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

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

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

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

Q2 dependence of σL and σT Hall C data at 6 GeV 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 The Q-6 QCD scaling prediction is reasonably consistent with recent JLab π+ σL data T. Horn et al., arXiv:0707.1794 (2007)

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)

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

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

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

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

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

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 1.6-3.5 2.4-3.4 0.2 0.40 3.0-6.0 2.3-3.1 0.5

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)

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)

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)

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

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

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 1.6-3.5 2.4-3.4 0.2 0.40 3.0-6.0 2.0-3.0 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)

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,

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

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

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

Q-n scaling after the Jlab Upgrade E12-07-105 (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 1.5-4.0 2.0-3.1 0.1 0.40 2.1-5.5 2.0-3.0 0.2 0.55 4.0-9.1 2.0-2.9 0.5 Data will provide important information about feasibility of GPD experiments at JLab 12 GeV kinematics

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

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]

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