1. Scaling Study of the L-T Separated p(e,e’π+)n Cross Section at Large Q2
Tanja Horn
Jefferson Lab
GW Seminar
Washington, DC
November 2007

2. DIS and Parton Distribution Functions
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)
Forward Compton amplitude can be directly related to DIS cross section via optical theorem 2 ~

3. Generalized Parton Distributions
Deep Virtual Compton Scattering
Deep Virtual Meson Production
x-ξ
x+ξ
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

4. Leading Twist GPDs
At leading twist, there are four independent GPDs for each quark, gluon type
x is the light cone momentum fraction of struck parton (x ≠ xB)
ξ defined by Δ+ = -2ξ(p+Δ/2)+
Longitudinal fraction of the momentum transfer, t
Parameterizes the skewedness
t=Δ2, momentum transfer to nucleon

5. GPDs and DIS ~ H
In the limit of ξ → 0 and t → 0, H and reduce to ordinary parton distributions
E and not accessible in DIS – parton helicity flip is forbidden ~ E

6. GPDs and Elastic Scattering
First moments of GPDs yield usual elastic form factors
F1,F2 = Dirac and Pauli form factors
GA, GP = axial vector and pseudo scalar form factors
Common formalism can describe DIS and elastic scattering

7. GPDs and Quark Imaging t
x+ξ
x-ξ
“take out”
“put back”
GPDs contain more information than parton densities and form factors alone
GPDs describe the probability to probe a parton of momentum fraction x, at a transverse distance b^
transverse spatial distribution of quark
Access to dynamic properties

8. GPDs and Total Angular Momentum
Second moments of GPDs at t=0 give expectation value of nucleon spin
Nucleon spin
can be inferred from (from GPDs) and (from DIS)
X. Ji, PRL 78, 610

9. Experimental Access to GPDs DVCS
Deeply Virtual Compton Scattering sensitive to a combination of all 4 GPDs →
Large background from Bethe-Heitler
Azimuthal asymmetries can access DVCS and BH interference terms
~ ~
H,E, H,E

10. GPDs and Exclusive Meson Production
Vector mesons (r,w,f) sensitive to H and E
Pseudo scalar mesons sensitive to and
Detection of final states easier – but interpretation complicated by convolution with meson wave function (additional soft object) ~ H ~ E

11. GPD “Measurements”
GPDs are not observables – they are a framework that allows us to describe a wide variety of processes
DIS, elastic scattering, exclusive reactions
We already have constraints on GPDs from:
DIS: H(x,0,0) = q(x) and H(x,0,0) = Dq(x)
Elastic scattering: ∫dx x H(x,x,t) = F1(t)
To fully understand GPDs, we need a program to measure:
a variety of exclusive processes
vector mesons, DVCS, pseudo scalar mesons
a broad range of phase space (t, xB) ~

12. GPD Program at JLab DVCS
Beam-spin asymmetry [Stepanyan et al, PRL 87, , 2001]
E00-110, DVCS at 6 GeV (Hall A)
E01-113, DVCS at 6 GeV with CLAS
Meson Production: many studies of exclusive cross sections exist, but contribution of σT unknown at higher energies
Hall B: E (ρ, ω)
Q2: GeV2, -t<1.5 (GeV/c)2
Hall C: Fpi1, E91-003, Fpi2, pionCT (π±)
Q2 range for precision L/T to 2.45 GeV2
Hall A, Hall B: DVCS, e1-6 (π° - unseparated)
A major motivation for the 12 GeV upgrade is a program of Deep Exclusive Measurements to constrain GPDs

13. 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

14. Pion Electroproduction Kinematics
Q2= |q|2 – ω2
t=(q - pπ)2
W=√-Q2 + M2 + 2Mω
scattering plane
reaction plane
The lab cross section can be expressed in terms of virtual photon flux, Jacobian and virtual photon cross section.
The virtual photon cross section can be written in terms of contributions from transversely and longitudinally polarized photons.

15. Jefferson Lab Two superconducting Linacs
Three experimental Halls operating concurrently
E<~ 5.7 GeV
Hadron-parton transition region
C.W. beam with currents of up to 100 uA
Luminosity ~1038
Fπ measurements 15

16. Pion Electroproduction in Hall C
Three experiments took data to the highest possible value of Q2 with 6 GeV beam at JLab
Full L/T/TT/LT separation in π+ production
Measurement of separated π+/π- ratio to test the reaction mechanism
HMS: 6 GeV
SOS: 1.7 GeV
Exp Q2
(GeV2)
W (GeV)
|t|
(Gev)2 Ee
(GeV)
Fpi1
1.95
Fpi2
1.6,2.45
2.22
0.093,0.189
πCT
2.15, 4.0
2.2

17. Experimental Configuration
Hall C spectrometers
Coincidence measurement
SOS detects e-
HMS detects π+
Targets
Liquid 4-cm H/D cells
Al (dummy) target for background measurement
12C solid targets for optics calibration
HMS Aerogel Cerenkov
Improves p/π+/K+ PID at large momenta, first use in 2003
Built by Yerevan group
[Nucl. Instrum. Meth. A548(2005)364] 17

18. p(e,e’π+)n Event Selection
Coincidence measurement between charged pions in HMS and electrons in SOS
Coincidence time resolution ~ ps
Cut: ± 1ns
Protons in HMS rejected using coincidence time and aerogel Cerenkov
Electrons in SOS identified by gas Cerenkov and Calorimeter
Exclusive neutron final state selected with missing mass cut
0.92 ‹ MM ‹ 0.98 GeV
After PID cuts almost no random coincidences 18

19. Fpi2 Kinematic Coverage
Have full coverage in φ BUT acceptance not uniform
Measure σTT and σLT by taking data at three angles: θπ=0, +4, -3 degrees
W/Q2 phase space covered at low and high ε is different
For L/T separation use cuts to define common W/Q2 phase space
Radial coordinate: -t, azimuthal coordinate: φ
Θπ=0
Θπ=+4
Θπ=-3
-t=0.1
-t=0.3
Q2=1.60, High ε
Q2=2.45 GeV2
Q2=1.60 GeV2 19

20. Determination of σL
σL is isolated using the Rosenbluth separation technique
Measure the cross section at two beam energies and fixed W, Q2, -t
Simultaneous fit using the measured azimuthal angle (φπ) allows for extracting L, T, LT, and TT
Careful evaluation of the systematic uncertainties is important due to the 1/ε amplification in the σL extraction
Spectrometer acceptance, kinematics, and efficiencies 20

21. Cross section W-dependence
σπ depends on W, -t, Q2
Cross section W-dependence given by: (W2-M2)n
Fpi1/Fpi2 data suggest that a n~2 is appropriate
πCT data were taken at central W=2.2 GeV
Relatively small sensitivity to variations in W, ~1% at Q2=2.15 GeV2
Fit: n=1.8
Fπ1
Fπ2
W-dependence of σπ makes sense – but what about –t and Q2?

22. t-dependence of separated cross sections
T. Horn et al., arXiv: (2007)
VGL/Regge describes σL reasonably well
Fit to the t-dependence allows for extracting Fπ
σT contributes significantly at Q2=4.0 GeV2
Interference terms →0 as Q2 increases
Λπ2=0.518 GeV2

23. Q2 dependence of σL and σT
Hall C data at 6 GeV: 3 different experiments
The Q-6 QCD scaling prediction 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
T. Horn et al., arXiv: (2007)

24. 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
T. Horn, Ph.D. thesis, University of Maryland (2006)

25. Transverse Contributions
T. Horn et al., Phys. Rev. Lett. 97, (2006)
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

26. Regge Exchange Contributions
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

27. 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

28. 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)
Fπ data still far from hard QCD calculations
Not in QCD factorization regime
Or additional soft contribution from the pion wave function
Additional soft contribution would be inconsistent with Q-6 scaling for the cross section
AdS/CFT describes Q2-dependence, and provides a reasonable description of the magnitude
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)

29. Compton Scattering Scaling Predictions
Expected scaling behavior
Fixed θ*: dσ/dt ~ s-n(θ),
nhard(θ) =6
Experimental fits are consistent with the prediction within the uncertainty
But is this sufficient? θ
ndata 60
5.9±0.3 90
7.1±0.4
105
6.2±1.4
M. A. Shupe et al., Phys. Rev. D19, 1921 (1979)

30. Compton Scattering and Soft Contributions
Soft contributions can result in deviations from expected scaling behavior [A. Radyushkin, Phys. Rev. D58 (1998) ]
Fixed θ*: dσ/dt ~ s-n(θ),
nhard(θ) =6
If similar soft effects are important in π+ production, then the observed scaling would be accidental θ
ndata
nsoft 60
5.9±0.3
6.1 90
7.1±0.4
6.7
105
6.2±1.4
7.0
M. A. Shupe et al., Phys. Rev. D19, 1921 (1979)
dσ/dt ~ A s-n

31. Factorization at 12 GeV?
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
Extraction of GPDs from unseparated observables relies on the dominance of σL – but are transverse contributions really small?
Effect from σT 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 π+ 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 π± production

32. 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

33. Experiment Overview The kinematics for the LD2/π- measurement
Measure separated cross sections for the p(e,e’π+)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
Phase space for L/T separations with SHMS+HMS x Q2
(GeV2) W
(GeV) -t
(GeV/c)2
0.31
0.1
0.40
0.2
0.55
0.5
The kinematics for the LD2/π- measurement

34. 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 -

35. 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)

36. 12 GeV Proposals Actions 12 GeV Proposal # TITLE CONTACT PERSON HALL
DAYS
PAC Action
Hadronization in Nuclei by Deep Inelastic
Electron Scattering
B.Norum C 15
Conditional Approval
Precision Measurement of the Parity-Violating Asymmetry in Deep Inelastic Scattering off Deuterium using Baseline 12 GeV Equipment in Hall C
P. Reimer 36
The Nuclear Transparency of Pion-photoproduction from 4He at 12 GeV
D. Dutta
14.5
Defer
Measurement of the Neutron Magnetic Form Factor at High Q2 Using the Ratio Method on Deuterium
G. Gilfoyle B 56
Approval
Scaling Study of the L-T Separated Pion Electroproduction Cross Section at 11 GeV
T. Horn 42
The A-dependence of J/Psi Photoproduction near Threshold
E. Chudakov 23
Studies of Spin-Orbit Correlations with Longitudinally Polarized Target
H. Avakian
103
Precision Measurement of the Proton Elastic Cross Section at High Q2
B. Moffit A 31
Large Acceptance Proton Form Factor Ratio Measurements at 13 and 15 (GeV/c)2 Using Recoil Polarization Method
L. Pentchev 60

37. 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
Requires good understanding of spectrometer optics and acceptance
Collimator to define acceptance
Radiative heating studies of horizontal bend magnet

38. Fπ Backgrounds Studies at 12 GeV?
–tmin<0.2 GeV2 constraint limits Q2 reach of Fp measurements
Measurement of σL for p0 could help constrain pQCD backgrounds
JLab PAC31 proposal
(T. Horn, D. Gaskell, G. Huber)
In a GPD framework, p+ and p0 cross sections involve different combinations of same GPDs – but p0 has no pole contribution
VGG GPD-based calculation
pole
non-pole p+ p0 38

39. Factorization 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

40. Measurement of K+ Form Factor
Similar to p+ form factor, elastic K+ scattering from electrons used to measure charged kaon for factor at low Q2 [Amendolia et al, PLB 178, 435 (1986)]
Can “kaon cloud” of the proton be used in the same way as the pion to extract kaon form factor via p(e,e’K+)Λ ?
Kaon pole further from kinematically allowed region, but mass is larger
Can we demonstrate that the “pole” term dominates the reaction mechanism?

41. Kaon Form Factor at Large Q2
JLAB experiment E extracted –t dependence of K+ longitudinal cross section near Q2=1 GeV2
A trial Kaon FF extraction was attempted using a simple Chew-Low extrapolation technique
gKLN poorly known
Assume form factor follows monopole form
Used measurements at Q2=0.75 and 1 GeV2 to constrain gKLN and FK simultaneously
Improved extraction possible using VGL model?

42. Test Extraction of K+ Form Factor
G. Niculescu, PhD. Thesis, Hampton U.
-t dependence shows some “pole-like” behavior
“Chew-Low” type extraction

43. Form Factor Summary
Fπ is a good observable to study the transition from collective degrees of freedom to quarks and gluons
Fπ measurements from JLab yield high quality data – in part due to
Continuous electron beam provided by JLab accelerator
Magnetic spectrometers and detectors with well-understood properties
Studies of FK at higher electron beam energies will allow to reach the kinematic range where direct measurement of the kaon form factor were made even better
Due to the larger mass, lattice calculations of kaon form factors are facilitated
Planned proposal for PAC34 (T. Horn, D. Gaskell, P. Markowitz) 43