L-T Separated Kaon production Cross Sections from 5-11 GeV

1. L-T Separated Kaon production Cross Sections from 5-11 GeV P. Bosted, S. Covrig, H. Fenker, R. Ent, D. Gaskell, T. Horn*, M. Jones, J. LeRose, D. Mack, G.R. Smith, S. Wood, G. Huber, A. Semenov, Z. Papandreou, W. Boeglin, P. Markowitz, B. Raue, J. Reinhold, F. Klein, P. Nadel-Turonski, A. Asaturyan, A. Mkrtchyan, H. Mkrtchyan, V. Tadevosyan, D. Dutta, M. Kohl, P. Monaghan, L. Tang, D. Hornidge, A. Sarty, E. Beise, G. Niculescu, I. Niculescu, K. Aniol, E. Brash, V. Punjabi, C. Perdrisat, Y. Ilieva, F. Cusanno, F. Garibaldi, M. Iodice, S. Marrone, P. King, J. Roche JLab, Regina, FIU, CUA, Yerevan, Mississippi, Hampton, Mount Allison, Saint Mary’s, UMd, JMU, California State, CNU, Norfolk, W&M, South Carolina, INF, Ohio Hall C User’s meeting 30 January 2009

2. Meson Reaction Dynamics e’ e • Meson production can be described by the t-channel exchange meson pole term in the limit of small –t and large W • Pole term is dominated by longitudinally polarized photons • Meson form factor describes the spatial distribution of the nucleon Q2 π, K, etc. W t N(p’) N(p) t-channel process • At sufficiently high Q2, the process should be understandable in terms of the “handbag” diagram • The non-perturbative (soft) physics is represented by the GPDs • Shown to factorize from QCD perturbative processes for longitudinal photons [Collins, Frankfurt, Strikman, 1997] π, K, etc. hard pointlike handbag

3. Form Factors and GPDs • Form factors and GPDs are essential to understand the structure of nucleons, which make up nucleons and mesons (q-q systems) - π, K, etc • But measurements of form factors and GPDs have certain prerequisites: • Before we can start looking at form factors, we must make sure that σL is dominated by the meson pole term at low -t • Before we can learn about GPDs, we must demonstrate that factorization applies φ φ Fπ,K π,K π, K, etc. φ • A comparison of pion and kaon production data may shed further light on the reaction mechanism, and intriguing 6 GeV pion results Hard Scattering GPD

4. Context • Understanding of the kaon production mechanism is important in our study of hadron structure • GPD studies require evidence of soft-hard factorization • Flavor degrees of freedom provide important information for QCD model building and understanding of basic coupling constants • K+Λ and K+Σ° have been relatively unexplored because of lack of the necessary experimental facilities • There are practically no precision L-T separated data for exclusive K+ production from the proton above the resonance region • Limited knowledge of L/T ratio at higher energies limits the interpretability of unseparated cross sections in kaon production • Relative σL and σT contributions are also needed for GPD extractions since they rely on the dominance of σL

5. Transverse Contributions Hall C 6 GeV data (W=1.84 GeV) • In the resonance region at Q2=2.0 GeV2σT is not small • In pion production, σT is also much larger than predicted by the VGL/Regge model [PRL97:192001 (2006)] • Why is σT so large? Difficult to draw a conclusion from current data • Limited W and Q2 range • Significant uncertainty due to scaling in xB and –t K+Λ K+Σ˚ σL 0.5<Q2<2.0 GeV2 VGL/Regge σT K+Λ K+Σ˚ High quality σL and σT data for both kaon and pion would provide important information for understanding the meson reaction mechanism

6. R=σL/σT: Kaon form factor prerequisite • Meson form factor extraction requires a good reaction model • Need high quality data to develop these models • Current knowledge of σL and σTabove the resonance region is insufficient • Role of the t-channel kaon exchange in amplitude unclear • Not clear how to understand reaction mechanism through current models VGL/Regge (Λ2K=0.68 GeV2) Nucleon resonance data scaled to W=1.84 GeV L/T separations above the resonance region are essential for building reliable models, which are also needed for form factor extractions

7. High Q2: Q-n scaling of σL and σT Hall C p+ production data at 6 GeV • The QCD scaling prediction is reasonably consistent with recent JLab π+σL data, BUTσT does not follow the scaling expectation • To access physics contained in GPDs, one is limited to the kinematic regime where hard-soft factorization applies Q2=2.7-3.9 GeV2 Q2=1.4-2.2 GeV2 • A test is the Q2 dependence of the cross section: • σL~ Q-6 to leading order • σT ~Q-8 • As Q2 gets large: σL >> σT σL σT T. Horn et al., Phys. Rev. C78, 058201 (2008) Kaon production data would allow for a quasi model-independent comparison that is more robust than calculations based on QCD factorization and present GPD models

8. Bonus: Fπ,K - a factorization puzzle? T. Horn et al., Phys. Rev. Lett. 97 (2006) 192001. T. Horn et al., arXiv:0707.1794 (2007). • The Q2 dependence of Fπ is also consistent with hard-soft factorization prediction (Q-2) 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 A.P. Bakulev et al, Phys. Rev. D70 (2004)] Comparing the observed Q2 dependence of σL,T and FFmagnitude with kaon production would allow for better understanding of the onset of factorization

9. Motivation Summary • The charged kaon L/T cross section is of significant interest to the study of GPDs and form factors at 12 GeV • Can only learn about GPDs if soft-hard factorization applies • If transverse contributions are large, the accessible phase space may be limited • If σL not dominated by the K+ pole term at low -t, we cannot extract the form factor from the data and interpretation of unseparated data questionable • Our theoretical understanding of hard exclusive reactions will benefit from L/T separated kaon data over a large kinematic range • Constraints for QCD model building using both pion and kaon data • Understanding of basic coupling constants (Σ°/Λratio) • Quasi model-independent comparison of pion and kaon data would allow a better understanding of the onset of factorization

10. Experiment Overview • Measure the separated cross sections at varying –t and xB • If K+ pole dominates σL allows for extraction of the kaon ff (W>2.5 GeV) • Measure separated cross sections for the p(e,e’K+)Λ(Σ°) reaction at two fixed values of –t and xB • Q2 coverage is a factor of 2-3 larger compared to 6 GeV at much smaller –t • Facilitates tests of Q2 dependence even if L/T ratio less favorable than predicted Q2=3.0 GeV2 was optimized to be used for both t-channel and Q-n scaling tests

11. 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)

12. Separation in a Multi-Dimensional Phase Space Low ε High ε • Cuts are placed on the data to equalize the Q2-W range measured at the different ε-settings • Multiple SHMS settings (±3° 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 SHMS+3° SHMS-3° Radial coordinate (-t), Azimuthal coordinate (φ)

13. Kaon PID Heavy Gas Cherenkov and 60 cm of empty space • π+/K+ separation provided by heavy gas Cerenkov for pSHMS>3.4 GeV/c • For reliable K+/p separation above 3 GeV/c an aerogel Cerenkov is essential • Provision has been made in the SHMS detector stack for two threshold aerogel detectors TOF • Four sets of aerogel would provide reliable K+/p separation over the full momentum range (2.6-7.1 GeV/c) • Alternate PID methods (such as RICH) are also possible Kaon 12 GeV Kinematics π/K Discrimination power Heavy Gas Cerenkov Momentum (GeV/c)

14. Expected Missing Mass Resolution • Missing mass resolution (~30 MeV) is clearly sufficient to separate Λ and Σ° final states • Acceptance allows for simultaneous studies of both Λ and Σ° channels • Total effect of the Λ tail and possible collimator punch-through to K+Σ° projected to be <1/10 of the size of the tail e+p→e’+K+Λ(Σ°) Λ SHMS+HMS Σ° Simulation at Q2=2.0 GeV2 , W=3.0 and high ε

15. Projections of R=σL/σT • Empirical kaon parameterization based on Hall C data was used in rate estimates • Conservative assumptions on the evolution of L/T ratio • Projected Δ(L/T)=28-60% (10-33% using VGL/Regge) for typical kinematics • PR12-09-011 may indicate larger values of R, with associated smaller uncertainties • Reaching Q2=8 GeV2 may ultimately be possible VGL/Regge calculation Hall C parameterization VGL/Regge Fπ param

16. Projected Uncertainties for σL and σT σL σT • High quality kaon L/T separation above the resonance region • Projected uncertainties for σL and σT use the L/T ratio from Hall C parameterization PR12-09-011: Precision data for W > 2.5 GeV

17. Projected Uncertainties for the Kaon FF • If the K+ pole dominates low -t σL, we would for the first time extract FK above the resonance region (W>2.5 GeV) • Projected uncertainties for σL use the L/T ratio from Hall C parameterization

18. Projected Uncertainties for Q-n scaling p(e,e’K+)Λ xB=0.25 • QCD scaling predicts σL~Q-6and σT~Q-8 • Projected uncertainties use R from the Hall C parameterization 1/Q4 1/Q6 Fit: 1/Qn 1/Q8 Is onset of scaling different for kaon than pion? Kaons and pions together provide quasi model-independent study

19. PR12-09-011 Summary • L/T separated K+ cross sections will be essential for our understanding of the reaction mechanism at 12 GeV • If transverse contributions are found to be large, the accessible phase space for GPD studies may be limited • Basic coupling constants in kaon production (Σ°/Λ ratio) • If t-channel exchange dominates σL, we can perform the first reliable extraction of the kaon form factor above the resonance region • L/T separated K+ data over a wide kinematic range will have a significant impact on our understanding of hard exclusive reactions • Constraints on QCD model building using both pion and kaon data • Quasi model-independent comparison of kaon and pion data would allow better understanding of the onset of factorization Request 47 days to provide first precision L/T separated kaon production data above the resonance region. Excellent candidate for early running.

20. Backup material

21. PR12-09-011 Beam Time

22. Systematic Uncertainties

23. Overlap with pion data • No significant improvement in statistics through overlap with the approved p(e,e’π+)n experiments • Covers only a small region at very high –t, which is not interesting for studies of form factors or GPDs • Most events are off the focal plane • exclusive K+ peak lies at -5.5%<δSHMS<-2% • Missing Mass tail cut off by SHMS acceptance • Would require that aerogels installed during pion experiments as well Proposed kaon experiment Approved pion experiments

24. Transverse Contributions in Pion production • In pion production, magnitude of σT has been controversial for a long time • VGL/Regge model systematically underestimates σT, for which it seems to have limited predictive power VGL σL VGL σT T. Horn et al., Phys. Rev. Lett. 97, 192001 (2006)

25. Bonus: Interference Terms K+Λ(Σ°) as calculated in VGL/Regge model Q2=0.4 GeV2 • In the hard scattering limit, these terms are expected to scale: • σLT ~ Q-7 • σTT ~Q-8 • Additional information about the reaction mechanism may be obtained for free if one performs a full cross section separation Q2=3.5 GeV2

26. Significance of multiple epsilon points • Additional epsilon settings require additional beam time • Resulting benefit in systematic uncertainty must be weighted against the increased statistical uncertainty