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

Meson Reaction Dynamics N(p) W t Q2 N(p’) π, K, etc. 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 t-channel process π, K, etc. hard 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] Picture behind the mechanism pointlike handbag

Form Factors and GPDs - Fπ,K Form factors and GPDs are essential to understand the structure of nucleons, which make up nucleons and mesons (q-q systems) - Fπ,K π, K, etc φ 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 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 Why we need to understand the mechanism to measure things Hard Scattering GPD

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

Transverse Contributions Hall C 6 GeV data (W=1.84 GeV) σL σT 0.5<Q2<2.0 GeV2 In the resonance region at Q2=2.0 GeV2 σT 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˚ VGL/Regge 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

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 σT above 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

High Q2: Q-n scaling of σL and σT T. Horn et al., Phys. Rev. C78, 058201 (2008) Hall C p+ production data at 6 GeV Q2=1.4-2.2 GeV2 Q2=2.7-3.9 GeV2 σL σT To access physics contained in GPDs, one is limited to the kinematic regime where hard-soft factorization applies 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 The QCD scaling prediction is reasonably consistent with recent JLab π+ σL data, BUT σT does not follow the scaling expectation 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

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 FF magnitude with kaon production would allow for better understanding of the onset of factorization

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°/Λ ratio) Quasi model-independent comparison of pion and kaon data would allow a better understanding of the onset of factorization

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 x Q2 (GeV2) W (GeV) -t (GeV/c)2 0.1-0.2 0.4-3.0 2.5-3.1 0.06-0.2 0.25 1.7-3.5 2.5-3.4 0.2 0.40 3.0-5.5 2.3-3.0 0.5 Q2=3.0 GeV2 was optimized to be used for both t-channel and Q-n scaling tests

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 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)

Kaon PID 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 Heavy Gas Cherenkov and 60 cm of empty space TOF Momentum (GeV/c) π/K Discrimination power Kaon 12 GeV Kinematics Heavy Gas Cerenkov 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

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

Projections of R=σL/σT VGL/Regge calculation 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 Hall C parameterization VGL/Regge Fπ param

Projected Uncertainties for σL and 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

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

Projected Uncertainties for Q-n scaling p(e,e’K+)Λ xB=0.25 QCD scaling predicts σL~Q-6 and σT~Q-8 Projected uncertainties use R from the Hall C parameterization 1/Q4 1/Q6 x Q2 (GeV2) W (GeV) -t (GeV/c)2 0.25 1.7-3.5 2.5-3.4 0.2 0.40 3.0-5.5 2.3-3.0 0.5 Fit: 1/Qn 1/Q8 Is onset of scaling different for kaon than pion? Kaons and pions together provide quasi model-independent study

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.

Backup material

PR12-09-011 Beam Time Total 1123.6 (46.8 days) Q2 (GeV2) xB LH2 (hrs) Dummy Overhead (hrs) Total (hrs) 0.40 0.072 189.4 12.9 8 210.3 Subtotal low Q2 210.3 (18.7%) 1.25 0.122 29.5 2.1 39.6 2.00 0.182 113.4 7.9 12 133.3 Subtotal react mech 172.9 (15.4% ) 1.70 0.25 39.4 2.8 50.2 3.00 159.3 11.2 178.5 3.50 103.5 0.7 112.2 19.2 1.3 28.5 4.40 62.6 4.4 75.0 5.50 179.5 12.5 200.0 Subtotal Q-n scaling 644.4 (57.3%) Subtotal LH2/K+ 895.8 55.8 76 1027.6 Calibrations 96.0 (8.5%) Total 1123.6 (46.8 days)

Systematic Uncertainties Source pt-to-pt (%) t-correlated Scale earlier (%) Scale later (%) Acceptance 0.4 2.0 1.0 PID 0.5 Coincidence Blocking 0.2 Tracking Efficiency 0.1 1.5 Charge Target Thickness 0.8 Kinematics Kaon Absorption Kaon Decay 3.0 Radiative Corrections Monte Carlo Model Total 0.6 4.7 4.2

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 x Q2 (GeV2) W (GeV) -t (GeV/c)2 0.1-0.2 0.4-3.0 2.5-3.1 0.06-0.2 0.25 1.7-3.5 2.5-3.4 0.2 0.40 3.0-5.5 2.3-3.0 0.5 x Q2 (GeV2) W (GeV) -t (GeV/c)2 0.16 1.6 3.0 0.03 0.21 2.45 3.2 0.05 0.31 2.73 2.6 0.12 4.0 3.1

Transverse Contributions in Pion production VGL σL VGL σT 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 T. Horn et al., Phys. Rev. Lett. 97, 192001 (2006)

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

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