Hall C Summer Meeting 4 August 2008

1. 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 fromExclusive Meson Production • 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 From: Diehl, Kugler, Schaefer, CW 2005

5. Q2 dependence of σL and σT Hall C data at 6 GeV • The Q-6QCD scaling prediction is reasonably consistent with recent JLab π+σL data Q2=2.7-3.9 GeV2 Q2=1.4-2.2 GeV2 • To access physics contained in GPDs, one is limited to the kinematic regime where hard-soft factorization applies σL σT T. Horn et al., arXiv:0707.1794 (2007)

6. Fπ - a factorization puzzle? T. Horn et al., Phys. Rev. Lett. 97 (2006) 192001. • 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:0707.1794 (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:0709.0500 (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 • 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 p(e,e’K+)Λ p(e,e’K+)Σ° W=1.84 GeV W=1.84 GeV

9. K+ Form Factor at 6 GeV • JLAB experiment E93-018 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)

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 E93-108 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 Resolution Λ • 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-6and σT~Q-8 • Projected uncertainties use R as determined from VGL/Regge p(e,e’K+)Λ xB=0.25 1/Q4 1/Q6 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, andΛ2K*=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. Fit: 1/Qn Q-n scaling after the Jlab Upgrade • E12-07-105 (T. Horn et al) approved for 42 days in Hall C • QCD scaling predicts σL~Q-6and σT~Q-8 • Projected uncertainties for σL are improved by a factor of more than two compared to 6 GeV • Data will provide important information about feasibility of GPD experiments at JLab 12 GeV kinematics

25. Fπ after the JLab Upgrade • Experiment (E12-06-101) 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 πelectroproduction 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