Coupled-Channels Partial-Wave Analysis of Kaon Photoproduction

1. Coupled-Channels Partial-WaveAnalysis of Kaon Photoproduction Olaf Scholten KVI / Univ. of Groningen The Netherlands NFQCD10, Kyoto INFQCD10

2. Overview Motivation: obtain a description of scattering data at moderate energies and have a dynamic description of some resonances • Virtues of K-matrix model • Importance of coupled channels effects • Reproducing the data • Determine Structure resonances • Coupling to various decay branches • Input to QCD modeling • Outlook, dynamic generation resonances INFQCD10

3. The K-matrix model • Full coupled channels in large model space • Non-perturbative • Unitary • Gauge invariant • Covariant • Crossing symmetric INFQCD10

4. c symmetry partial wave projected INFQCD10

5. Recently added: (Λ(1520)+K) INFQCD10

6. Photo-induced Φ-meson production S. Ozaki et al, PRC80(2009)035201 Tree-level calculation: monotonically rising cross section Data has structure Resonance? probably not INFQCD10

7. (N+γ N+Φ) Coupled Channels I Resonance in (K+Λ(1520)  N+Φ) as pure hidden strangeness ½- resonance > No direct coupling to entrance channel > Large interference effects S. Ozaki, A. Hosaka, and O. S., Phys. Rev. C 80, 035201 (2009) INFQCD10

8. (N+γ N+Φ) Coupled Channels II Backward rise in differential cross sections INFQCD10

9. Photo-induced η production I CB-ELSA data R. SHYAM AND O. S., PHYS REV C 78, 065201 (2008) INFQCD10

10. Photo-induced η production CB-ELSA data R. SHYAM AND O. S., PHYS REV C 78, 065201 (2008) INFQCD10

11. Photo-induced K+Λ & K+Σ Decomposition of cross section in to resonance contributions Big difference between the two INFQCD10 R. Shyam, O. S., H. Lenske, arXiv:0911.3351 [hep-ph]

12. Effects coupled channels A.Usov, O.S., PRC72,25205 gNhS11 -> - gNhS11 No r-meson σtot [μb] Invariant mass [GeV] INFQCD10

13. Chi-square fitting in K-matrix • pion & photon sector fixed • vary only ‘strange’ parameters • How unique is fit? Alexander Usov Dave Iereland Note: Highly non-linear ~30 parameters Observables at many energies many iterations  code optimization > 3 fits with similar chi-square INFQCD10

14. Cross sections&Recoil polarizations K+ - L Data: SAPHIR 4 different fits plotted with 1.8 < Χ2/df < 2.0 K+ - S0 K0 - S+ INFQCD10

15. Partial wave phase shifts K+ - L K+ - S0 K0 - S+ INFQCD10

16. Summary • Coupled channels effects are large • Lambda photo-production • phi-meson photo-production • Good reproduction of data can be obtained in effective-Lagrangian approach, however partial wave decomposition is ambiguous • need complete set of polarization observables • may help to implement causality in theory • relate Real & Imaginary parts phase shifts • dynamic generation resonances INFQCD10

17. Need to implement: • Driving terms consistent with chiral symmetry  Low energy theorems  crossing symmetry • Unitarity; consistency imaginary part scattering amplitude • non perturbative at high energies • Causality=analyticity; consistency Real & Imaginary parts amplitude • Self energies (molecular resonances) • Vertex corrections Different aproaches: • Dressed K-matrix • Renormalized loop corrections INFQCD10

18. “Dressed K-matrix” Use ‘Dressed’ - 3-point vertex - propagators Crossing symm. PRC64(2001)24005 Sergey Kondratyuk & O.S. Non perturbative, Keeping Unitarity, Crossing Dressed From dispersion relation From K-matrix From dispersion relation INFQCD10

19. Off Shell Restore analyticity ‘Dressed K-matrix’ PRC64(2001)24005 Sergey Kondratyuk & O.S. INFQCD10

20. Results vertex functions p N N Bare form factor Converged vertex function Soft vertex functions are generated through pion-loop corrections INFQCD10 Numerically very difficult

21. Cusp in Compton Amplitude Cusp due to analyticity Dressed Bare Data INFQCD10

22. Nucleon Polarizabilities Proton Neutron Model data Model data a 12.1 11.9±0.6 12.7 12.5±1.7 b 2.4 1.9±0.6 1.8 2.7±1.8 Full Bare Gellas, et al., Phys. Lett. 85, 14 Hemmert, et al.,PRD. 57, 5746 INFQCD10 S. Kondratyuk & OS, PRC 64 (2001) 24005

23. Renormalized loops Aim: compare 2 approaches; - Dyson loop - Renormalized Analytic K-matrix Renormalization: • Pole position and residue positive and negative E pole Guarantees correct value and derivative amplitude at threshold O.S, S. Tamenaga, H. Toki PRC 75, 055203 S-type diagrams, only loop corrections: Self-energy in Dyson approach INFQCD10

24. Analytic K-matrix Normal K-Matrix includes open channels only • Below 140 MeV: (g+N) • Above : (g+N) and (p+N) Discontinuous  breaking analyticity • Analytic continuation K-matrix • Analytic continuation of momentum below thr. • Renormalize value and derivative at threshold Finite renormalization constants INFQCD10

25. Loop corrections through Dyson equation or Analytic continuation with Setsuo Tamenaga and Hiroshi Toki PRC75(2007) 55203 Simple at s-level diagrams; problem: crossing is violated INFQCD10

26. Summary Motivation: obtain a description of scattering data and have a dynamic description of some resonances Good progress in implementing unitarity crossing causality However, we are not there yet! INFQCD10