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 (Q 2 ) allows one to probe short distances Sensitivity to partonic degrees of freedom At sufficiently high Q 2, 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 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 (  ) allow for transverse imaging of the nucleon From: Diehl, Kugler, Schaefer, CW 2005

Q 2 dependence of σ L and σ T The Q -6 QCD scaling prediction is reasonably consistent with recent JLab π + σ L data T. Horn et al., arXiv: (2007) Hall C data at 6 GeV Q 2 = GeV 2 Q 2 = GeV 2 σLσL σTσT To access physics contained in GPDs, one is limited to the kinematic regime where hard- soft factorization applies

T. Horn et al., Phys. Rev. Lett. 97 (2006) F π - a factorization puzzle? T. Horn et al., arXiv: (2007). F π has a simple prediction in perturbative QCD The Q 2 dependence of F π is also consistent with hard-soft factorization prediction (Q -2 ) already at values Q 2 >1 GeV 2 But the observed magnitude of F π 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 H.J. Kwee and R.F. Lebed, arXiv:0708:4054 (2007) H.R.Grigoryan and A.V.Radyushkin, arXiv: (2007) A.P. Bakulev et al, Phys. Rev. D70 (2004)]

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

Q 2 dependence of σ Kaon Many measurements of exclusive p(e,e’ K + ) Λ(Σ°) exist, but contribution of σ T unknown at higher energies Difficult to draw a conclusion about the reaction mechanism –Limited Q 2 range –Significant uncertainty due to scaling in x B and -t W=1.84 GeV p(e,e’K + ) Λ p(e,e’K + ) Σ°

K + Form Factor at 6 GeV -t dependence shows some “pole-like” behavior JLAB experiment E extracted –t dependence of σ L K+ near Q 2 =1 GeV 2 –Trial Kaon FF extraction was attempted using a simple Chew-Low extrapolation technique Q 2 =1.0 GeV 2 Q 2 =0.75 GeV 2 g KLN poorly known W=1.84 GeV t=m K 2 (kaon pole)

Motivation Summary Studies of kaon electroproduction provide a way to determine if scaling behavior observed in F π would manifest itself in a similar system Direct comparison of the scaling properties of σ L provides another important tool in the search of the onset of factorization –σ L is expected to evolve towards Q -6 scaling at sufficiently large Q 2 –Transverse contributions are suppressed by an additional factor of Q -2 x B dependence of σ L 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 Q 2 dependence of σ L and better extraction of the kaon form factor Measure the Q 2 dependence of the p(e,e’ K + ) Λ ( Σ° ) cross section at fixed x B and –t to search for evidence of hard-soft factorization –Separate the cross section components: L, T, LT, TT –The highest Q 2 for any L/T separation in K+ electroproduction Also measure the Q 2 dependence of the kaon form factor to shed new light on the apparent pion form factor scaling puzzle

Experiment Overview xQ 2 (GeV 2 ) W (GeV) -t (GeV/c) Measure separated cross sections for the p(e,e’ K + ) Λ ( Σ° ) reaction at two values of x B –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) Planned proposal for PAC34 –T. Horn, P. Markowitz, G. Huber

The virtual photon cross section can be written in terms of contributions from transversely and longitudinally polarized photons. Cross Section Separation Separate σ L, σ T, σ LT, and σ TT by simultaneous fit using measured azimuthal angle (φ K ) and knowledge of photon polarization (ε)

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

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

Expected Missing Mass Resolution Simulation at Q 2 =2.0 GeV 2, W=3.0 and high ε Missing mass resolution is very good Acceptance allows for simultaneous studies of both Λ and Σ° channels Kinematic dependences of the ratio Λ Σ°

Predictions for the Q 2 dependence of R=σ L /σ T 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 Q 2 =8 possible (still under study) VGL/Regge F π param

QCD scaling predicts σ L ~Q -6 and σ T ~Q -8 Projected uncertainties use R as determined from VGL/Regge Projected Uncertainties for Q -n scaling 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) xQ 2 (GeV 2 ) W (GeV) -t (GeV/c) p(e,e’K + ) Λ x B =0.25 1/Q 6 1/Q 4 1/Q 8

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

Summary First measurement of kaon electroproduction above the resonance region Meaningful studies of the Q 2 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 σ L over a wide kinematic range provides another important tool in the search of the onset of factorization –σ L is expected to evolve towards Q -6 scaling at sufficiently large Q 2 –Transverse contributions are suppressed by an additional factor of Q -2

Projected Uncertainties for σ L at constant Q 2 x B scan at Q 2 =3 GeV 2 Expect significant x-dependence is non-pole contributes –Provides information about non- pole contributions Axial only Pion pole only Axial and pole

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

QCD scaling predicts σ L ~Q -6 and σ T ~Q -8 Projected uncertainties for σ L are improved by a factor of more than two compared to 6 GeV Q -n scaling after the Jlab Upgrade Fit: 1/Q n Data will provide important information about feasibility of GPD experiments at JLab 12 GeV kinematics xQ 2 (GeV 2 ) W (GeV) -t (GeV/c) E (T. Horn et al) approved for 42 days in Hall C

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 Q 2 =6 GeV 2 May expect to see the onset of perturbative regime F π after the JLab Upgrade

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 Q 2 scaling regime (partonic picture) has been reached One of the most stringent tests of factorization is the Q 2 dependence of the π electroproduction cross section –σ L scales to leading order as Q -6 –σ T scales as Q -8 –As Q 2 becomes large: σ L >> σ T Factorization Factorization theorems for meson electroproduction have been proven rigorously only for longitudinal photons [Collins, Frankfurt, Strikman, 1997] Q 2 ?

Pion/Kaon ratio studies Overlap with Fpi-3 at Q 2 =6 GeV 2 Additional info about reaction mechanism through π + / K + ratios QCD Factorization