
                                                                                      cones of radius 1.3 centered on the 2
                                                                                      highest ET jets
                        0.2

                                                                                      Low xjets (resolved) γp interactions
                                                                                             γ
                         0
                              0       0.2   0.4   0.6      0.8           1            have ∼ 2× as much ET density as
                                                                      jets
                                                                     xγ               direct γp.


   Factorization and factorization breaking in non-diffractive scattering at HERA/ Bruce Straub/ ISMD 2005                     14
                                         Photoproduction ET Spectrum Compared to NLO QCD
                                         H1 inclusive jet photoproduction
dσep /dE jet [nb/GeV]                                                                                     NLO      results    corrected     by
                                                         H1 data Q2 ≤ 0.01 GeV2 ( × RF )
                               2                                                                          1 + δhadr = (1 + δfrag )(1 + δue)
                          10                             H1 data Q2 ≤ 1 GeV2

                          10                             NLO (1+ δhadr.)                                  1 + δfrag corrects for fragmentation.
         T




                                                         NLO
                           1                      GRV,CTEQ5M
                                                                                                          The underlying event correction
                               -1
                          10                                                                              1 + δue is defined as the ratio of cross
                               -2                                                                         sections with and without a simulated
                          10
                                                                                                          underlying event which was tuned
                               -3
                          10        incl. k⊥ algor. (D=1)                                                 to describe the energy flow between
                               -4
                                    -1 ≤ η
                                          jet
                                                 ≤ 2.5
                                                                                                          jets.
                          10
                                    164 ≤ Wγ p ≤ 242 GeV
                               -5




                                                                                                  1+δue
                          10                                                                                2
    (σ-σTheory)/σTheory




                                                                         NLO (1+ δhadr.)                  1.8
                           0.4
                           0.2                                           LO (1+ δhadr.)                   1.6
                             0                                                                            1.4
                          -0.2                                                                            1.2
                          -0.4                                                                              1
                          -0.6               ,            H1 data                                         0.8
                                                                                                                10   20   30   40   50   60   70
                                    10           20        30       40     50      60      70                                                     ETjet
 European Physical Journal C29 (2003) 497-513                                       E jet [GeV]
                                                                                      T



     Factorization and factorization breaking in non-diffractive scattering at HERA/ Bruce Straub/ ISMD 2005                                              15
                            Forward Neutron Production in DIS and γP
                                     ZEUS
     20

     18

     16

     14

     12

     10
                                                                                   xL = Pn/Pp
      8

      6                                                                            Probability of producing a neutron
                                                                                   is about 1/2 that observed in pp
      4                                                                            collisions at the ISR.

      2                                                                         γp collisions are 20-30% less likely
                                                                                to produce a neutron compared to
      0
          0.2    0.3     0.4      0.5      0.6     0.7      0.8     0.9       1 NC DIS, although no Q2 dependence
                                                                                is observed for Q2 > 4.
Nucl. Physics B637 (2002) 3-56


Factorization and factorization breaking in non-diffractive scattering at HERA/ Bruce Straub/ ISMD 2005             16
                                                Forward Neutron Production in DIS and γP
                                                   ZEUS
                        1.4
                                                                                     Small γ = High Q2, No Rescatter, n detected
                        1.2

                         1

                        0.8

                        0.6

                        0.4

                        0.2

                         0
                          0.2       0.3   0.4    0.5   0.6   0.7   0.8   0.9     1

                        0.06                                                         Large γ = Low Q2 −→ Rescatter.
        fln=σ2j+n/σ2j




                                          H1 data
                                          RAPGAP-π/PYTHIA-MI                         rnπ smaller at lower xL −→ Rescatter
                        0.05
                                          PYTHIA/PYTHIA (*0.6)

                        0.04              γp
                        0.03

                        0.02

                        0.01

                              0
                                  0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9           1
                                                                           jet
                                                                         xγ
Eur. Phys. J. C41 (2005) 273-286


Factorization and factorization breaking in non-diffractive scattering at HERA/ Bruce Straub/ ISMD 2005                        17
                             Dipole Model of Deep Inelastic Scattering
                                                                                            2
                                                                               γ   *
                                                                                                     γ
                                                                                                         *
                                                                                                                 Detector

     γ*                                    γ*


                                                                                    p            p                                  Y
                                                                                                                            γ
                                                                                                                                *
                                                                                                             p
                                                                                            a
          p                            p                                                1
                                                                               γ                     γ
                                                                                *                    *
                                                                                                                 Detector

The Optical Theorem relates the amplitude
for elastic γ ∗p scattering (no cut) to the
inclusive γ ∗p cross section (with the cut).                                        p            p
                                                                                                             p              γ
                                                                                                                                *   Y
The total cross section is a sum of all                                                     b
diagrams with all possible Pomeron (gluon
                                                                                            2
ladder) exchanges. Diagram (a) above right                                     γ*
                                                                                                     γ*          Detector
gives the leading term to the diffractive cross
section.
                                                                                    p            p                                  Y
                                                                                                                            γ
                                                                                                                                *
                                                                                                             p
J.Bartels, M.Salvadore, G.P.Vacca,Eur.Phys.J. C42 (2005) 53-71
                                                                                            c
H.Kowalski, D.Teaney, Phys.Rev. D68 (2003) 114005


Factorization and factorization breaking in non-diffractive scattering at HERA/ Bruce Straub/ ISMD 2005                                 18
                             Dipole Model of Deep Inelastic Scattering

The γ ∗p cross section for k-cut Pomerons                                                                                                              10




                                                                   F2




                                                                                                                                               F2
vs. impact parameter b is                                                   1

                                                                                                                                                        1



      dσk    Ω(b)k
                                                                                -1
                                                                           10
                                                                                                                                                            -1

           =        exp(−Ω(b)), where                                                                                                                  10


      d2 b    k!                                                           10
                                                                                -2
                                                                                                                                                            -2

           π2 2       2          2
                                                                                                                                                       10


     Ω=       r αs(µ ) xg(x, µ ) T (b)
           NC                                                              10
                                                                                -3

                                                                                          10
                                                                                               -5
                                                                                                         10
                                                                                                              -4
                                                                                                                       10
                                                                                                                            -3
                                                                                                                                 10
                                                                                                                                      -2
                                                                                                                                                       10
                                                                                                                                                            -3

                                                                                                                                                                      10
                                                                                                                                                                           -5
                                                                                                                                                                                     10
                                                                                                                                                                                          -4
                                                                                                                                                                                                10
                                                                                                                                                                                                     -3
                                                                                                                                                                                                          10
                                                                                                                                                                                                               -2



is the Opacity written in terms of the dipole                                                                                              x                                                                        x


radius r, the gluon density xg(x, µ2 ) and                                                Contributions to F2 from k-cut Pomerons (H.Kowalski).
the transverse shape of the proton T (b).




                                                                   ratio




                                                                                                                                               ratio
To get the total cross section, F2, average                                     1                                                                           1


the dipole cross secctions over the photon
wave function ψ(r, z) and integrate over the                                10
                                                                                     -1
                                                                                                                                                        10
                                                                                                                                                                 -1


impact parameter

       Q2                              dz ∗                dσk
                       Z          Z                Z                                 -2                                                                          -2
                                                                            10                                                                          10
 k                           2                            2                                         -5         -4           -3        -2                                        -5         -4        -3        -2

F2 =                       d r            ψ ψ           d b 2 .                            10            10            10        10
                                                                                                                                       x
                                                                                                                                                                       10            10         10        10
                                                                                                                                                                                                                x
     4π 2 αem                          4π                  d b
                                                                                      Fraction of F2 due to single Pomeron exchange, multiple

                                                                                                                    Pomeron exchange, and diffraction.



Factorization and factorization breaking in non-diffractive scattering at HERA/ Bruce Straub/ ISMD 2005                                                                                                                 19
                                                       Conclusions


• Factorization holds very well in non-diffractive interactions of protons with
  point-like photons

• Universal parton densities can describe ep, direct γp, and hard p¯
                                                                   p
  interactions

• Fragmentation functions measured in DIS are quite compatible with those
  measured in e+e−.




Factorization and factorization breaking in non-diffractive scattering at HERA/ Bruce Straub/ ISMD 2005   20
                                                       Conclusions


• In resolved photoproduction, which is a hadron-hadron collision, multiple-
  interaction models describe the data better than LO models without multiple
  interactions.
    • The underlying event produces about twice as much ET in resolved
      photoproduction compared to direct
    • Resolved γp cross sections exceed NLO QCD predictions, at high ET
    • HERA experiments should measure event shapes and energy flow in γp
      more systematically, instead of focusing entirely on jets

• The probability to produce a forward neutron is process dependent, highest
  in pp collisions, and lowest in γp interactions.

• The dipole model relates the cross section for multiple gluon exchange to
  the diffractive cross section. Even at the relatively high Q2 of 40 GeV2,
  the model predicts that multiple gluon exchange makes up 6-8% of the DIS
  cross section

Factorization and factorization breaking in non-diffractive scattering at HERA/ Bruce Straub/ ISMD 2005   21

				
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