Scaling Study of the L-T Separated p(e,e

1
Scaling Study of the L-T Separated p(e,ep)n
Cross Section at Large Q2
P. Bosted, H. Fenker, D. Gaskell, T. Horn, M.
Jones, D. Mack, G.R. Smith, M. Spata, M. Epps,
S. Wood, C. Butuceanu, G. Huber, G.J. Lolos, Z.
Papandreou, A. Sarty, W. Boeglin, P. Markowitz,
A. Asaturyan, A. Mkrtchyan, H. Mkrtchyan, V.
Tadevosyan, E. Brash, C. Perdrisat, K. Aniol, E.
Christy, C.E. Keppel, L. Tang, V. Tvaskis, D.
Hornidge, V. Punjabi, J. Calarco, G. Niculescu,
I. Niculescu JLab, Regina, FIU, Yerevan, CNU,
WM, California State, Hampton, Mount Allison,
Saint Marys, Norfolk, New Hampshire, JMU

• Motivation
• Experimental Details
• Summary

PAC 32
August 2007
2
Partons and Factorization

• Deep Inelastic Scattering (DIS) can be factorized
  into short and long distance physics in the limit
  of large Q2 and at fixed values of xB
• Hard scattering can be calculated in perturbative
  QCD (pQCD)
• Soft physics is described by Parton Distribution
  Functions (PDFs)
• A similar factorization of scales is expected for
  hard exclusive processes DVCS is simplest
• Generalized Parton Distributions (GPDs) are a
  generalization of PDFs, where initial and final
  quark-gluon momenta are not identical
• Unified concepts of quark parton density and
  elastic form factors
• Transverse spatial distribution of quarks
• Spin decomposition of the nucleon

3
Hard-Soft Factorization

• To access physics contained in GPDs, one is
  limited to the kinematic regime where hard-soft
  factorization applies
• No single criterion for the applicability, but
  tests of necessary conditions can provide
  evidence that the Q2 scaling regime has been
  reached

• One of the most stringent tests of factorization
  is the Q2 dependence of the p electroproduction
  cross section
• sL scales to leading order as Q-6
• sT scales as Q-8
• As Q2 becomes large sL gtgt sT

Factorization

• Factorization theorems for meson
  electroproduction have been proven rigorously
  only for longitudinal photons
• Dominance of sL is important as it contains the
  GPD one would like to extract

4
Context

• Determining the applicability of the GPD
  mechanism is a high priority for the 12 GeV
  program
• Only if hard-soft factorization applies can GPDs
  be extracted
• Extraction of GPDs from unseparated observables
  relies on the dominance of sL - what about
  transverse contributions?
• Effect from sT may cancel in asymmetries and
  ratios need to know the relative contribution
  of L and T
• Precision separated L/T data from JLab suggest
  that transverse contributions to the p cross
  section are larger than predicted by Regge
  calculations and the constituent quark model
• Limited knowledge of L/T ratio at higher energies
  limits the interpretability of unseparated cross
  sections in p production

5
Q2 dependence of sL and sT
Hall C data at 6 GeV 3 different experiments

• The Q-6 QCD scaling law is consistent with the
  JLab sL data
• Limited Q2 coverage and large uncertainties make
  it difficult to draw a conclusion
• The two additional factorization predictions that
  sLgtgtsT and sTQ-8 are not consistent with the
  data
• Testing the applicability of factorization
  requires larger kinematic coverage and improved
  precision

Q22.7-3.9 GeV2
Q21.4-2.2 GeV2
sL
sT
Horn et al., arXiv0707.1794 (2007)
Vanderhaeghen, Guidal and Laget, Phys. Rev. C57,
1454 (1998).
Vanderhaeghen, Guichon and Guidal, Phys. Rev.
D60 (1999).
6
Q2 Scaling of the Interference Terms
Preliminary from Fpi1, Fpi2

• Scaling prediction based on transverse content to
  the amplitude
• sLT Q-7
• sTT Q-8
• Limited Q2 coverage complicates the
  interpretation
• Interference terms decrease in magnitude as Q2
  increases

Q2 range is small
7
Motivation - Applicability of the GPD formalism

• One of the most stringent tests of QCD
  factorization is the Q2 dependence of separated
  cross sections
• Scaling of asymmetries or charge ratios may
  indicate cancellation of higher order
  corrections, but are not a stringent test of
  factorization itself
• Many studies of exclusive meson cross sections
  exist, but contribution of sT unknown at higher
  energies
• JLab measurements from
• Hall B E99-105 (?, ?)
• Q2 1.5-3.5 GeV2, -tlt1.5 (GeV/c)2
• Hall C Fp1, E91-003, Fp2, pionCT (p)
• Q2 range for precision L/T to 2.45 GeV2
• Hall A, Hall B DVCS, e1-6 (p - unseparated)

8
Transverse contributions results from Fp-2
Fp-2 L/T data at W2.2 GeV

• Even at Q22.45 GeV2, sT is not small
• But electroproduction is a multi-variable phase
  space
• At fixed W, tmin increases with Q2 and sL
  decreases more rapidly than sT
• Scaling tests need high precision separated cross
  sections at fixed xB and -t

VGL sL
VGL sT
Note -tmin is different
Horn et al., Phys. Rev. Lett. 97, 192001 (2006)
Vanderhaeghen, Guidal and Laget, Phys. Rev. C57,
1454 (1998).
9
Motivation Summary

• L/T separated cross sections will play a large
  role in guiding the 12 GeV GPD program
• If transverse contributions are larger than
  anticipated, the accessible phase space for GPD
  studies may be limited
• The charged pion L/T ratio is of significant
  interest to the study of p cross sections at 12
  GeV
• If sL is small, absolute measurements will
  require information from a double-arm
  spectrometer setup interpretation of asymmetry
  measurements questionable
• Our theoretical understanding of hard exclusive
  reactions will benefit from L/T separated data
  over a large kinematic range
• puzzle of the relatively large p transverse
  cross section

10
Experiment Goals

• Measure the Q2 dependence of the p(e,ep)n cross
  section at fixed xB and t to search for evidence
  of hard-soft factorization
• Separate the cross section components L, T, LT,
  TT
• The highest Q2 for any L/T separation in p
  electroproduction
• Also determine the L/T ratio for p- production to
  test the possibility to determine sL without an
  explicit L/T separation

11
Experiment Overview
Phase space for L/T separations with SHMSHMS

• Measure separated cross sections for the
  p(e,ep)n reaction at three values of xB
• Near parallel kinematics to separate L,T,LT,TT
• The Q2 coverage is a factor of 3-4 larger
  compared to 6 GeV
• Facilitates tests of the Q2 dependence even if
  L/T is less favorable than predicted

Overlap, but only for 6 of proposed beam time
x Q2 (GeV2) W (GeV) -t (GeV/c)2
0.31 1.5-4.0 2.0-3.1 0.1
0.40 2.1-5.5 2.0-3.0 0.2
0.55 4.0-9.1 2.0-2.9 0.5
The kinematics for the LD2/p- measurement
12
Cross Section Separation

• The virtual photon cross section can be written
  in terms of contributions from transversely and
  longitudinally polarized photons.

• Separate sL, sT, sLT, and sTT by simultaneous fit
  using measured azimuthal angle (fp) and
  knowledge of photon polarization (e)

13
Separation in a Multi-Dimensional Phase Space

• Cuts are placed on the data to equalize the Q2-W
  range measured at the different e-settings

• Multiple SHMS settings (2 left and right of the
  q vector) are used to obtain good f coverage over
  a range of t
• Measuring 0ltflt2p allows to determine L, T, LT and
  TT
• Determine LT, TT for xB0.31, 0.40 only
• For xB0.55 apply a parallel cut on ?p

SHMS2
SHMS-2
High e
Radial coordinate (-t), Azimuthal coordinate (f)
14
Expected Missing Mass Resolution

• Missing mass resolution is very good
• Good p/K separation using Cerenkov, and
  accidental coincidence subtraction
• Decay products from real e- K coincidences
  cannot be eliminated in this way, but are
  projected to be lt0.1 for most settings
• Largely eliminated after applying offline
  analysis cuts

Simulation at Q29.1 GeV2 and high e
15
Predictions for the Q2 dependence of RsL/sT

• Fp parameterization was used for the L/T ratio in
  this proposal
• Projected ?(L/T)10-25 for typical kinematics
• For xB0.55, the projected ratio shows a rapid
  increase in the uncertainty between 9-10 GeV2
• Future predictions may indicate larger values of
  R, and thus lower uncertainties
• Reaching Q210 GeV2 would require only minor
  modification to the current run plan

VGL/Regge
Fp param
16
Projected Uncertainties for Q-n scaling

• QCD scaling predicts sLQ-6 and sTQ-8
• Projected uncertainties for sL use the Fp
  parameterization for L/T ratio

Fit 1/Qn
xB dnL dnT dnLT dnTT
0.31 0.3 0.2 0.5 0.6
0.40 0.4 0.3 0.7 0.8
0.55 2.5 1.0 - -
17
Projected Uncertainties for sL at constant Q2

• xB scan at Q24 GeV2
• Can easily distinguish between pole and axial
  contributions within the framework of GPD
  calculations
• Provides information about non-pole contributions
• May constrain longitudinal backgrounds in the
  extraction of Fp

Axial only
Pion pole only
Axial and pole
18
p- cross section measure sL without explicit
L/T?

• Fp1 and Fp2 saw sL/sT larger for p- than for p
• If sT is small, one may extract sL from the
  unseparated cross sections
• Scaling prediction for sT/sL is Q-2
• Measure L/T from p- production to an absolute
  precision of 0.1-0.3
• Uncertainties assume R sL/sT for p p- is at
  least 12 (based on Fp1 and Fp2 results)

19
Accidental Rates for the LD2/p- measurement

• Online coincidence time window may be relatively
  large, e.g. t40 ns, but rates are still well
  within DAQ design specifications
• The offline timing window will be smaller (t2
  ns)
• After PID cuts random coincidences will be mostly
  eliminated

Assume 14500 electron rejection
NO PID
Singles Rates low e
Q2 (GeV2) e- SHMS (kHz) p- SHMS (kHz) K-SHMS (kHz) p-HMS (kHz) e- HMS (kHz) Raccidental t40ns (Hz) Raccidental t40ns (Hz)
2.12 41.5 4.9 0.07 1.9 1.2 5.8 0.6
4.00 497.4 2.5 0.03 2.3 0.2 51.2 0.3
5.50 847.6 1.4 0.03 2.6 0.1 93.7 0.2
20
Beam Time Estimate
Q2 (GeV2) xB LH2 (hrs) Dummy Overhead (hrs) Total (hrs)
1.45 0.311 1.4 0.2 8 9.6
2.73 0.311 7.3 0.6 8 15.9
4.00 0.311 9.0 0.6 8 17.6
Subtotal x0.311 43.1 (1.8 days)
2.12 0.40 1.8 0.2 8 10.0
4.00 0.40 17.5 0.9 8 26.7
5.50 0.40 34.7 2.5 8 45.2
Subtotal x0.40 81.9 (3.4 days)
4.00 0.55 7.0 0.5 8 15.9
6.60 0.55 164.1 11.5 8 183.6
9.10 0.55 462.4 32.4 8 502.8
Subtotal x0.55 702.3 (29.3 days)
Subtotal LH2/p 705.6 49.7 72 827.3
LD2/p- 72.0
Calibrations 48.0
Beam energy 48.0
Total 995.3 (41.4 days)
21
Summary

• L/T separated p cross sections will be essential
  for understanding the reaction mechanism at 12
  GeV
• If transverse contributions are larger than
  anticipated, this may influence the accessible
  phase space for GPD studies
• L/T separated p data over a wide kinematic range
  will have a significant impact on our
  understanding of hard exclusive reactions
• Relative contribution of sL and sT in p
  production - interpretation of asymmetry and
  ratios
• The charged pion L/T ratios will provide valuable
  information for p cross section measurements with
  CLAS12
• If sL is small, absolute measurements may be
  limited to focusing spectrometers
• p- data will check the possibility of measuring
  sL without explicit L/T separation

22
Systematic Uncertainties
Source pt-to-pt () t-correlated Scale ()
Acceptance 0.4 0.4 1.0
PID 0.4
Coincidence Blocking 0.2
Tracking Efficiency 0.1 0.1 1.5
Charge 0.2 0.5
Target Thickness 0.2 0.8
Kinematics 0.2
Pion Absorption 0.1 1.5
Pion Decay 0.03 0.5
Radiative Corrections 0.1 0.4 2.0
Monte Carlo Model 0.2 1.0 0.5
Total 0.6 1.6 3.3
23
Simulated p(e,e,K)X

• Good p/K separation can be accomplished
  (Cerenkov, and accidental coincidence
  subtraction)
• Decay products from real e- K coincidences
  cannot be eliminated in this way, but are
  projected to be lt0.1 for most settings.

24
RL/T for p- data Fp-1 and Fp-2

• Fp-1 and Fp-2 saw sL/sT larger for p- than for p
• Combined with Fp-1 p-data suggests that the trend
  increases with Q2

25
Parallel Cut

• To ensure parallel kinematics place a cut on ?/f
• Eliminate interference terms by averaging over f

26
LD2 missing mass

• Lose events to missing mass cut at 2p threshold
• included in rate estimates

• Cross section using p- from deuterium and p from
  hydrogen and deuterium

2p threshold

• Correct for proton and neutron mass difference
  when applying the cut

27
Uncertainty in sL

• Assuming equal correlated sytematic uncertainties
  at each e

• Due to amplification by 1/?e, uncertainty in sL
  is dominated by uncorrelated systematic
  uncertainty
• If R more favorable, precision in sL improves
  even for small ?e

28
Two ? exchange?

• In the Rosenbluth separation of the proton
  electric form factor, 2? contributions may be
  important because one is trying to separate a
  small cross section (electric) from a much larger
  (magnetic) one.
• 2? exchange is not expected to be a significant
  issue in the extraction of ?L in pion
  electroproduction.

e-range to be covered
Q26 GeV2 calculation performed by Tjon and
Melnitchouk. CorrectiondFULL-dMoTsai
29
Interference terms from pionCT

• Interference terms decrease in magnitude as Q2
  increases
• Scaling prediction based on transverse content to
  the amplitude
• sLT Q-7
• sTT Q-8

Horn et al., arXiv0707.1794 (2007)
Vanderhaeghen, Guidal and Laget, Phys. Rev. C57,
1454 (1998).
30
Contribution of L and T
VGL/Regge model calculation

• At fixed W, -tmin increases as Q2 increases
• L is dominated by the pole, so decreases faster
  then T
• BUT, for fixed kinematics, there is reasonable
  expectation that sT/sL ltlt 1 as W and Q2 increase

31
Higher Order Corrections
Calculation using the VGG model

• Higher order corrections play a significant role
  at accessible energies
• Soft term may mimic the expected LO QCD Q2
  scaling
• Precision cross sections will constrain
  predictions for higher order corrections
• Not measurable in asymmetries

32
Non-pole contributions to sL in the GPD Framework
VGG/GPD prediction

• Typically assume that the pion pole dominates at
  low -t

• But, at leading order, the axial term still
  contributes
• As Q2 increases, the ratio becomes less favorable

• A better understanding of these non-pole
  contributions would also help to constrain
  backgrounds in the extraction of Fp