1. Hall C Summer Meeting 4 August 2008
Meson Form Factors and Reaction Mechanism
Tanja Horn
Hall C Summer Meeting
4 August 2008

2. 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

3. 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

4. GPDs from Exclusive Meson Production
From: Diehl, Kugler, Schaefer, CW 2005
Interest: spin/flavor structure of quark GPDs – mesons select spin
Requires L/T separation to facilitate interpretation, which is complicated by convolution with meson distribution amplitude (DA)
Vector mesons (r,w,f) allow for transverse imaging of the nucleon

5. Q2 dependence of σL and σT
Hall C data at 6 GeV
Q2= GeV2
Q2= GeV2
To access physics contained in GPDs, one is limited to the kinematic regime where hard-soft factorization applies σL σT
The Q-6 QCD scaling prediction is reasonably consistent with recent JLab π+ σL data
T. Horn et al., arXiv: (2007)

6. Fπ - a factorization puzzle?
T. Horn et al., Phys. Rev. Lett. 97 (2006)
Fπ has a simple prediction in perturbative QCD
The Q2 dependence of Fπ is also consistent with hard-soft factorization prediction (Q-2) already at values Q2>1 GeV2
But the observed magnitude of Fπ is larger than the hard QCD prediction
Could be due to QCD factorization not being applicable in this regime
Or insufficient knowledge about additional soft contributions from the meson 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)

7. Strangeness in GPDs and exclusive processes
Kaon production probes polarized GPDs analogous to pions
High –t meson production to learn about the reaction mechanism
QCD factorization
Kaon pole term is expected to be prominent
Kaon form factor measurements
Relatively model independent pole dominance test through

8. Q2 dependence of σKaon
p(e,e’K+)Λ
p(e,e’K+)Σ°
W=1.84 GeV
W=1.84 GeV
Many measurements of exclusive p(e,e’K+)Λ(Σ°) exist, but contribution of σT unknown at higher energies
Difficult to draw a conclusion about the reaction mechanism
Limited Q2 range
Significant uncertainty due to scaling in xB and -t

9. 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
W=1.84 GeV
Q2=0.75 GeV2
t=mK2 (kaon pole)
-t dependence shows some “pole-like” behavior

10. Motivation Summary
Studies of kaon electroproduction provide a way to determine if scaling behavior observed in Fπ would manifest itself in a similar system
Direct comparison of the scaling properties of σL provides another important tool in the search of the onset of factorization
σL is expected to evolve towards Q-6 scaling at sufficiently large Q2
Transverse contributions are suppressed by an additional factor of Q-2
xB dependence of σL in Σ° production could provide information about pole and non-pole contributions

11. Experiment Goals
To meet motivation requirements perform the measurement above the resonance region – first time for W>2.5 GeV
Allows for meaningful studies of the Q2 dependence of σL and better extraction of the kaon form factor
Measure the Q2 dependence of the p(e,e’K+)Λ(Σ°) 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 K+ electroproduction
Also measure the Q2 dependence of the kaon form factor to shed new light on the apparent pion form factor scaling puzzle

12. Experiment Overview Planned proposal for PAC34
T. Horn, P. Markowitz, G. Huber
Measure separated cross sections for the p(e,e’K+)Λ(Σ°) reaction at two values of xB
Near parallel kinematics to separate L,T,LT,TT
Measure the separated cross sections at varying –t allows for extraction of kaon ff (W>2.5 GeV) x Q2
(GeV2) W
(GeV) -t
(GeV/c)2
0.25
0.2
0.40
0.5

13. 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 (φK) and knowledge of photon polarization (ε)

14. Separation in a Multi-Dimensional Phase Space
Low ε
Cuts are placed on the data to equalize the Q2-W range measured at the different ε-settings
High ε
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=0.25 only
For xB=0.40 apply a “parallel” cut on θK
SHMS+2°
SHMS-2°
High ε
Radial coordinate (-t),
Azimuthal coordinate (φ)

15. Kaon PID
E Kaon PID
Aerogel Cerenkov is essential for proper kaon identification at lower momenta as time-of-flight alone is not sufficient
TOF
Aerogel Cerenkov
Discrimination power
Kaon 12 GeV Kinematics
Heavy Gas Cerenkov
Momentum (GeV/c)

16. Expected Missing Mass ResolutionΛ
Missing mass resolution is very good
Acceptance allows for simultaneous studies of both Λ and Σ° channels
Kinematic dependences of the ratio Σ°
Simulation at Q2=2.0 GeV2 , W=3.0 and high ε

17. Predictions for the Q2 dependence of R=σL/σT
VGL/Regge parameterization was used for the L/T ratio
Projected Δ(L/T)=30-50% for typical kinematics
Future predictions may indicate larger values of R, and thus lower uncertainties
Reaching Q2=8 possible (still under study)
VGL/Regge
Fπ param

18. Projected Uncertainties for Q-n scaling
QCD scaling predicts σL~Q-6 and σT~Q-8
Projected uncertainties use R as determined from VGL/Regge
p(e,e’K+)Λ
xB=0.25
1/Q4
1/Q6 x Q2
(GeV2) W
(GeV) -t
(GeV/c)2
0.25
0.2
0.40
0.5
1/Q8
Data will provide important information about the onset of factorization in 12 GeV kinematics and may provide a way to study effects related to SU(3)

19. Projected Uncertainties for the Kaon FF Q-2 dependence
p(e,e’K+)Λ
First measurement of FK well above the resonance region
Measure form factor to Q2=3 GeV2 with good overlap with elastic scattering data
W>2.5 GeV
Limited by t<0.2 GeV2 requirement to minimize non-pole contributions
Data will provide important information the apparent scaling puzzle observed in the pion ff
For VGL/Regge calculation, assume Λ2K=0.67 GeV2, and Λ2K*=1.5 GeV2,

20. Summary
First measurement of kaon electroproduction above the resonance region
Meaningful studies of the Q2 dependence of the cross section and kaon ff extractions
L/T separated K+ cross sections will be essential for our understanding of the reaction mechanism at 12 GeV
determine if scaling behavior observed in pion production would manifest itself in a similar system
Direct comparison of the scaling properties of σL over a wide kinematic range provides another important tool in the search of the onset of factorization
σL is expected to evolve towards Q-6 scaling at sufficiently large Q2
Transverse contributions are suppressed by an additional factor of Q-2

22. Projected Uncertainties for σL at constant Q2
xB scan at Q2=3 GeV2
Expect significant x-dependence is non-pole contributes
Provides information about non-pole contributions
Axial only
Pion pole only
Axial and pole

23. Uncertainty in σL
Assuming equal correlated sytematic uncertainties at each ε
Due to amplification by 1/Δε, uncertainty in σL is dominated by uncorrelated systematic uncertainty
If R more favorable, precision in σL improves even for small Δε

24. Q-n scaling after the Jlab Upgrade
E (T. Horn et al) approved for 42 days in Hall C
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 x Q2
(GeV2) W
(GeV) -t
(GeV/c)2
0.31
0.1
0.40
0.2
0.55
0.5
Data will provide important information about feasibility of GPD experiments at JLab 12 GeV kinematics

25. 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

26. 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]

27. Pion/Kaon ratio studies
Overlap with Fpi-3 at Q2=6 GeV2
Additional info about reaction mechanism through π+/K+ ratios
QCD Factorization