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 related to DIS cross section via optical theorem

3. Generalized Parton Distributions
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
GPDs provide information about correlations between partons of different momentum

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)
t=Δ2, momentum transfer to nucleon
ξ defined by Δ+ = -2ξ(p+Δ/2)+
Longitudinal fraction of the momentum transfer, t
Parameterizes the skewedness

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
Unified concepts of quark parton density and elastic form factors
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 Angular Momentum
Intuitive link to total angular momentum when x=0 and D=D^
At x=0, x=xB and the probability interpretation is again valid
D^ can be viewed as the Fourier transform of impact parameter, b^
GPDs describe probability to probe parton of momentum fraction x, at a transverse distance b^
L = r x p

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. Experimental Access to GPDs 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 DA
Factorization only applies for longitudinal photons ~ 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), etc.
To get new information from GPDs, we need a program that will 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
E99-105, Deeply Virtual Electroproduction of Vector Mesons (CLAS)
A major initiative 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. Rho and omega cross sections
M. A. Shupe et al., Phys. Rev. D19, 1921 (1979)

15. 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)

16. 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 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

17. Extracting Fπ from Pion Electroproduction Data
W=√-Q2 + M2 + 2Mω
reaction plane
The lab cross section can be expressed:
scattering plane
Q2= |q|2 – ω2
t=(q - pπ)2
In t-pole approximation:
In most analyses Fπ is extracted from σL data using a model incorporating pion electroproduction ( we use VGL/Regge)

18. πCT – pion electroproduction at even higher Q2
During πCT experiment (see Xin’s talk) also took π production data at high and low ε allowing for L-T separation
Q2=2.15, 4.0 GeV2
Targets: LH2, LD2, 12C, 63Cu, 197Au – focus here is on H2, further analysis of nuclear targets underway
HMS: 6 GeV
SOS: 1.7 GeV
Exp Q2
(GeV2)
W (GeV)
|t|
(Gev)2 Ee
(GeV)
Fπ-1
1.95
Fπ-2
1.6,2.45
2.22
0.093,0.189
πCT
2.15, 4.0
2.2
πCT: higher Q2, larger -t

19. πCT – Kinematics
Typically

20. πCT – Analysis Issues not so good
Typically place cut on W/Q2 to equalize phase space – cannot do this here
Solution: central W/Q2 from geometric mean of high/low ε points
W(ε1) Q2 Q2
W(ε2) W W
not so good

21. πCT Cross Section Extraction
Compare experimental yields to Monte Carlo of the experiment
Model for H(e,e’π+) based on pion electroproduction data
Radiative effects, pion decay, energy loss, multiple scattering
COSY model for spectrometer optics
Extract σL by simultaneous fit using measured azimuthal angle (φπ) and knowledge of photon polarization (ε).

22. πCT – cross section W-dependence
σπ depends on W, -t, Q2
Cross section W-dependence given by: (W2-M2)n
Fπ1/Fπ2 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
Fπ1
Fit: n=1.8
Fπ2
W-dependence of σπ makes sense – but what about –t and Q2?

23. πCT – separated cross sections t-dependence
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

24. 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)

25. 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

26. 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)

27. 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

28. Scaling tests for nuclear targets

29. 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

30. 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)

31. 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

32. Context Only if hard-soft factorization applies can GPDs be extracted
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 σL - what about transverse contributions?
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

33. 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 σT unknown at higher energies
JLab measurements from:
Hall B: E (ρ, ω)
Q2: GeV2, -t<1.5 (GeV/c)2
Hall C: Fπ1, E91-003, Fπ2, pionCT (π±)
Q2 range for precision L/T to 2.45 GeV2
Hall A, Hall B: DVCS, e1-6 (π° - unseparated)

34. 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 π± cross sections at 12 GeV
If σL 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 π+ transverse cross section

35. Experiment Goals Separate the cross section components: L, T, LT, TT
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

36. Experiment Overview The kinematics for the LD2/π- measurement
Phase space for L/T separations with SHMS+HMS
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
Overlap, but only for 6% of proposed beam time 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

37. Cross Section Separation
The virtual photon cross section can be written in terms of contributions from transversely and longitudinally polarized photons.
Separate σL, σT, σLT, and σTT by simultaneous fit using measured azimuthal angle (φπ) and knowledge of photon polarization (ε)

38. Separation in a Multi-Dimensional Phase Space
High ε
Low ε
Cuts are placed on the data to equalize the Q2-W range measured at the different ε-settings
Multiple SHMS settings (±2° left and right of the q vector) are used to obtain good φ coverage over a range of –t
Measuring 0<φ<2π allows to determine L, T, LT and TT
Determine LT, TT for xB=0.31, 0.40 only
For xB=0.55 apply a “parallel” cut on θπ
SHMS+2°
SHMS-2°
High ε
Radial coordinate (-t),
Azimuthal coordinate (φ)

39. Expected Missing Mass Resolution
e+p→e’+π+n
SHMS+HMS
Missing mass resolution is very good
Good π+/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 <0.1% for most settings
Largely eliminated after applying offline analysis cuts
Simulation at Q2=9.1 GeV2 and high ε

40. 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 -

41. Predictions for the Q2 dependence of R=σL/σT
Fπ parameterization was used for the L/T ratio in this proposal
Projected Δ(L/T)=10-25% for typical kinematics
For xB=0.55, 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 Q2=10 GeV2 would require only minor modification to the current run plan
VGL/Regge
Fπ param

42. 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)

43. 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

44. 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

45. 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

46. 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”

47. Observables in Hard Exclusive Reactions
To say anything about GPDs, we must be confident we are in a regime where soft-hard factorization applies (large Q2)
Higher order corrections may be large for absolute cross sections
for Q2 < 10 GeV2
Ratios have a better chance of exhibiting precocious factorization –
higher order effects in numerator and denominator “cancel”
Asymmetries (DVCS beam-spin and beam-charge asymmetry) and
cross section ratios (sp/sh) are our best chance for being in the
factorization regime at JLab energies