The Regge-plus-Resonance (RPR) model for Kaon Production on the Proton and the Neutron

FACULTY OF SCIENCES The Regge-plus-Resonance (RPR) model for Kaon Production on the Proton and the Neutron L. De Cruz, D.G. Ireland, P. Vancraeyveld, T. Vrancx Department of Physics and Astronomy, Ghent University, Belgium Department of Physics and Astronomy, Glasgow University, UK Jefferson Lab, May 17-20, 2011

Outline Motivation (Why should one study N(γ, K )Λ and N(γ, K )Σ?) Models for open strangeness production Regge-plus-resonance (RPR) approach to kaon photoproduction Kaon production on the proton 1 RPR results for kaon photoproduction DESCRIPTION AND PREDICTION 2 RPR results for kaon electroproduction PREDICTION Kaon photoproduction on the neutron (deuteron) 1 RPR results for kaon photoproduction PREDICTION Conclusions and outlook Jan Ryckebusch (Ghent University) RPR Model for Kaon Production May 19, 2011 2 / 34

Models 2 for open strangenes < 0.65 production I c.m. dσ/dcosθ (µb) 1.5 Challenges 1 for model builders P Λ 0 1 0-1 5 cosθ K γ cross sections are of the order of µb (pion production is mb) threshold 0 s 1.6 GeV (overlapping 1 resonances) no obvious indications for dominant resonance(s) in the energy 0 dependence of the cross section (BACKGROUND DIAGRAMS!) s (GeV) p(γ, 1.6K + 1.8 )Λ results 2 2.2 from 2.4 CLAS 2.6 2.8(PRC 81, 025201 (2010)) dσ/dcosθ (µb) P Λ 2 0.65 cosθ K < 0.75 1.5 1 c.m. -1 s (GeV) 1.6 1.8 2 2.2 2.4 2.6 2.8 dσ/dcosθ (µb) 2 1 0 1 c.m. 0.75 cosθ K < 0.85 dσ/dcosθ (µb) c.m. 4 0.85 cosθ K < 0.95 3 2 1 0 1 P Λ 0 P Λ 0-1 s (GeV) 1.6 1.8 2 2.2 2.4 2.6 2.8-1 s (GeV) 1.6 1.8 2 2.2 2.4 2.6 2.8 6. (Color online) dσ/dcos θk c.m. (µb) and P results vs. s (GeV) in bins of cos θk c.m. plotted with several model predictions. Average ts are given by Eq. (14). Model predictions are those of Kaon-MAID [21] (solid green line), the Bonn-Gatchina group [9] (dashed, and KAON-MAID the RPR model [22] (dashed redbonn-gatchina line). See text for commentary. RPR (Ghent)

Models for open strangeness production II Models for electromagnetically induced kaon production single-channel (single-step) approaches (KAON-MAID,...) coupled-channel (multi-step) approaches 1 Bonn-Gatchina (coupled-channel partial wave analysis (πn, ηn, KY )) (Sarantsev, Anisovich, Nikonov, Klempt, Thoma ; EPJA 34, 243 (2007)) 2 Giessen: (Shklyar, Lenske, Mosel ; PRC 72, 015210 (2005)) 3 EBAC: (Saghai, David, Julá-Diaz, Lee ; EPJA 31, 512 (2007)) Issues with regard to coupled-channel approaches highly multidimensional in parameter space centered on the real photon data (γ????) demanding analysis framework: HR and computer time consuming constraining background contributions in the weak channels is challenging Jan Ryckebusch (Ghent University) RPR Model for Kaon Production May 19, 2011 4 / 34

Models for open strangeness production III???? Economical model for N(γ, K )Y and N(e, e K )Y with few parameters and predictive power???? predict results for neutron targets from parameters of proton targets predict N(e, e K )Y from fitted N(γ, K )Y simple enough such that it can be used in hypernuclear calculations, neutrino-nucleus response calculations,... Jan Ryckebusch (Ghent University) RPR Model for Kaon Production May 19, 2011 5 / 34

Models for open strangeness production III???? Economical model for N(γ, K )Y and N(e, e K )Y with few parameters and predictive power???? predict results for neutron targets from parameters of proton targets predict N(e, e K )Y from fitted N(γ, K )Y simple enough such that it can be used in hypernuclear calculations, neutrino-nucleus response calculations,... Regge-inspired models Jan Ryckebusch (Ghent University) RPR Model for Kaon Production May 19, 2011 5 / 34

The Regge-plus-resonance model I + + The RPR strategy: PRC73, 045207 (2006) 1 Construct Regge model for high-energy (=background) amplitude, and constrain parameters to the available high-energy data. 2 Add resonance contributions (N and/or ) to obtain the full RPR amplitude, and fit parameters to the resonance region data. Jan Ryckebusch (Ghent University) RPR Model for Kaon Production May 19, 2011 6 / 34

The Regge-plus-resonance (RPR) model II 1 ) 2-1 10 + γ p K Λ dσ/dt ( µb/gev -2 10-3 10-4 10 5 GeV 8 GeV 11 GeV 16 GeV 1.5 2.0 2 -t (GeV ) 3 parameters Background contributions Exchange of K (494) and K (892) Regge trajectories in t channel Valid for s and forward angles Describes gross features of data in the resonance region (duality) Jan Ryckebusch (Ghent University) RPR Model for Kaon Production May 19, 2011 7 / 34

The Regge-plus-resonance (RPR) model III dσ/dω (µb/sr) 0.30 0.25 0.20 0.15 0.10 * cosθ K + 0 p(γ,k )Σ = 0.65 Regge 5 Regge + resonances 0 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 W (GeV) + + Resonant contributions enrich Regge background with nucleon and delta resonances standard Feynman s-channel diagrams EM form factors from Bonn CQM Jan Ryckebusch (Ghent University) RPR Model for Kaon Production May 19, 2011 8 / 34

Resonance physics with the RPR model: the p(γ, K + )Λ case I Resonances used in this analysis: S 11 (1535) S 11 (1650) P 11 (1710) P 11 (1900) m D 13 (1700) P 13 (1720) D 13 (1900) m P 13 (1900) D 15 (1675) F 15 (1680) F 15 (2000) : PDG status m: missing resonance, predicted by CQMs Strategy consider all possible combinations of above list of resonances use a genetic algorithm to find optimum model and its parameters the fitness of a particular N combination and corresponding parameters a is determined by: f fitness = 1 1+χ 2 ( a) CHALLENGE: there are 2048 possible combinations to evaluate!!! Jan Ryckebusch (Ghent University) RPR Model for Kaon Production May 19, 2011 9 / 34

Figure of merit for the 2048 N combinations 10 Reduced chi^2 of model 9 8 7 6 5 4 0 5 10 15 20 Number of free parameters (N*) Jan Ryckebusch (Ghent University) RPR Model for Kaon Production May 19, 2011 10 / 34

Figure of merit for the 2048 N combinations 10 Reduced chi^2 of model 9 8 7 6 5 4 0 5 10 15 20 Number of free parameters (N*) Jan Ryckebusch (Ghent University) RPR Model for Kaon Production May 19, 2011 10 / 34

Figure of merit for the 2048 N combinations Reduced chi^2 of model 10 9 8 7 6 5 4 0 5 10 15 20 Number of free parameters (N*) Fitted parameters: cutoff parameter Λ in the hadronic form factor coupling strengths: 1 for J = 1 2 3 for J 3 2 5 parameters: S 11 (1650) + P 11 (1710) + P 13 (1900) 14 parameters: S 11 (1535) + S 11 (1650)+ P 13 (1720) + D 13 (1900) + P 13 (1900) + P 11 (1900) + F 15 (1680) + D 15 (1675) 20 parameters: all 11 N s Jan Ryckebusch (Ghent University) RPR Model for Kaon Production May 19, 2011 10 / 34

Three p(γ, K + models )Λ: differential differential cross sections cross section 0.4 0.3 0.2 = 1575 MeV = 1875 MeV dσ/dω (µb/sr) 0.1 0.4 CLAS_2006 Bradford PRC_73_035202 SAPHIR_2004 Glander EPJA_19_251 0.3 0.2 0.1 = 2175 MeV LEPS_2007 Hicks PRC_76_042201 dcs CLAS_2009 McCracken PRC_81_025201 dcs 14 parameters 5 parameters 19 parameters - - cosθ K Jan Ryckebusch (Ghent University) RPR Model for Kaon Production May 19, 2011 11 / 34 *

p(γ, K + ) Λ: recoil polarisation = 980 MeV = 1222 MeV P = 1466 MeV CLAS_2004 McNabb PRC_69_042201 GRAAL_2007 Lleres EPJA_31_79 CLAS_2009 McCracken PRC_81_025201 rec 14 parameters 5 parameters 19 parameters * cosθ K Jan Ryckebusch (Ghent University) RPR Model for Kaon Production May 19, 2011 12 / 34

p( γ, K + ) Λ: beam-recoil polarisation O x O x 1.5 = 1272 MeV = 1321 MeV 1.5 1.5 = 1421 MeV 1.5 = 1466 MeV 1.5 1.5 1.5 * cosθ K

p( γ, K + ) Λ: beam-recoil polarisation O x 1.5 1.5 = 980 MeV = 1027 MeV = 1074 MeV 1.5 1.5 = 1122 MeV = 1171 MeV = 1222 MeV O x 1.5 1.5 = 1272 MeV = 1321 MeV = 1372 MeV 1.5 1.5 1.5 = 1421 MeV = 1466 MeV GRAAL_2008 Lleres arxiv_0807_3839 br 14 parameters 5 parameters 19 parameters 1.5 1.5 * cosθ K

p(e, e K + )Λ: structure functions for Q 2 = 0.65 GeV 2 0.3 0.2 W = 1650 MeV W = 1775 MeV W = 1925 MeV W = 2050 MeV 0.3 0.2 (µb/sr) σ T +εσ L 0.1 0.1 0.1 0.1 CLAS_2007 Ambrozewicz PRC_75_045203_2.567 14 parameters 5 parameters 0.2 0.2 19 parameters 0.3 0.3 0.3 0.2 W = 1650 MeV W = 1775 MeV 0.2 W = 1925 MeV 0.2 W = 2050 MeV (µb/sr) 0.1 0.1 0.1 σ TT 0.1 0.1 0.1 0.2 0.2 0.2 0.3 0.3 0.3 0.2 W = 1650 MeV W = 1775 MeV 0.2 W = 1925 MeV 0.2 W = 2050 MeV (µb/sr) 0.1 0.1 0.1 σ TL 0.1 0.1 0.1 0.2 0.2 0.2 0.3 0.3 0.3 * cosθ K

p( e, e K + ) Λ: transferred polarisation electron beam energy = 4.261 GeV electron beam energy = 5.754 GeV P z P z 14 parameters 14 parameters 5 parameters 5 parameters 19 parameters 19 parameters CLAS_2009 Carman PRC_79_065205 transfpol_ebeam4g CLAS_2009 Carman PRC_79_065205 transfpol_ebeam6g P x P x 2 2 Q = 1.56 GeV * cosθ K = 4.1 + 3.92 W 0.84 W 1600 1800 2000 2200 2400 2600 2 2 2 Q = 2.54 GeV * cosθ K = 3.74 + 3.48 W 0.69 W 1600 1800 2000 2200 2400 2600 2 W (MeV) W (MeV) Jan Ryckebusch (Ghent University) RPR Model for Kaon Production May 19, 2011 15 / 34

Importance of the P 13 (1900) / D 13 (1900) Models that include P 13 (1900) Models that include D 13 (1900) By comparison: D 13 (1700) 10 10 10 Reduced chi^2 of model 9 8 7 6 Reduced chi^2 of model 9 8 7 6 Reduced chi^2 of model 9 8 7 6 5 5 5 4 0 5 10 15 20 Number of free parameters (N*) 4 0 5 10 15 20 Number of free parameters (N*) 4 0 5 10 15 20 Number of free parameters (N*) P 13 (1900): PDG status D 13 (1900): missing resonance Jan Ryckebusch (Ghent University) RPR Model for Kaon Production May 19, 2011 16 / 34

Neutral-kaon production: p(γ, K 0 )Σ + I dσ/dω (µb/sr) 0.30 0.25 0.20 0.15 0.10 5 0.25 0.20 0.15 0.10 5 Regge Regge + resonances LEPS-PRL97(2006)082003 CLAS-PRC69(2004)042201R SAPHIR-EPJA19(2004)251 SAPHIR-EPJA24(2005)275 CLAS-Ph.D. Carnahan (2003) * cosθ K * cosθ K + 0 p(γ,k )Σ p(γ,k = 0.65 0 + )Σ = 0.70 p(γ, K + )Σ 0 p(γ, K 0 )Σ + K (494)-exchange vanishes isospin relations at strong vertex g K ( )0 Σ + N ( ) = 2g K ( )+ Σ 0 N ( ) Fit ratio of EM coupling constants κ K 0 (892)K 0 (494) κ K + (892)K + (494) = 5 ± 1 Fair description of data (χ 2 /n.d.f. = 3.4). 0 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 W (GeV) + + Jan Ryckebusch (Ghent University) RPR Model for Kaon Production May 19, 2011 17 / 34

Neutral-kaon production : p(γ, K 0 )Σ + II Differential cross section and photon asymmetry dσ/dω (µb/sr) 0.10 8 6 4 2 lab E γ = 1100 MeV lab E γ = 1700 MeV lab E γ = 2200 MeV 0 + p(γ,k )Σ 1.5 Recoil asymmetry - Regge + resonances - CB/ELSA-TAPS-EPJA31(2007)61 SAPHIR-EPJA24(2005)275-1.5 - - - - * cosθ K Jan Ryckebusch (Ghent University) RPR Model for Kaon Production May 19, 2011 18 / 34

Kaon production from the neutron (deuteron) I Why studying kaon production on the neutron? The N spectrum according to the Relativistic Constituent Quark Model of the Bonn group extract the n(γ, K )Y amplitude: complementary information about N investigate nuclear-medium effects study of the hyperon-nucleon potential hypernuclear spectroscopy final-state interactions in 2 H(γ, KY )N Jan Ryckebusch (Ghent University) RPR Model for Kaon Production May 19, 2011 19 / 34

Kaon production from the neutron (deuteron) II An RPR model for kaon production on the neutron (deuteron) Elementary-production operator: RPR model Describes K + Λ and K + Σ 0 channels from the proton Parameters for the neutron derived from the ones of the proton (isospin!) Dnp-vertex: relativistic FSI: YN Y N Jan Ryckebusch (Ghent University) RPR Model for Kaon Production May 19, 2011 20 / 34

Kaon production from the free neutron n(γ, K + )Σ I Resonance S 11 (1650) P 11 (1710) P 13 (1720) P 13 (1900) SAID PRC53(1996)430 κ N n κ N p 0.22 ± 7 κ N n κ N p 0.29 ± 2.23 κ (1) N n κ (1) N p κ (2) N n κ (2) N p κ (1) N n κ (1) N p κ (2) N n κ (2) N p 0.38 ± 2.00 0 ± 8 Unknown 0 ± 2.00 0 ± 2.00 Photocoupling helicity amplitudes from SAID analysis p(γ, K + )Σ 0 n(γ, K + )Σ isospin relations at strong vertex g K ( )+ Σ N ( )0 = 2 g K ( )+ Σ 0 N ( )+ 2 gk + Σ 0 = g K + Σ 0 + ratio of helicity amplitudes at EM vertex κ nn κ pn = An 1/2 A p,... 1/2 + + Jan Ryckebusch (Ghent University) RPR Model for Kaon Production May 19, 2011 21 / 34

Kaon production from the free neutron n(γ, K + )Σ II dσ/dω (µb/sr) Photon-beam asymmetry Σ 0.6 0.4 0.3 0.2 0.1 n(γ,k + )Σ - cosθ* K = 0.85 1800 2000 2200 2400 2600 2800 W (MeV) - - Regge Regge + resonances LEPS, PRL97(2006)082003 CLAS, PLB688(2010)289 1800 2000 2200 W (MeV) p(γ, K + )Σ 0 n(γ, K + )Σ isospin relations at strong vertex ratio of helicity amplitudes at EM vertex N helicity amplitudes subject to error bars! P. Vancraeyveld et al. PLB681(2009)428 + + Jan Ryckebusch (Ghent University) RPR Model for Kaon Production May 19, 2011 22 / 34

Kaon production from the free neutron n(γ, K + )Σ III dσ/dω (µb/sr) 0.40 0.35 0.30 0.25 0.20 0.15 0.10 5 * cosθ K = -0.25 Regge Regge + resonances CLAS-PLB688(2010)289 LEPS-PRL97(2006)082003 0 1800 2000 2200 2400 2600 * cosθ K = 0.25 1800 2000 2200 2400 2600 W (MeV) * θ K cos = 0.75 + - n(γ,k )Σ 1800 2000 2200 2400 2600 Jan Ryckebusch (Ghent University) RPR Model for Kaon Production May 19, 2011 23 / 34

Kaon production from the deuteron: formalism (I) Plane-wave impulse approximation covariant Dnp-vertex elementary-production operator: Regge-plus-resonance model + Hyperon-nucleon final-state interactions hyperon-nucleon interaction: Juelich model Jan Ryckebusch (Ghent University) RPR Model for Kaon Production May 19, 2011 24 / 34

Kaon production from the deuteron: formalism (II) Hyperon-nucleon final-state interactions = i p N 32π 2 dω N M(YN Y N ) W YN u Y Γ λγ RPR m N + /p T m 2 N p2 T Γ λ D Dnp CuT N Hyperon-nucleon interaction Juelich model (PRC72(2005)044005) elastic + inelastic rescattering restrict to on-shell rescattering no sub-threshold production Jan Ryckebusch (Ghent University) RPR Model for Kaon Production May 19, 2011 25 / 34

RPR predictions for 2 H(γ, K 0 )YN 0 (nb/mev) dσ/dp K 2.5 2.0 1.5 2.5 2.0 1.5 2 0 H(γ,K )YN 0.9<E γ < [GeV] 0.9<cosθ K 0< PRC78(2008)014001 (x4) 0 K Λ 0 0 + 0 0 K Λ+K Σ +K Σ Regge Regge + resonances <E γ <1.1 [GeV] 0.9<cosθ K 0< 0 100 200 300 400 500 600 700 p (MeV) 0 K LNS: PRC78 (2008) 014001 Semi-inclusive K 0 production = K 0 Λ + K 0 Σ 0 + K 0 Σ + Only forward angles dσ dp K = 2π dσ 0.9 dp K dω K d cos θ K RPR predictions Eγ lab = 950 MeV near K 0 Σ threshold data is underpredicted Eγ lab = 1050 MeV 2 quasi-elastic peaks good predictions Jan Ryckebusch (Ghent University) RPR Model for Kaon Production May 19, 2011 26 / 34

0 RPR predictions for 2 H(γ, K 0 )YN (nb/mev) dσ/dp K 2.5 2.0 1.5 2.5 2.0 1.5 2 0 H(γ,K )YN 0.9<E γ < [GeV] 0.9<cosθ K 0< PRC78(2008)014001 (x4) RPWIA YN-FSI <E γ <1.1 [GeV] 0.9<cosθ K 0< 0 100 200 300 400 500 600 700 p (MeV) 0 K LNS: PRC78 (2008) 014001 Semi-inclusive K 0 production = K 0 Λ + K 0 Σ 0 + K 0 Σ + Only forward angles dσ dp K = 2π dσ 0.9 dp K dω K d cos θ K RPR predictions Eγ lab = 950 MeV near K 0 Σ threshold data is underpredicted Eγ lab = 1050 MeV 2 quasi-elastic peaks good predictions effect of YN FSI is small Jan Ryckebusch (Ghent University) RPR Model for Kaon Production May 19, 2011 26 / 34

Conclusions These are exciting times for modelers in open strangeness production (high-quality data over extended energy range, proton AND neutron targets, single and double polarization data, complete measurements, hypernuclear results at the horizon) Regge-plus-resonance (RPR) approach fixes Regge background at high energies adds N s and s in the resonance region economical and gauge-invariant description of K + Λ and K + Σ 0 channels for threshold Eγ lab 16 GeV RPR has predictive power K 0 production electroproduction K production from the neutron (deuteron) Jan Ryckebusch (Ghent University) RPR Model for Kaon Production May 19, 2011 27 / 34