Role of the N (2080) resonance in the γp K + Λ(1520) reaction

Transcription

1 Role of the N (2080) resonance in the γp K + Λ(1520) reaction Ju-Jun Xie ( ) IFIC, University of Valencia, Spain Collaborator: Juan Nieves Phys. Rev. C 82, Nstar2011, Jlab, USA, 05/19/2011 1

2 Outline 1. Introduction 2. Our approach Effective Lagrangian method. We will take into account the t channel K exchange, the contribution of N and N (2080) in the s channel, and a contact term. 3. Results 4. Conclusions Ju-Jun Xie ( Nstar2011, Jlab, USA, 05/19/2011 2

3 Introduction 1. The Λ(1520) ( Λ ) photoproduction in the γp K + Λ reaction is an interesting tool to gain a deeper understanding of the interaction among strange hadrons and also on the nature of baryon resonances. 2. This reaction has been examined at photon energies below 2.4 GeV in the Spring-8 LEPS experiment. For an invariant γp mass around 2.11 GeV, a bump structure in the differential cross section at forward K + angels was reported, which might hint to a sizable contribution from nucleon resonances in the s channel. ( N. Muramatsu et al. (LEPS Collaboration), Phys. Rev. Lett. 103, (2009); H. Kohri et al. (LEPS Collaboration), Phys. Rev. Lett. 104, (2010). ) 3. Several phenomenological models, that used an effective hadron Lagrangian approach, can reproduce the high energy data reasonable well, but they fail to describe the bump structure in the new LEPS data. Ju-Jun Xie ( Nstar2011, Jlab, USA, 05/19/2011 3

4 Why N (2080) 1. The information about nucleon resonances in the relevant mass region ( 2.1) GeV is scarce. 1), N (2080), J P = 3/2, status: **; 2), N (2090), J P = 1/2, status: *; 3), N (2100), J P = 1/2 +, status: *. 2. We rely on theoretical predictions based in a quark model (QM) for baryons. The two-star D wave J P = 3/2 N (2080) ( N ) is predicted to have visible contributions to the γp K + Λ reaction. ( S. Capstick, Phys. Rev. D 46, 2864 (1992); S. Capstick, and W. Roberts, Phys. Rev. D 58, (1998).) 3. The evidence of its existence is poor or only fair. Its total decay width and branching ratios are not experimentally known, either. Thus, the LEPS measurements could be used to determine some of the properties of this resonance. Ju-Jun Xie ( Nstar2011, Jlab, USA, 05/19/2011 4

5 Our Model γ K + k 1 λ p 1 p k 2 s p K q p 2 s Λ Λ(1520) p N (2080) We consider the K exchange in the t channel, the contribution of N and N (2080) in the s channel, and a contact term. Ju-Jun Xie ( Nstar2011, Jlab, USA, 05/19/2011 5

6 Interaction Lagrangian Densities L γkk = ie(k µ K + K + µ K )A µ, (1) L KpΛ = g KNΛ Λ µ ( µ K )γ 5 p + h.c., (2) m K L γpp = e p ( /A κ p 2M N σ µν ( ν A µ ) ) p + h.c., (3) L γkpλ = ie g KNΛ m K Λ µ A µ K γ 5 p + h.c., (4) L γnn = ief 1 2m N N µγ ν F µν N ef 2 (2m N ) 2 N µf µν ν N + h.c., (5) L KΛ N = g 1 Λ m µγ 5 γ α ( α K)N µ + K ig 2 Λ µγ 5 ( µ ν K) N ν + h.c., (6) m 2 K Ju-Jun Xie ( Nstar2011, Jlab, USA, 05/19/2011 6

7 Rarita-Schwinger spinor for Λ(1520) and N (2080) and, s u ρ (p, s)ū σ (p, s) = /p + M 2M P ρσ(p), (7) P ρσ (p) = g ρσ γ ργ σ + 2 3M 2p ρp σ + 1 3M (γ ρp σ γ σ p ρ ). (8) Ju-Jun Xie ( Nstar2011, Jlab, USA, 05/19/2011 7

8 Scattering amplitudes The reduced A µν i it i = ū µ (p 2, s Λ )A µν i u(k 2, s p )ɛ ν (k 1, λ) (9) amplitudes read: A µν t = e g KNΛ 1 m K q 2 m 2 q µ (q ν p ν 1 )γ 5 f c, (10) K A µν s = e g KNΛ 1 m K s MN 2 p µ 1 γ 5{ /k1 γ ν f s + ( /k 2 + M N )γ ν f c +( /k 1 + /k 2 + M N )i κ p σ νρ k ρ 2M 1 f } s, (11) N A µν c = e g KNΛ m K g µν γ 5 f c, (12) /k 1 + /k 2 + M N A µν R = γ 5( g 1 /p 1 g µρ g 2 m K m 2 p µ 1 pρ 1 ) K s MN 2 P ρσ + im N Γ N ( ef1 (k1 σ 2m γν g σν /k 1 ) + ef 2 N (2m N ) 2(kσ 1 kν 2 gσν k 1 k 2 ) ) f R, (13) Ju-Jun Xie ( Nstar2011, Jlab, USA, 05/19/2011 8

9 Form factors We take the following parameterization for the four-dimensional form-factors f i = Λ 4 i Λ 4 i + (q2 i M 2 i f c = f s + f t f s f t, and 1. We respect gauge invariance. )2, i = s, t, R (14) q 2 s = q 2 R = s, q2 t = q2, M s = M N, M R = M N, M t = m K. (15) 2. Those form factors have been widely used in the literature. (K. Ohta, Phys. Rev. C 40, 1335 (1989); H. Haberzettl et al., Phys. Rev. C 58, R40(1998).) 3. We will consider different cut-off values for the background and resonant terms, i.e. Λ s = Λ t Λ R. Ju-Jun Xie ( Nstar2011, Jlab, USA, 05/19/2011 9

10 Parameters 1. g KNΛ = 10.5, determined from the Λ pk decay width. 2. N Nγ coupling constants f 1 and f 2, obtained from the N helicity amplitudes A 1/2 and A 3/2 ; A p 1/2 = e 6 kγ 12 M N M N kγ M N A p 3/2 = e 2 4M N M N where k γ = (MN 2 MN 2 )/(2M N ). ( ( f 1 + f 2 4MN 2 M N (M N + M N ) f 1 + f 2 4M N (M N + M N ) ) ), (16), (17) 3. The strong couplings g 1, g 2 and the cut-off parameters Λ s = Λ t and Λ R are free parameters, and we will fit them to the new LEPS data. Ju-Jun Xie ( Nstar2011, Jlab, USA, 05/19/

11 Cross Sections The differential cross section, in the center of mass frame (c.m.), for a polarized photon beam reads, dσ = k1 C.M. p C.M. ( 1 M N M Λ 1 ) dω C.M. 4π 2 (s MN 2 T 2 )2 2 s p,s Λ = 1 dσ 2π d(cos θ C.M. ) {1 Σ cos 2 (φ C.M. α)} (18) ε γ α Y φ X p 1 θ γ, k Z Ju-Jun Xie ( Nstar2011, Jlab, USA, 05/19/

12 We have performed three different fits. Input Parameters Fit A Fit B Fit C A p 1/2 [GeV 1/2 ] ± ± A p 3/2 [GeV 1/2 ] ± ± ef ± ± 0.07 ef ± ± 0.07 M N [MeV] 2080 Γ N [MeV] 300 Ju-Jun Xie ( Nstar2011, Jlab, USA, 05/19/

13 Fitted Parameters g ± ± ± 0.3 g ± ± ± 1.8 Λ s = Λ t [MeV] 613 ± ± ± 2 Λ R [MeV] 990 ± ± ± 55 ef ± ef ± M N [MeV] 2138 ± ± 8 Γ N [MeV] 168 ± ± 24 χ 2 /dof Ju-Jun Xie ( Nstar2011, Jlab, USA, 05/19/

14 Predicted Observables A p 1/2 [GeV 1/2 ] ± A p 3/2 [GeV 1/2 ] ± Γ N Λ K [MeV] 110 ± ± ± 7 Γ N Λ K Γ N [%] 36 ± ± ± 2.8 Γ N Λ K = + p C.M. 1 M N (E Λ M Λ ) 18πM 2 Λ p C.M. { p C.M. 1 4 g2 2 m 4 K (2E Λ M Λ ) (M N + M Λ ) g 1 g 2 ( MN + M Λ M N M N m 3 K ) 2 (E 2 Λ E Λ M Λ M 2 Λ ) g2 1 m 2 K } (19) Ju-Jun Xie ( Nstar2011, Jlab, USA, 05/19/

15 Numerical Results cos c.m. = cos c.m. =0.75 d /dcos c.m. ( b) 0.5 d /dcos c.m. ( b) E (GeV) E (GeV) 1.0 cos c.m. = cos c.m. =0.95 d /dcos c.m ( b) 0.5 d /dcos c.m. ( b) E (GeV) E (GeV) Results have been obtained from the eight parameter fit C. Ju-Jun Xie ( Nstar2011, Jlab, USA, 05/19/

16 Numerical Results (Fit C) d /dcos c.m. ( b) o < c.m. <150 o E (GeV) d /dcos c.m. ( b) o < c.m. <180 o E (GeV) 1. Blue horizontal line shaded region (right panel), θ c.m. = ; 2. Blue horizontal line shaded region (left panel), θ c.m. = ; 3. red vertical line shaded region in both panels, θ c.m. = Ju-Jun Xie ( Nstar2011, Jlab, USA, 05/19/

17 Numerical Results (Fit C) GeV< E <2.4 GeV d /dcos c.m. ( b) c.m. (degrees) 1. Red horizontal lines, E γ = 1.9 GeV; 2. Blue vertical lines, E γ = 2.4 GeV. Ju-Jun Xie ( Nstar2011, Jlab, USA, 05/19/

18 Polar angle average photon-beam asymmetry Σ E (GeV) Σ = dσ d(cos θ C.M. ) Σ(cos θ C.M., E γ)d(cos θ C.M. ) dσ d(cos θ C.M. ) d(cos θ C.M. ), (20) Ju-Jun Xie ( Nstar2011, Jlab, USA, 05/19/

19 Conclusions 1. We have studied the γp Λ K + reaction at low energies within a effective Lagrangian approach. In particular, we have paid an special attention to a bump structure in the differential cross section at forward K + angles reported in the recent SPring-8 LEPS experiment. Starting from the background contributions studied in previous works, we have shown that this bump might be described thanks to the inclusion of the nucleon resonance N (2080) (spin-parity J P = 3/2 ). We have fitted its mass, width and hadronic Λ K + and electromagnetic N Nγ couplings to data. 2. We have found that this resonance would have a large decay width into Λ K, which will be compatible with the findings of the QM approach of Capstick and collaborators. 3. Our predictions for the backward angles and the polar angle average photonbeam asymmetry are not so good when compared with the experimental data. Ju-Jun Xie ( Nstar2011, Jlab, USA, 05/19/

20 Thank you very much for your attention!! Ju-Jun Xie ( Nstar2011, Jlab, USA, 05/19/