Theory of the electromagnetic production of hyperons

Transcription

1 Theory of the electromagnetic production of hyperons Petr Bydžovský and Dalibor Skoupil Nuclear Physics Institute, AV CR, Řež/Prague Czech Republic International Conference on Hypernuclear and Strange Particle Physics, Barcelona, October 1-5, 212.

2 Dedicated to dear colleague Sla vek Sotona ( January 29, 1939; April 6, 212) P. Bydz ovsky (NPI R ez ) Theory of the electromagnetic production HYP12, October 1-5, / 23

3 Overview of the talk Introduction Isobar models Regge-plus-resonance model Results K photoproduction on deuteron K + photo- and electroproduction on proton at small angles K + electroproduction on proton at small Q 2 Summary and outlook P. Bydžovský (NPI Řež) Theory of the electromagnetic production HYP12, October 1-5, / 23

4 Electroproduction of kaons and hyperons on nucleons e + N e + K + Y 6 channels: N = p, n; K = K +, K ; Y = Λ, Σ, Σ +, Σ. One-photon-exchange approximation separation of electron and hadron parts photoproduction by virtual photons (q 2 γ <, Q 2 = q 2 γ) γ v (q γ ) + N K + Y P. Bydžovský (NPI Řež) Theory of the electromagnetic production HYP12, October 1-5, / 23

5 Description of kaon electromagnetic production Isobar model (single-channel description) Saclay-Lyon, Kaon-MAID, Gent-Isobar Regge-plus-resonance model (Regge background) RPR-27, RPR-211 Multipole analysis Mart and Sulaksono Quark model (resonances included) Zhenping Li et al. Unitary approach (coupled channels) Giessen, Bonn-Gatchina, Julia-Diaz et al. Chiral unitary framework (chiral Lagrangian, coupled channels) Borasoy et al. Regge model (E γ > 4 GeV, small ) Regge97 (VGL), Regge211 (Gent) P. Bydžovský (NPI Řež) Theory of the electromagnetic production HYP12, October 1-5, / 23

6 Isobar model Meson-baryon final-state interaction T = V + V G t re-scattering, e.g. t(nπ K Λ) couplings with other channels Single-channel approximation: T = V violation of unitarity description of t(λk ΛK) effective coupling constants include a part of the re-scattering effects Driving term V : effective hadronic Lagrangian (fields, couplings) perturbation expansion on the tree-level (most of g s > 1) s-, t-, and u-channel exchanges; contact term (gauge invariance) many possible resonances in the intermediate states large number of models with a good χ 2 P. Bydžovský (NPI Řež) Theory of the electromagnetic production HYP12, October 1-5, / 23

7 Isobar model Constraints on the models: SU(3) symmetry 4.4 g KNΛ / 4π 3..8 g KNΣ / 4π 1.3 crossing symmetry - description of Γ(K p γ Λ) Large contributions to the background part of the amplitude from the Born diagrams reduced: hadronic form factors - dipole, Gaussian, multidipole-gauss - inclusion of a hadron structure - gauge invariance a contact term hyperon exchanges in u-channel (non resonant contributions) the problem is avoided in the Regge-plus-resonance model The resonant part - exchanges of nucleon resonances in s channel P. Bydžovský (NPI Řež) Theory of the electromagnetic production HYP12, October 1-5, / 23

8 Comparison of the Saclay-Lyon and Kaon-MAID models Saclay-Lyon A Kaon-MAID Born terms N, Λ, Σ, K N, Λ, Σ, K Resonances: meson K (89), K 1 (127) K (89), K 1 (127) nucleon N(172) N(172), N(165), N(171), N(1895) hyperon Λ(147), Λ(167), Λ(181), Σ(166) Hadronic f. f. no dipole Constraints SU(3), crossing SU(3) An overview and comparison of older isobar models in P.B.,F.Cusanno, S.Frullani,F.Garibaldi,M.Iodice,M.Sotona,G.M.Urciuoli, arxiv:nucl-th/3539 P. Bydžovský (NPI Řež) Theory of the electromagnetic production HYP12, October 1-5, / 23

9 Dynamics of the Saclay-Lyon and Kaon-MAID models Contributions to the cross section near the threshold Coupling constants for the Born terms g KNΛ g KNΣ (SLA) (KM) Suppression of Born t. - hyperons (SLA) - hadronic f. f. (KM) Coupling constants for the K 1 exchange G V G T (SLA) (KM) important in K Λ dσ / dω [µb/sr] Saclay-Lyon A γ + p --> K + + Λ entire SLA B+hyperons B(p,K,Λ,Σ ) SLA without K 1 E γ lab = 1 GeV W = 1.66 GeV N*(165) Kaon-MAID B(p,K,Λ,Σ ) KM without K 1 entire KM P. Bydžovský (NPI Řež) Theory of the electromagnetic production HYP12, October 1-5, / 23

10 Regge-plus-resonance model Invariant amplitude: M = M bgr (Regge) + M res (isobar) the background part - exchanges of the K and K trajectories { M bgr P Regge (s, t) = (s/s ) α(t) π α 1 sin π α(t) Γ(1 + α(t)) e iπα(t) } with α(t) = α (t m 2 ); the resonant part - exchanges of nucleon resonances in the s-channel M res P Feyn (s) = 1 s m 2 + imγ strong hadronic form factors (Gaussian, multidipole-gauss) - a smooth transition into the high-energy ( Regge ) region. P. Bydžovský (NPI Řež) Theory of the electromagnetic production HYP12, October 1-5, / 23

11 Merits of the Regge-plus-resonance model: describes the world data from the threshold up to 16 GeV; the background part contains only 3 parameters which can be fixed by high-energy data ( s > 2.6 GeV); no large contributions from the Born terms as in the isobar models - no hadronic form factors for the background part. Problems: application of the Regge formalism to small-energy region - parametrization of the non-resonant diagrams; double counting (duality hypothesis) in the resonance region - the number of included s-channel resonances is small, - the background is re-fitted; uncertainties due to rotating/constant phases - solved by Lesley De Cruz et al in a careful Bayesian analysis of new data the new version of the model, RPR-211. P. Bydžovský (NPI Řež) Theory of the electromagnetic production HYP12, October 1-5, / 23

12 Comparison of isobar and Regge-plus-resonance models H2: isobar model with hadronic f.f.; fit to CLAS data; nucleon resonances: S 11 (165), P 11 (171), P 13 (172), D 13 (1895); hyperon resonances: S 1 (167), S 1 (18) RPR: fit to CLAS and LEPS data (cross sections) with resonances S 11 (1535) S 11 (165), P 11 (171), P 13 (172), D 13 (1895); multidipole-gauss hadronic f.f.; motivated by RPR-211B [Lesley De Cruz, PhD thesis, Ghent University, 211] dσ / dω [µb/sr] E γ lab = 1.3 GeV Bleckman et al SAPHIR3 CLAS Saclay-Lyon A Kaon-MAID H2 RPR RPR c.m. [deg] p(γ, K + )Λ SAPHIR3 CLAS LEPS E γ lab = 2.2 GeV c.m. [deg] RPR-27: Corthals et al, 27, version RPR-2+D13 P.B., M. Sotona, Nucl. Phys. A 835 (21) 246 P. Bydžovský (NPI Řež) Theory of the electromagnetic production HYP12, October 1-5, / 23

13 Results Test of models in the K photoproduction on deuteron NKS1 data [Tsukada et al, PRC 78(28)141, PRC 83(211)3994(E)] PWIA calculation [P.B.,M.Sotona, O.Hashimoto,T.Takahashi, arxiv:nucl-th/41235]; Σ production is negligible below 1 GeV PH1(2): dσ/dω = s s [1 + e (s s )] (a P (x) ± a 1 P 1 (x) + a 2 P 2 (x)) enhancement of the K distribution at backward angles dσ/dp K [µb/(gev/c)] < E γ lab < 1. GeV (averaged).9 < cos( lab ) < 1. (integrated) KM SLA PH1 PH2 dσ / dω [µb/sr] E γ lab =.97 GeV Kaon-MAID SLA PH1 PH p K [GeV/c] cos θ c.m. K P. Bydžovský (NPI Řež) Theory of the electromagnetic production HYP12, October 1-5, / 23

14 Results K + production at small kaon angles [P.B.,M.Sotona,T.Motoba,K.Itonaga,K.Ogawa, O.Hashimoto, NPA883(212)199; T.Motoba, P.B.,M.Sotona,K.Itonaga, ProgThPhysSuppl.185(21)185; P.B.,T.Mart, PRC76(27)6522] electroproduction: σ full = σ T + ɛ σ L + ɛσ TT + 2ɛ(1 + ɛ)σ TL, Φ K = SL:.41 = (ɛ=.7, Q 2 =.7 (GeV/c) 2 ) dσ / dω [µb/sr] p(γ, K + )Λ W = 2.24 GeV Brown72 E94-17 data CLAS LEPS SAPHIR RPR-27 RPR Saclay-Lyon A H2 (with h.f.f.) c.m. [deg] Electroproduction data: Brown72 [PRL28(1972)186] W = 2.17 GeV, Q 2 =.18 (GeV/c) 2, θk c.m. = 5.9 E94-17 (JLab, Hall A) W = 2.2 GeV, Q 2 =.7 (GeV/c) 2, θk c.m. = 6 Large contributions from longitudinal couplings OR W-dependence in σ T? P. Bydžovský (NPI Řež) Theory of the electromagnetic production HYP12, October 1-5, / 23

15 A possible test of models at forward angles DWIA calculation of the cross sections for the electroproduction of hypernuclei M. Sotona, S. Frullani, Prog. Theor.Phys.Suppl.117(1994)151 elementary amplitude: Saclay-Lyon A JLab data E94-17: W= 2.2 GeV, Q 2 =.7 (GeV/c) 2 dσ/(dω e dω K de e de exc ) [nb/(sr 2 GeV MeV)] C(e,e K ) Λ B M.Iodice,...M.Sotona,... JLab data 1 -, 2 - DWIA Phys.Rev.Lett.99(27) , 3 + s 1/2Λ p 1/2Λ, p 3/2Λ 1-2 -, 1-2 +, , Excitation Energy [MeV] E x cross sections (MeV) (nb/st 2 /GeV) Exp. Theor ± ± ± ± P. B., M. Sotona, Nucl. Phys. A 835 (21) 246 P. Bydžovský (NPI Řež) Theory of the electromagnetic production HYP12, October 1-5, / 23

16 Photoproduction of K + Λ at forward kaon angles, higher energies: RPR-27: Regge-plus-resonance (RPR-2+D13) [Corthals et al,prc73(26)4527] Regge97: Regge model, fit to SLAC data [Guidal et al,npa627(1997)645] Regge211: Regge m., fit to CLAS data 2.6 < W < 3 GeV [De Cruz etal,phd.t.,ghent,211] RPR: Regge-plus-resonance, our fit to CLAS and LEPS cross sections for W < 2.5 GeV. Normalization discrepancy of SLAC and CLAS data [Dey and Meyer, arxiv: [hep-ph]] dσ/dω [µb/sr] W = 2.24 GeV W = 3.2 GeV W = 3.99 GeV SLAC CLAS LEPS SAPHIR E94-17 RPR-27 Regge97 Regge211 RPR c.m c.m c.m. P. Bydžovský (NPI Řež) Theory of the electromagnetic production HYP12, October 1-5, / 23

17 W-dependence of σ T at small kaon angles Regge211,RPR Regge97 problem of data discrepancy dσ/dω [µb/sr] dσ/dω [µb/sr] CLAS9 W = 2.4 GeV E lab = 1.74 GeV γ CLAS9 CLAS9 CLAS9 E lab = 2.19 GeV γ Elab = 2.9 GeV γ E lab = 3.81 GeV γ W = 2.52 GeV W = 2.84 GeV W = 2.24 GeV SLAC69 SLAC69 SLAC69 SLAC69 E lab γ = 5 GeV E lab γ = 8 GeV E lab = 11 GeV E lab = 16 GeV γ γ W = 3.2 GeV W = 3.99 GeV W = 4.64 GeV W = 5.56 GeV Regge97 RPR Regge P. Bydžovský (NPI Řež) Theory of the electromagnetic production HYP12, October 1-5, / 23

18 Quasi-photoproduction on proton (very small Q 2 ) Extension of the photoproduction amplitude to electroproduction (Q 2 ) electromagnetic form factors couplings of baryon fields to the longitudinal mode of virtual photon can be fixated from data on very small Q 2 (e.m.f.fs. 1, ) MAMI data: Q 2 =.36 (GeV/c) 2, W = 1.75 GeV, ɛ =.4, Φ K = are consistent with the photoproduction CLAS and SAPHIR data σ full is dominated by σ T? predictions without the longitudinal couplings, the Saclay-Lyon model σ full = σ T + ɛ σ L + ɛσ TT + 2ɛ(1 + ɛ)σ TL dσ / dω [nb/sr] σ LT σ TT Saclay-Lyon model σ T p(e,e K + )Λ full σ T σ L σ TT σ LT c.m. [deg] σ L P. Bydžovský (NPI Řež) Theory of the electromagnetic production HYP12, October 1-5, / 23

19 MAMI data P. Achenbach et al (A1 Collaboration), Eur.Phys.J.A 48(212)14 P. Achenbach et al, Nucl.Phys.A 881 (212) 187 KM reduced: the longitudinal couplings are switched off KM new: new version of Kaon-MAID with weaker longitudinal couplings, e.g for P 13 (172) and for D 13 (1895) T. Mart and L. Tiator, 211 c.m. dσ v / dω K [nb/sr] MAMI SAPHIR (Q 2 =) CLAS (Q 2 =) KM new KM KM reduced SL p(e,e K + )Λ c.m. dσ v / dω K [nb/sr] p(e,e K + )Λ cos c.m. =.35 MAMI SAPHIR CLAS KM KM reduced SL KM new cos c.m Q 2 [(GeV/c) 2 ] P. Bydžovský (NPI Řež) Theory of the electromagnetic production HYP12, October 1-5, / 23

20 Summary and outlook data on the K photoproduction off deuteron and electroproduction of hypernuclei (DWIA calculations) can be used to test the isobar and RPR models at very small kaon angles; MAMI data at very small Q 2 around W = 1.75 GeV says that near the photoproduction point σ(electroproduction) σ(photoproduction) which suggest that in the isobar model the longitudinal couplings of the virtual photon to baryon fields are not too much important; Regge-plus-resonance model is a promising tool for description of the forward-angle kaon photoproduction (covers a large energy region) application in the DWIA calculations of the hypernucleusproduction cross sections. P. Bydžovský (NPI Řež) Theory of the electromagnetic production HYP12, October 1-5, / 23

21 Slávek Sotona - the founder member of the hypernuclear group in NPI Řež in 197 s together with Jan Žofka ( 1991) and Lubomír Majling; - with Žofka, Majling, Mareš and Richter won the Award of the Czechoslovak Academy of Sciences in 1992; - organizer of the conferences Mesons and Light Nuclei 1995 (Stráž pod Ralskem), 1998, 21. Dealt with meson and electron induced production of hyperons and hypernuclei in collaboration with H. Bando, V.N. Fetisov and R.A. Eramzhian. P. Bydžovský (NPI Řež) Theory of the electromagnetic production HYP12, October 1-5, / 23

22 Sla vek was a member of the Jefferson Lab Hall A Collaboration - experiment E High resolution 1p shell Hypernuclear Spectroscopy : proposal and analysis of results [Iodice et al, PRL99(27)5251; Cusanno et al, PRL13(29)2251]; a new proposal E Intensive cooperation with the group in ISS Rome. A member of NKS/NKS2 Collaboration in Department of Physics in Tohoku University [Watanabe et al, PLB661(27)269; Tsukada et al, PRC78(28)6522]. Long-term cooperation with Toshio Motoba and Kazunori Itonaga [Motoba et al, Prog.Theor.Phys.Suppl.117(1994)123; Itonaga et al, PRC49(1994)145; Motoba et al, Prog.Theor.Phys.Suppl.185(21)185; Bydzovsky et al, NPA883(212)199]. Indian-Summer School, 26 P. Bydz ovsky (NPI R ez ) Hall A in Jefferson Laboratory, 25 Theory of the electromagnetic production HYP12, October 1-5, / 23

23 Slávek s friends and closest collaborators Claudio Ciofi degli Atti János Révai Salvatore Frullani Toshio Motoba Kazunori Itonaga Ota Richter Osamu Hashimoto Franco Garibaldi P. Bydžovský (NPI Řež) Theory of the electromagnetic production HYP12, October 1-5, / 23