1. T. Horn, G. Huber, P. Markowitz: “L/T separated kaon production cross sections” L-T Separated Kaon production Cross Sections from 5-11 GeV Hall C User’s meeting30 January 2009 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

2. T. Horn, G. Huber, P. Markowitz: “L/T separated kaon production cross sections” Meson Reaction Dynamics At sufficiently high Q 2, 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] t-channel process handbag e e’ N(p) W t Q2Q2 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 π, K, etc. hard pointlike

3. T. Horn, G. Huber, P. Markowitz: “L/T separated kaon production cross sections” 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) But measurements of form factors and GPDs have certain prerequisites: Before we can start looking at form factors, we must make sure that σ L is dominated by the meson pole term at low -t Before we can learn about GPDs, we must demonstrate that factorization applies A comparison of pion and kaon production data may shed further light on the reaction mechanism, and intriguing 6 GeV pion results F π,K π, K, etc φ φ Hard Scattering GPD π, K, etc. φ - π,Kπ,K

4. T. Horn, G. Huber, P. Markowitz: “L/T separated kaon production cross sections” Context Limited knowledge of L/T ratio at higher energies limits the interpretability of unseparated cross sections in kaon production –Relative σ L and σ T contributions are also needed for GPD extractions since they rely on the dominance of σ L 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

5. T. Horn, G. Huber, P. Markowitz: “L/T separated kaon production cross sections” Transverse Contributions In the resonance region at Q 2 =2.0 GeV 2 σ T is not small In pion production, σ T is also much larger than predicted by the VGL/Regge model [PRL97:192001 (2006)] Why is σ T so large? Difficult to draw a conclusion from current data –Limited W and Q 2 range –Significant uncertainty due to scaling in x B and –t K + Σ˚ K+ΛK+Λ K+ΛK+Λ σLσL σTσT 0.5<Q 2 <2.0 GeV 2 High quality σ L and σ T data for both kaon and pion would provide important information for understanding the meson reaction mechanism Hall C 6 GeV data (W=1.84 GeV) VGL/Regge

6. T. Horn, G. Huber, P. Markowitz: “L/T separated kaon production cross sections” R=σ L /σ T : Kaon form factor prerequisite Meson form factor extraction requires a good reaction model –Need high quality data to develop these models Current knowledge of σ L and σ T 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 L/T separations above the resonance region are essential for building reliable models, which are also needed for form factor extractions VGL/Regge ( Λ 2 K =0.68 GeV 2 ) Nucleon resonance data scaled to W=1.84 GeV

7. T. Horn, G. Huber, P. Markowitz: “L/T separated kaon production cross sections” High Q 2 : Q - n scaling of σ L and σ T The QCD scaling prediction is reasonably consistent with recent JLab π + σ L data, BUT σ T does not follow the scaling expectation T. Horn et al., Phys. Rev. C78, 058201 (2008) Hall C  + production data at 6 GeV Q 2 =1.4-2.2 GeV 2 Q 2 =2.7-3.9 GeV 2 σLσL σTσT To access physics contained in GPDs, one is limited to the kinematic regime where hard-soft factorization applies 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 A test is the Q 2 dependence of the cross section: –σ L ~ Q -6 to leading order –σ T ~Q -8 –As Q 2 gets large: σ L >> σ T

8. T. Horn, G. Huber, P. Markowitz: “L/T separated kaon production cross sections” T. Horn et al., Phys. Rev. Lett. 97 (2006) 192001. Bonus: F π,K - a factorization puzzle? T. Horn et al., arXiv:0707.1794 (2007). The Q 2 dependence of F π is also consistent with hard-soft factorization prediction (Q -2 ) 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 A.P. Bakulev et al, Phys. Rev. D70 (2004)] Comparing the observed Q 2 dependence of σ L,T and FF magnitude with kaon production would allow for better understanding of the onset of factorization

9. T. Horn, G. Huber, P. Markowitz: “L/T separated kaon production cross sections” 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 σ L 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

10. T. Horn, G. Huber, P. Markowitz: “L/T separated kaon production cross sections” Experiment Overview xQ 2 (GeV 2 ) W (GeV) -t (GeV/c) 2 0.1-0.20.4-3.02.5-3.10.06-0.2 0.251.7-3.52.5-3.40.2 0.403.0-5.52.3-3.00.5 Measure the separated cross sections at varying –t and x B –If K + pole dominates σ L 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 x B –Q 2 coverage is a factor of 2-3 larger compared to 6 GeV at much smaller –t –Facilitates tests of Q 2 dependence even if L/T ratio less favorable than predicted Q 2 =3.0 GeV 2 was optimized to be used for both t-channel and Q -n scaling tests

11. T. Horn, G. Huber, P. Markowitz: “L/T separated kaon production cross sections” 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)

12. T. Horn, G. Huber, P. Markowitz: “L/T separated kaon production cross sections” Separation in a Multi-Dimensional Phase Space 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<2 π allows to determine L, T, LT and TT SHMS+3° Cuts are placed on the data to equalize the Q 2 -W range measured at the different ε -settings Low ε High ε SHMS-3° Radial coordinate (-t), Azimuthal coordinate (φ)

13. T. Horn, G. Huber, P. Markowitz: “L/T separated kaon production cross sections” Heavy Gas Cherenkov and 60 cm of empty space Kaon PID π + / K + separation provided by heavy gas Cerenkov for p SHMS >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 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

14. T. Horn, G. Huber, P. Markowitz: “L/T separated kaon production cross sections” Expected Missing Mass Resolution Simulation at Q 2 =2.0 GeV 2, W=3.0 and high ε 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 Λ Σ° e+p → e’+ K + Λ(Σ°) SHMS+HMS

15. T. Horn, G. Huber, P. Markowitz: “L/T separated kaon production cross sections” Projections of R=σ L /σ T 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 Q 2 =8 GeV 2 may ultimately be possible VGL/Regge F π param VGL/Regge calculation Hall C parameterization

16. T. Horn, G. Huber, P. Markowitz: “L/T separated kaon production cross sections” Projected Uncertainties for σ L and σ T Projected uncertainties for σ L and σ T use the L/T ratio from Hall C parameterization High quality kaon L/T separation above the resonance region σLσL σTσT PR12-09-011: Precision data for W > 2.5 GeV

17. T. Horn, G. Huber, P. Markowitz: “L/T separated kaon production cross sections” Projected Uncertainties for the Kaon FF If the K + pole dominates low -t σ L, we would for the first time extract F K above the resonance region (W>2.5 GeV) Projected uncertainties for σ L use the L/T ratio from Hall C parameterization

18. T. Horn, G. Huber, P. Markowitz: “L/T separated kaon production cross sections” QCD scaling predicts σ L ~Q -6 and σ T ~Q -8 Projected uncertainties use R from the Hall C parameterization Projected Uncertainties for Q -n scaling p(e,e’K + ) Λ x B =0.25 1/Q 6 1/Q 4 1/Q 8 xQ 2 (GeV 2 ) W (GeV) -t (GeV/c) 2 0.251.7-3.52.5-3.40.2 0.403.0-5.52.3-3.00.5 Is onset of scaling different for kaon than pion? Kaons and pions together provide quasi model-independent study Fit: 1/Q n

19. T. Horn, G. Huber, P. Markowitz: “L/T separated kaon production cross sections” 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 σ L, 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. T. Horn, G. Huber, P. Markowitz: “L/T separated kaon production cross sections” Backup material

21. T. Horn, G. Huber, P. Markowitz: “L/T separated kaon production cross sections” PR12-09-011 Beam Time Q 2 (GeV 2 ) xB LH2 (hrs)DummyOverhead (hrs)Total (hrs) 0.400.072189.412.98210.3 Subtotal low Q 2 210.3 (18.7%) 1.250.12229.52.1839.6 2.000.182113.47.912133.3 Subtotal react mech 172.9 (15.4% ) 1.700.2539.42.8850.2 3.000.25159.311.28178.5 3.500.25103.50.78112.2 3.000.4019.21.3828.5 4.400.4062.64.4875.0 5.500.40179.512.58200.0 Subtotal Q -n scaling 644.4 (57.3%) Subtotal LH 2 / K + 895.855.8761027.6 Calibrations96.0 (8.5%) Total1123.6 (46.8 days)

22. T. Horn, G. Huber, P. Markowitz: “L/T separated kaon production cross sections” Systematic Uncertainties Source pt-to-pt (%) t-correlated (%) Scale earlier (%) Scale later (%) Acceptance0.4 2.01.0 PID0.41.00.5 Coincidence Blocking 0.2 Tracking Efficiency0.1 1.5 Charge0.20.5 Target Thickness0.20.8 Kinematics0.41.0 Kaon Absorption0.5 Kaon Decay1.03.0 Radiative Corrections 0.10.42.0 Monte Carlo Model0.21.00.5 Total0.62.04.74.2

23. T. Horn, G. Huber, P. Markowitz: “L/T separated kaon production cross sections” Overlap with pion data xQ 2 (GeV 2 ) W (GeV) -t (GeV/c) 2 0.1-0.20.4-3.02.5-3.10.06-0.2 0.251.7-3.52.5-3.40.2 0.403.0-5.52.3-3.00.5 Would require that aerogels installed during pion experiments as well xQ 2 (GeV 2 ) W (GeV) -t (GeV/c) 2 0.161.63.00.03 0.212.453.20.05 0.312.732.60.12 0.314.03.10.12 Proposed kaon experimentApproved pion experiments 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%<δ SHMS <-2% –Missing Mass tail cut off by SHMS acceptance

24. T. Horn, G. Huber, P. Markowitz: “L/T separated kaon production cross sections” Transverse Contributions in Pion production In pion production, magnitude of σ T has been controversial for a long time –VGL/Regge model systematically underestimates σ T, for which it seems to have limited predictive power T. Horn et al., Phys. Rev. Lett. 97, 192001 (2006) VGL σ L VGL σ T

25. T. Horn, G. Huber, P. Markowitz: “L/T separated kaon production cross sections” Bonus: Interference Terms In the hard scattering limit, these terms are expected to scale: –σ LT ~ Q -7 –σ TT ~Q -8 Additional information about the reaction mechanism may be obtained for free if one performs a full cross section separation K + Λ( Σ° ) as calculated in VGL/Regge model Q 2 =0.4 GeV 2 Q 2 =3.5 GeV 2

26. T. Horn, G. Huber, P. Markowitz: “L/T separated kaon production cross sections” 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