1. Scaling Study of the L-T Separated p(e,e’π+)n Cross Section at Large Q2
Tanja Horn
Jefferson Lab
APS/DNP meeting 2007
DNP07
October 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 t
x+ξ
x-ξ
“take out”
“put back”

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 π electroproduction cross section
σL scales to leading order as Q-6
σT scales as Q-8
As Q2 becomes large: σL >> σT
Factorization
Q2 ?
Factorization theorems for meson electroproduction have been proven rigorously only for longitudinal photons

4. Q2 dependence of σL and σT
Hall C data at 6 GeV: 3 different experiments
The Q-6 QCD scaling law is consistent with the JLab σL data
Limited Q2 coverage and large uncertainties make it difficult to draw a conclusion
The two additional factorization predictions that σL>>σT and σT~Q-8 are not consistent with the data
Testing the applicability of factorization requires larger kinematic coverage and improved precision
Q2= GeV2
Q2= GeV2 σL σT
Horn et al., arXiv: (2007)

5. Q2 Scaling of the Interference Terms
Preliminary from Fpi1, Fpi2
Scaling prediction based on transverse content to the amplitude
σLT ~ Q-7
σTT ~Q-8
Limited Q2 coverage complicates the interpretation
Interference terms decrease in magnitude as Q2 increases
Q2 range is small

6. Transverse Contributions
Fpi2 L/T data at W=2.2 GeV
VGL σL
VGL σT
Note: -tmin is different
Even at Q2=2.45 GeV2, σT is not small
But electroproduction is a multi-variable phase space
At fixed W, tmin increases with Q2 and σL decreases more rapidly than σT
Scaling tests need high precision separated cross sections at fixed xB and -t
Horn et al., Phys. Rev. Lett. 97, (2006)

7. Fπ and Factorization Tests
Fπ provides another test of the validity of QCD factorization
If one replaces the GPD in the handbag mechanism by the Nπ vertex and the pion DA, one obtains Fπ
The modified mechanism is also characterized by a single hard gluon exchange
Naively expect a correlation between pQCD calculations of Fπ and experimental data where factorization applies
Fπ scales to leading order as Q-2
Hard Scattering
Hard Scattering

8. Fπ in 2007
T. Horn et al., Phys. Rev. Lett. 97 (2006)
Q2>1 GeV2: Q2 dependence of Fπ is consistent with the power law behavior expected from the hard scattering mechanism (Q-2)
But the monopole fit would provide an equally good description
Fπ data still far from pQCD calculation
Not in QCD factorization regime
Or insufficient knowledge how to extend pQCD calculations to low Q2
AdS/CFT describes Q2-dependence, and provides a reasonable description of the magnitude
Includes confinement and constituent quark counting rule behavior
T. Horn et al., arXiv: (2007).
A.P. Bakulev et al, Phys. Rev. D70 (2004)]
H.J. Kwee and R.F. Lebed, arXiv:0708:4054 (2007)
H.R.Grigoryan and A.V.Radyushkin, arXiv: (2007)

9. Scaling Test at 12 GeV Experiment approved for 42 days in Hall C SHMS
E (T. Horn&G. Huber et al.)
Measure the Q2 dependence of the p(e,e’π+)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 π electroproduction
Also determine the L/T ratio for π- production to test the possibility to determine σL without an explicit L/T separation
SHMS
HMS x Q2
(GeV2) W
(GeV) -t
(GeV/c)2
0.31
0.1
0.40
0.2
0.55
0.5

10. Projected Uncertainties for Q-n scaling
QCD scaling predicts σL~Q-6 and σT~Q-8
Projected uncertainties for σL use an Fπ parameterization for L/T ratio
Based on previous π+ L/T data
Fit: 1/Qn xB
dnL
dnT
dnLT
dnTT
0.31
0.3
0.2
0.5
0.6
0.40
0.4
0.7
0.8
0.55
2.5
1.0 -

11. π- cross section – measure σL without explicit L/T?
Fpi1 and Fpi2 saw σL/σT larger for π- than for π+
If σT is small, one may extract σL from the unseparated cross sections
Scaling prediction for σT/σL is Q-2
Measure L/T from π- production to an absolute precision of
Uncertainties assume R= σL/σT for π+: π- is at least 1:2 (based on Fpi1 and Fpi2 results)

12. Fπ after the JLab Upgrade
Experiment (E ) approved for 55 days in Hall C
The 11 GeV electron beam and the SHMS in Hall C with θ=5.5º allows for
Precision data up to Q2=6 GeV2 to study the transition to hard QCD

13. Summary
The Q2-dependence of L/T separated π+ σL from Jefferson Lab is in relatively good agreement with the Q2-scaling prediction
σT still significant at Q2=3.91 GeV2, and drops more slowly than the Q-8 scaling expectation
The measured Q2-dependence of Fπ is also consistent with the Q2 scaling expected from the hard scattering mechanism, but pQCD calculations do not reproduce its magnitude
L/T separated π+ cross sections will be essential for understanding the reaction mechanism at 12 GeV (E )
Relative contribution of σL and σT in π+ production - interpretation of asymmetry and ratios
If transverse contributions are larger than anticipated, this may influence the accessible phase space for GPD studies
π- data will check the possibility of measuring σL without explicit L/T separation

14. Regge Exchange Contribution
Calculation by A.P. Szczepaniak et al. [arXiv: v2] suggest significant scaling violations at small –t and independent of Q2
Expect Q2 behavior characteristic for hadronic Regge amplitudes
σL,T ~ (Q-n) 2α(t)-1 x αL αT
0.31
0.46 ± 0.50
1.90 ± 0.36
0.45
0.92 ± 2.00
0.99 ± 0.51
HERMES π+ fit: α=0.31 ± 0.2 (0.26 < xB < 0.80), BUT not separated