Electroproduction of the Λ hyperon on the proton

Transkript

1 Electroproduction of the Λ hyperon on the proton Workshop on Perspectives of high resolution hypernuclear spectroscopy at JLab Petr Bydžovský, Nuclear Physics Institute, Řež, Czech Republic electroproduction e + p e + K + + Λ e + p e + K + + Σ e + p e + K + Σ + e + n e + K + Λ e + n e + K + Σ e + n e + K + + Σ I KΛ = 1 2 I KΣ = 1, I KΛ = 1 2 I KΣ = 1, (virtual)photoproduction a simpler process γ (v) + N K + Y P. Bydžovský (NPI Řež) Electroproduction of the Λ hyperon JLab, May 27 29, / 19

2 Description of electroproduction the electromagnetic part of the process is well known. the coupling constant is small α = e2 2π = the one-photon approximation: e e K N Y e e γ v N Y K no Coulomb distortion of e and e important for electroproduction on heavy nuclei leptonic and hadronic parts can be separated photoproduction is not a limit case of electroproduction (q 2 ) P. Bydžovský (NPI Řež) Electroproduction of the Λ hyperon JLab, May 27 29, / 19

3 kinematics E e, E e, θ e,, Φ K ) 1, Q 2 = q 2, ɛ = (1 + 2 q2 q tan 2 θe 2 2 s = (q + pp ) 2, t = (q p K ) 2, Φ K s = W ( Wthr, 2.6 ) GeV, W thr = 1.69 for KΛ the unpolarized cross section d 5 [ σ dσt de e dω = Γ + ɛ dσ L + ɛ dσ TT cos 2Φ K + 2ɛ(1+ɛ) dσ ] TL cos Φ K e dω K dω K dω K dω K dω K in Laboratory frame: ^ y ^x p' e θ e ^z p e Scattering (Leptonic) Plane γ q Φ θ p p Λ K Reaction (Hadronic) Plane K K P. Bydžovský (NPI Řež) Electroproduction of the Λ hyperon JLab, May 27 29, / 19

4 Motivation Which degrees of freedom are relevant? partons hadrons non perturbative regime of QCD: quark models isobar models many opened channels channel couplings, unitarity, final-state interaction multi-channel single-channel analysis description of the background part: f = f bgr + f res isobar Regge approach effective Lagrangian approach properties of baryon resonances in the 3rd resonance region (E lab γ parameters, structure, existence (missing states) SU(3) f symmetry: g πnn g KΛN dynamics of the process important resonances N, Y, K a satisfactory description of the process at small angles an input in hypernucleus calculations plenty of new experimental data studying all channels is important neutron target, production of K 1 GeV) P. Bydžovský (NPI Řež) Electroproduction of the Λ hyperon JLab, May 27 29, / 19

5 K + production in the small-angle region the elementary amplitude is an input in DWIA a good description of the elementary process is important for reliable predictions of the hypernucleus-production cross sections DWIA (frozen-nucleon approx.): Ψ H i χ γ χ K J µ (i) Ψ A J µ elementary hadron current in lab frame the main contribution of J µ is from a small region dσ / dω [µb/sr] DWIA p(γ, K + )Λ W = 2.24 GeV isobar&rpr models c.m. [deg] vice versa: the hypernucleus-production cross sections can be used to test the elementary models in the small-angle region P. Bydžovský (NPI Řež) Electroproduction of the Λ hyperon JLab, May 27 29, / 19

6 Angular dependence of the hypernucleus cross section electroproduction of 16 N Λ (E lab γ = 2.21 GeV, θe lab = 6 o ) magnitudes differ by factor of 1 generally a steeply decreasing dependence, the slope depends on the spin (J) the angular behaviour depends on the spin structure of the elementary amplitude at small more detailed information about the amplitude 16 O(e,e K + ) 16 N Λ E i =3.654 GeV, E f =1.445 GeV, θ e =6 16 O(e,e K + ) 16 N Λ E i =3.654 GeV, E f =1.445 GeV, θ e =6 SLA1 E=.3 MeV, J=1 - state 3. J=1 +, 2 + states at E approx. 11 MeV J= KMAID 1x 2. nb/sr 2 /GeV nb/sr 2 /GeV J=1 + KMAID 1x SLA e e P. Bydžovský (NPI Řež) Electroproduction of the Λ hyperon JLab, May 27 29, / 19

7 Methods of description single-channel analysis Isobar model effective hadronic Lagrangian description Adelseck-Saghai, Williams-Ji-Cotanch, Saclay-Lyon, Kaon-MAID, Gent isobar, Maxwell Regge-plus-resonance model hybrid isobar-regge description Gent group: RPR-27, RPR-211 multipole analysis Mart and Sulaksono multi-channel analysis unitary isobar approach (coupled channels) Giessen, Bonn-Gatchina, Dubna-Mainz-Taipei, Julia-Diaz et al, Usov et al, Shyam et al partial-wave analysis SAID chiral unitary framework chiral Lagrangian, coupled channels, threshold region Borasoy et al Quark model resonances included; Close, Zhenping Li et al P. Bydžovský (NPI Řež) Electroproduction of the Λ hyperon JLab, May 27 29, / 19

8 Isobar model meson-baryon FSI is neglected (channel couplings, re-scattering) one-channel approximation: T = V + V G t violation of unitarity effective coupling constants include a part of the FSI effects driving term V : effective hadron Lagrangian (fields, couplings, resonances, form factors) tree-level perturbation expansion s-, t-, and u-channel exchanges; contact term (gauge invariance) a set of relevant resonances in the intermediate states has to be selected (3rd resonance region: heavy, high-spin, or missing resonances) free parameters are fitted to data ( 1 2 parameters) many sets of resonances with a good χ 2 can be chosen large number of possible models constraints or better data analysis constraints on the models: SU(3) symmetry: 4.4 gknλ / 4π 3..8 g KNΣ / 4π 1.3 crossing symmetry: description of Γ(K p γ Λ) P. Bydžovský (NPI Řež) Electroproduction of the Λ hyperon JLab, May 27 29, / 19

9 Isobar model large contributions to the background part of the amplitude from the Born diagrams are reduced: hadronic form factors gauge invariance a contact term inclusion of a hadron structure dipole, Gauss, multidipole-gauss (high spin) form which cut-off parameter: hard soft? hyperon resonances in u channel which are relevant? hadronic form factors + hyperon exchanges this problem is avoided in the Regge-plus-resonance model the resonant part: s-channel exchanges of the nucleon resonances (resonance width in the Feynman propagator partial restoration of unitarity) electroproduction (Q 2 dependence) electromagnetic form factors (gauge invariance) EVDM (electron scattering data) for γnn and QM for the γnn transitions couplings of baryon fields to the photon transversal modes couplings to the longitudinal mode of the virtual photon ψ N Γγ ν ψ N µ F µν (spin 1/2) ψ ν N Γψ N µ F µν (spin 3/2) the coupling constants have to be determined in electroproduction P. Bydžovský (NPI Řež) Electroproduction of the Λ hyperon JLab, May 27 29, / 19

10 Regge-plus-resonance model Invariant amplitude: M = M bgr (Regge) + M res (isobar) the background part - exchanges of degenerate K and K trajectories M bgr (s, t) = P K Regge(s, t) β K (s, t) + P K Regge(s, t) β K (s, t) the Regge propagator + M p,elec Feyn PK Regge(s, t) (t m 2 K ) PRegge x (s, t) = (s/s αx (t) ) sin π α x (t) π α x Γ(1 + α x (t)) { } 1 iπαx e (t) the Regge trajectories: α x (t) = α x (t m 2 ), x = K, K the residue of the lowest pole γ v K + for t m 2 K P K Regge(s, t) β K (s, t) β K (s, t) t m 2 K p K + Λ only 3 parameters fixed by high-energy data (W>2.6 GeV) P. Bydžovský (NPI Řež) Electroproduction of the Λ hyperon JLab, May 27 29, / 19

11 Electroproduction of hypernuclei dσ/(dω e dω K de e de exc ) [nb/(sr 2 GeV MeV)] C(e,e K + ) , 1 - JLab data DWIA Excitation Energy [MeV] Λ B 1 -, 2 - data: JLab Hall A 2 +, 3 + exp. E94-17 s 1/2Λ p 1/2Λ, p 3/2Λ 2 +, , 1 + E lab γ θ lab e = 2.21 GeV = θ lab K = 6o Q 2 =.18 (GeV/c) 2 calculations with the Saclay-Lyon model in DWIA the elementary hadron current significantly contributes only for small and experiments are done at very small Q 2 predictions of isobar models have to be reliable for small and Q 2 σ TT sin 2, σ TL Q 2 sin, and σ L Q 2 σ T ( photoproduction cross section) should dominate (unpolarized case) the models could be well determined by the photoproduction data P. Bydžovský (NPI Řež) Electroproduction of the Λ hyperon JLab, May 27 29, / 19

12 World data for small and Q 2 kinematics W [GeV] DWIA calculations SAPHIR LEPS CLAS < Q 2 <.3 (GeV/c) 2 CLAS SAPHIR 23 LEPS GRAAL 27 Bleckmann 197 Azemoon 1975 Brauel 1979 Brown 1972 old data E GRAAL c.m. [deg] P. Bydžovský (NPI Řež) Electroproduction of the Λ hyperon JLab, May 27 29, / 19

13 Predictions of isobar and RPR models differ at very small and Q 2 photoproduction (σ T ) dominates the electroproduction cross section σ = σ T + ɛ σ L + ɛσ TT + 2ɛ(1 + ɛ)σ TL, Φ K = SL:.41 = (ɛ=.7, =6, Q 2 =.7 (GeV/c) 2 ) dσ / dω [µb/sr] Bleckmann Brown E94-17 SLA SL KM H2 RPR-1 p(γ, K + )Λ c.m. = 6 o E γ lab [GeV] Electroproduction data: Brown72 [ PRL28(1972)186] σ = σ T + ɛσ L W = GeV Q 2 =.18 and.29 (GeV/c) 2 θk c.m. = 5.9 and 6 E94-17 (JLab, Hall A) W = 2.2 GeV Q 2 =.7 (GeV/c) 2 θk c.m. = 6 Isobar model H2: N S 11 (165), P 11 (171), P 13 (172), D 13 (1895); Y S 1 (167), S 1 (18); hadronic form factors; fit to CLAS and LEPS data Regge-plus-resonance model RPR-1: N S 11 (1535) S 11 (165), P 11 (171), P 13 (172), D 13 (1895); multidipole-gauss hadronic f.f.; fit to CLAS and LEPS data. P. Bydžovský (NPI Řež) Electroproduction of the Λ hyperon JLab, May 27 29, / 19

14 Supression of σ(θ) at small due to the hadronic form factors The proton exchange: contributes to the background part of the amplitude is important contribution at small θk is suppressed by hadronic form factors, e.g. in KM and H2 models is not suppressed in SL and RPR models 1 the proton contribution without h.f.f..1.8 c.m. = 1 o = 5 o = 1 o dσ / dω [µb/sr] with h.f.f. (Λ =.64) g KNΛ = g KNΛ = lab E γ [GeV] lab E γ [GeV] P. Bydžovský (NPI Řež) Electroproduction of the Λ hyperon JLab, May 27 29, / 19

15 The angular dependence by isobar and RPR models H2 and RPR-1 fitted to CLAS and LEPS data a good agreement for 3 < < 15 for < 3 H2 suppressed by the hadronic form factor no suppression of the background part for the RPR-1 and SLA models SLA preffered by the hypernucleus data: DWIA calculations of 12 Λ B, 16 Λ N, and 9 Λ Li dσ / dω [µb/sr] p(γ, K + )Λ W = 2.24 GeV E lab = 2.21 GeV γ Brown72 E94-17 CLAS LEPS SAPHIR RPR-27 RPR-1 SLA RPR-2 H2 RPR-2 was fitted only to < < 9 RPR-1 RPR-2 g KΛp GK V GK T DWIA c.m. [deg] P. Bydžovský (NPI Řež) Electroproduction of the Λ hyperon JLab, May 27 29, / 19

16 The angular dependence by isobar and RPR models dσ / dω [µb/sr] W= 2.16 GeV E γ lab =2.25 GeV CLAS LEPS SAPHIR SL SLA KM H2 Gent A Gent B Gent C RPR c.m. [deg] note inconsistency of CLAS and SAPHIR data at θ 2 H2 fits very well the CLAS data but it fails for < 3 the CLAS data alone cannot fully determine the angular dependence of models Gent A, B, and C differ in the Λ bgr cut :.413, 1.538, and 1.856, respectively the hypernucleus electroproduction cross sections suggest that SL gives right predictions of the elementary cross section a forward-peaked cross section? P. Bydžovský (NPI Řež) Electroproduction of the Λ hyperon JLab, May 27 29, / 19

17 The very forward angular dependence above the resonance region 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) Electroproduction of the Λ hyperon JLab, May 27 29, / 19

18 The angular dependence near threshold by isobar and Giessen models data inconsistency for < 5 the Giessen model is consistent rather with SL than with H2, M2 or KM for < 3 dσ/dω [µb/sr] p(γ, K + )Λ E lab = 1.3 GeV γ W = 1.82 GeV CLAS 25 SAPHIR 23 Bleckmann;Decamp SAPHIR 1998 SLA KM M2 H2 WJC AS1 Giessen c.m. [deg] P. Bydžovský (NPI Řež) Electroproduction of the Λ hyperon JLab, May 27 29, / 19

19 Summary the calculations of hypernucleus electroproduction cross sections in DWIA require a proper understanding of the elementary process in the small and Q 2 kinematical region; predictions of the isobar and Regge-plus-resonance models for the cross sections still significantly differ in this kinematical region due to lack of data; the ample world data (CLAS, SAPHIR, LEPS,..) on the process cover mainly the region > 2 which is not enough to fully determine the angular dependence of the elementary cross section; new good quality data at very small and Q 2 are needed to test the models which then will be able to provide more reliable predictions of the cross sections for electroproduction of hypernuclei; the small-angle data can contribute to revealing dynamics of the models, e.g. the background description, a role of the hyperon resonances, hadronic form factors (Λ cut ). P. Bydžovský (NPI Řež) Electroproduction of the Λ hyperon JLab, May 27 29, / 19