1. The Transition from soft to hard physics through Meson Electroproduction
at Jlab and beyond
Tanja Horn
Jefferson Lab
UMd Seminar
College Park, MD
26 March 2008

2. Outline The dual nature of QCD: physics interest Exclusive processes
Observables for the fundamental degrees of freedom
Experiments to access information about the reaction mechanism
Cross section data and conclusions at current energies
Work in progress and future plans

3. Hadrons Atom (atomic number A):
Z electrons
Z protons, (A-Z) neutrons
Protons and neutrons are two examples of a larger category of strongly-interacting particles called hadrons
Two families of hadrons:
Baryons: valence qqq
Mesons: valence

4. Quarks and Leptons
The ground state of matter

5. QED vs. QCD QED The theory of electricity and magnetism
The theory of the strong force
QED
Slide from: Jlab Open House 2007

6. The Dual Nature of QCD
At short distances, we have a good understanding of strong interactions with perturbative QCD (pQCD)
Proton is not point like – elastic electron scattering [Hofstadter, 1961]
Quarks and gluons are the constituents – Deep Inelastic Scattering [Friedmann, Kendall and Taylor, 1990]
Asymptotic freedom [Gross, Politzer, Wilczek, 2004]
Long distance properties are understood in terms of chiral perturbation theory
Color confinement
From: W. Melnitchouk et al., Phys.Rept.406: ,2005

7. The Fundamental Issue
Confinement occurs at an intermediate distance scale
Lattice QCD and phenomenological models give insight into the hadron structure at the confinement scale
Need experimental observables of the fundamental degrees of freedom of QCD in coordinate space
Forward parton distributions do not resolve partons in space
Form Factors measure spatial distributions, but the resolution cannot be selected independent of momentum transfer
Need a combination of both!

8. Generalized Parton Distributions
Generalized Parton Distributions (GPDs) are a generalization of Parton Distribution Functions (PDFs), where initial and final quark-gluon momenta are not identical
x, momentum fraction variables
t=2.  Fourier Conjugate to impact parameter of quark or gluon.
Q2 = resolution of the probe

9. Exclusive Processes and GPDs
Increasing the virtuality of the photon (Q2) allows one to probe short distances
Sensitivity to partonic degrees of freedom
At sufficiently high Q2, the process should be understandable in terms of the “handbag” diagram
Incoming virtual photon scatters off one quark
interaction can be calculated in perturbative QCD
The non-perturbative (soft) physics is represented by the GPDs
Shown to factorize from QCD perturbative processes for longitudinal photons [Collins, Frankfurt, Strikman, 1997]
t-channel process
handbag

10. Experimental Access to GPDs: DVCS
q = k-k’ Q2 = q2>0 =q-q’ t=2
s = (k+p)2 xBj = Q2/(2p·q) W2 = (q+p)2
Using a polarized beam on an unpolarized target, two observables can be measured:

11. GPDs from Exclusive Meson Production
From: Diehl, Kugler, Schaefer, CW 2005
Interest: spin/flavor structure of GPDs – mesons select spin
Vector mesons (r,w,f) sensitive to H and E
Pseudo scalar mesons sensitive to and
Detection of final states easier – but interpretation is complicated by convolution with meson distribution amplitude (DA) ~ H ~ E

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: Fpi-1, E91-003, Fpi-2, 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. Tests of the Handbag Dominance
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 (partonic picture) 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 [Collins, Frankfurt, Strikman, 1997]

14. Designing a pion electroproduction experiment
Precision measurement of kinematics
Precision knowledge of the acceptance
Detect scattered electron and π
Need to know about the neutron as well
Q2= |q|2 – ω2
t=(q - pπ)2
W=√-Q2 + M2 + 2Mω
scattering plane
reaction plane
Can isolate L/T/LT/TT if one knows azimuthal angle (φ) and virtual photon polarization (ε) are known
For a given Q2, higher W allows for smaller tmin

15. Pion Electroproduction in Hall C
Three experiments took data to the highest possible value of Q2 with 6 GeV beam at Jlab: Fpi-1 (1997), Fpi-2 (2003), pionCT(2004)
Full separation of the L/T/TT/LT terms in the cross section
Ancillary measurements of the separated π+/π- ratio to test the reaction mechanism
Exp Q2
(GeV2) W
(GeV)
|t|
(Gev)2 Ee
Fpi-1
1.95
Fpi-2
1.6,2.45
2.22
0.093,0.189
πCT
2.15, 4.0
2.2

16. Experimental Setup Short Orbit Spectrometer (SOS) detects e-
HMS: 6 GeV
SOS: 1.7 GeV
Short Orbit Spectrometer (SOS) detects e-
High Momentum Spectrometer (HMS) detects π+
Relatively small acceptance – well understood
Kinematics well constrained, angles well reproducible
Cryogenic targets at high currents - relatively short experiments

17. Analysis: p(e,e’π+)n Event Selection
Coincidence measurement between charged pions in HMS and electrons in SOS
±1ns
Continous wave (CW) beam minimizes “accidental” coincidences
Excellent particle identification:
Protons in HMS rejected using coincidence time and aerogel Cerenkov
Electrons in SOS identified by gas Cerenkov and Calorimeter 17

18. p(e,e’π+)n Exclusivity
Easy to isolate the exclusive channel
Missing mass resolution easily excludes 2π contributions
Q2, x
t, φ e e’ p n π
Missing mass cut assures exclusivity 18

19. Analysis: Extraction of Observables
Radial coordinate: -t, azimuthal coordinate: φ
Θπ=0
Θπ=+4
Θπ=-3
-t=0.1
-t=0.3
Q2=1.60, High ε
Measure σTT and σLT by taking data at three angles: θπ=0, +4, -3 degrees
W/Q2 cuts define a common phase space at both epsilon points
Q2=2.45 GeV2
Q2=1.60 GeV2
Extract σL by a simultaneous fit of L, T, LT, TT using the measured azimuthal angle (φ) and knowledge of the photon polarization (ε) 19

20. Cross section W-dependence
σπ depends on W, -t, Q2
Cross section W-dependence given by: (W2-M2)n
Fpi-1/Fpi-2 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?

21. Cross section t-dependence
T. Horn et al., Phys. Rev. Lett. 97, (2006)
σL decreases with –t as expected due to the pion pole
The magnitude decreases at constant W with increasing Q2 as tmin increases with Q2
σT is largely flat in t
Magnitude decreases with increasing Q2
Still a large contribution at Q2=2.45 GeV2
VGL σL
VGL σT

22. Global t-dependence of σL
VGL σL
VGL σT
Scaled to W=2.19 GeV, Q2=0.7 GeV2
σL is dominated by the pion pole
An exponential t dependence describes the data from Jlab and earlier data from DESY quite well
t-dependence of σπ as expected – what about Q2?

23. Q2 dependence of σL and σT
Hall C data at 6 GeV
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
Q2= GeV2
Q2= GeV2 σL σT
T. Horn et al., arXiv: (2007)

24. Fπ - a factorization puzzle?
T. Horn et al., Phys. Rev. Lett. 97 (2006)
Fπ has a simple prediction in perturbative QCD
Q2>1 GeV2: Q2 dependence of Fπ is consistent with hard-soft factorization prediction (Q-2)
But globally Fπ data still far from hard QCD calculations
Not in QCD factorization regime?
Or additional soft contribution from the pion wave function?
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)

25. 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

26. Conclusions at 6 GeV
σL data consistent with hard-soft factorization prediction
relatively large uncertainties
Limited Q2 range
Fπ data consistent with hard-soft factorization prediction, but overall normalization is not right
soft contributions still important
Compton scattering experiments suggest that higher order effects dominate the Compton cross section

27. Factorization Tests at 12 GeV
Measurements with large kinematic coverage and improved precision
L/T separated π+ cross sections at fixed xB and –t
Factorization studies without L/T separation - studies of π-cross sections
Higher Q2 Fπ studies
Extension to strange channels

28. Hall C Factorization @ 12 GeV:
Experiment approved for 42 days in
Hall C
E (T. Horn et al.)
Super High Momentum Spectrometer (SHMS) detects pions
Small angles, large momenta
HMS detects electrons
SHMS
HMS x Q2
(GeV2) W
(GeV) -t
(GeV/c)2
0.31
0.1
0.40
0.2
0.55
0.5

29. E12-07-105 Kinematics Overview
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
Cross section becomes small as Q2 increases
High luminosity important (typical Jlab: 1038 cm-2 s-1)
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

30. Q-n scaling after the Jlab Upgrade
Fit: 1/Qn
QCD scaling predicts σL~Q-6 and σT~Q-8
Projected uncertainties for σL are improved by a factor of more than two compared to 6 GeV 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 -
Data will provide important information about feasibility of GPD experiments at JLab 12 GeV kinematics

31. π- cross section – measure σL without explicit L/T?
Fpi-1 and Fpi-2 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 Fpi-1 and Fpi-2 results)

32. 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
May expect to see the onset of perturbative regime

33. Fπ Background 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 6 GeV PAC31 proposal
(T. Horn et al.)
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 33

34. Strangeness in GPDs and exclusive processes
Kaon production probes polarized GPDs analogous to pions
Pole term is prominent in
K form factor measurements
New information about SU(3) in meson wave function
High –t meson production to learn about the reaction mechanism
QCD factorization ~ E

35. Hall C Kaon Electroproduction
Unseparated kaon cross sections from E93-018
Limited Q2 range
Difficult to draw a conclusion about the reaction mechanism

36. K+ Form Factor at 6 GeV
JLAB experiment E extracted –t dependence of σLK+ near Q2=1 GeV2
Trial Kaon FF extraction was attempted using a simple Chew-Low extrapolation technique
gKLN poorly known
Q2=1.0 GeV2
Q2=0.75 GeV2
-t dependence shows some “pole-like” behavior

37. Kaon electroproduction at 11 GeV
Planned proposal for PAC34
T. Horn, P. Markowitz et al.
Measure form factor to Q2=3 GeV2 with good overlap with elastic scattering data
Measure kaon electroproduction cross section to Q2=5 GeV2
Additional information about the reaction mechanism
Kinematics allow for comparison of the π+/K+ ratio for factorization studies

38. Factorization at 11 GeV Summary
L/T separated π+ cross sections will be essential for understanding the reaction mechanism at 12 GeV
Relative contribution of σL and σT in π+ production - interpretation of asymmetry and ratios
π- data will check the possibility of measuring σL without explicit L/T separation
Are energies sufficiently large to access GPDs with these data?
For DVCS: likely yes
For deep exclusive processes: probably not
Higher order contributions may contribute up to relatively large values of Q2 – Fpi prediction even at Q2=6 GeV2

39. GPD studies beyond JLab: EIC
Studies of exclusive processes is a new territory for colliders
Demanding in luminosity requirements
Particle detection not easy
Physics interest closely related to JLab 6 GeV and 12 GeV program
Feasibility studies at JLab (A. Bruell, T. Horn, C. Weiss, V. Guzey) in progress
π+n, π0p, K Λ channels

40. π+n at EIC: first estimates
Cross section parameterization from Ch. Weiss
Seems feasible at not too small values of x

41. π+n at EIC: angle and momentump e
Neutron is the largest momentum particle
Neutron at <1°
from beam line
Emitted at relatively small angle with respect to proton beam
Not in acceptance of main detector - need separate neutron detection (similar to HERA/LHC)

42. Summary
GPDs may provide the most complete information on the structure of the nucleon
Tests of hard-soft factorization are essential for our understanding of the dominant reaction mechanism
L/T separated π+ cross sections at 6 GeV lack precision
L/T separated π+ data over a wide kinematic range at 12 GeV will have a significant impact on our understanding of hard exclusive reactions
Relative contribution of σL and σT in π+ production - interpretation of asymmetry and ratios
Experimental access to GPDs may require the additional energy range of an electron ion collider

43. Extraction of Fπ from p(e,e’π+)n data
π+ electroproduction can only access t<0 (away from pole)
Early experiments used “Chew- Low” technique
measured –t dependence
Extrapolate to physical pole
This method is unreliable – different fit forms consistent with data yet yield very different FF
A more reliable approach is to use a model incorporating the + production mechanism and the `spectator’ nucleon to extract F(Q2) from L.
 t-pole “extrapolation” is implicit, but one is only fitting data in the physical region

44. Check of the pion electroproduction technique
Does electroproduction really measure the physical form-factor since we are starting with an off- shell pion?
This can be tested making p(e,e’+)n measurements at same kinematics as +e elastics
Looks good so far:
Ackermann electroproduction data at Q2 = 0.35 GeV2 consistent with extrapolation of SPS elastic data.

45. Fπ and Factorization Tests
Hard Scattering
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
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

46. K+ Form Factor Extraction
At low Q2 measure charged kaon form factor similar to p+ using elastic K+ scattering from electrons [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 σL from p(e,e’K+)Λ ?
Kaon pole
pion pole
H(e,e’K+)
This can be tested making p(e,e’K+)n measurements at same kinematics as K+e elastics
H(e,e’π+)

47. σT global t-dependence
Scaled to W=2.19 GeV, Q2=0.7 GeV2
An exponential t dependence describes the data from Jlab and earlier data from DESY quite well
Slope is less steep then for sigL, but clearly sigT is not independent of t and Q2
t-dependence of σπ as expected – what about Q2?