Microscopic Model to Nucleon Spectra in Hypernuclear Non Mesonic Weak Decay

Transcription

1 The11 th International Conference on Hypernuclear and Strange Particle Physics (Hyp-XI), Barcelona, Spain. October 2, 2012 p. 1/1 Microscopic Model to Nucleon Spectra in Hypernuclear Non Mesonic Weak Decay E. Bauer Departamento de Física, Universidad Nacional de La Plata, and Instituto de Física La Plata, CONICET, La Plata 1900, Argentina

2 The11 th International Conference on Hypernuclear and Strange Particle Physics (Hyp-XI), Barcelona, Spain. October 2, 2012 p. 2/1 Outline of the talk Introduction to Λ-Weak Decay in Hypernuclei

3 The11 th International Conference on Hypernuclear and Strange Particle Physics (Hyp-XI), Barcelona, Spain. October 2, 2012 p. 2/1 Outline of the talk Introduction to Λ-Weak Decay in Hypernuclei Theoretical Framework: the Microscopic Model

4 The11 th International Conference on Hypernuclear and Strange Particle Physics (Hyp-XI), Barcelona, Spain. October 2, 2012 p. 2/1 Outline of the talk Introduction to Λ-Weak Decay in Hypernuclei Theoretical Framework: the Microscopic Model Results & Comparison with Data

5 The11 th International Conference on Hypernuclear and Strange Particle Physics (Hyp-XI), Barcelona, Spain. October 2, 2012 p. 2/1 Outline of the talk Introduction to Λ-Weak Decay in Hypernuclei Theoretical Framework: the Microscopic Model Results & Comparison with Data Conclusions

6 The11 th International Conference on Hypernuclear and Strange Particle Physics (Hyp-XI), Barcelona, Spain. October 2, 2012 p. 3/1 Weak decay modes ofλ-hypernuclei Mesonic decay, Γ M = Γ π +Γ π 0, Non-Mesonic decay, Γ NM = Γ NM (ΛN nn) ΓM N Λ π ΓNM N π, ρ,... Λ N N dominant in free space blocked by Pauli Principle only in hypernuclei dominant for medium and heavy hypernuclei Γ T = Γ M +Γ NM

7 The11 th International Conference on Hypernuclear and Strange Particle Physics (Hyp-XI), Barcelona, Spain. October 2, 2012 p. 4/1 Non-mesonic weak decay One-nucleon induced: Γ 1 (ΛN nn), Γ 1 Γ n (Λn nn)+γ p (Λp np) Two-nucleon induced: Γ 2 (ΛNN nnn), Γ 2 Γ nn (Λnn nnn)+γ np (Λnp nnp)+γ pp (Λpp npp) Γ1 N Λ V ΛN NN N N Γ2 N N N V ΛN NN V NN Λ N N Γ NM = Γ 1 +Γ 2

8 The11 th International Conference on Hypernuclear and Strange Particle Physics (Hyp-XI), Barcelona, Spain. October 2, 2012 p. 5/1 The non-mesonic decay width Fermi Golden Rule: Γ NM = f f V ΛN NN 0 2 δ(e f E 0 )

9 The11 th International Conference on Hypernuclear and Strange Particle Physics (Hyp-XI), Barcelona, Spain. October 2, 2012 p. 5/1 The non-mesonic decay width Fermi Golden Rule: Γ NM = f f V ΛN NN 0 2 δ(e f E 0 ) 0 :hypernuclear ground state, with energy E 0

10 The11 th International Conference on Hypernuclear and Strange Particle Physics (Hyp-XI), Barcelona, Spain. October 2, 2012 p. 5/1 The non-mesonic decay width Fermi Golden Rule: Γ NM = f f V ΛN NN 0 2 δ(e f E 0 ) 0 :hypernuclear ground state, with energy E 0 V ΛN NN : two-body weak transition potential, including the exchange of the complete octets of pseudoscalar and vector mesons (π, η, K, ρ, ω and K )

11 The11 th International Conference on Hypernuclear and Strange Particle Physics (Hyp-XI), Barcelona, Spain. October 2, 2012 p. 5/1 The non-mesonic decay width Fermi Golden Rule: Γ NM = f f V ΛN NN 0 2 δ(e f E 0 ) 0 :hypernuclear ground state, with energy E 0 V ΛN NN : two-body weak transition potential, including the exchange of the complete octets of pseudoscalar and vector mesons (π, η, K, ρ, ω and K ) f : final state, with energy E f f = 2p1h for Γ 1 f = 3p2h for Γ 2

12 The11 th International Conference on Hypernuclear and Strange Particle Physics (Hyp-XI), Barcelona, Spain. October 2, 2012 p. 6/1 Introduction to the Microscopic Model A simple model, N n = 2 Γ n + Γ p N p = Γ p N nn = Γ n N np = Γ p from these expressions one can write, Γ n Γ p = 1 2 (N n N p 1) or Γ n Γ p = N nn N np The next step is to add Γ 2 Γ nn +Γ np +Γ pp, where, Γ Γ/Γ NM

13 The11 th International Conference on Hypernuclear and Strange Particle Physics (Hyp-XI), Barcelona, Spain. October 2, 2012 p. 7/1 AddingΓ 2, N n = 2 Γ n + Γ p +3 Γ nn +2 Γ np + Γ pp, N p = Γ p + Γ np +2 Γ pp, N nn = Γ n +3 Γ nn + Γ np, N np = Γ p +2 Γ np +2 Γ pp, N pp = Γ pp. Up to this point, the decay widths (Γ s) can be extracted straightaway from the spectra. But now we add FSI: N n = 2 Γ n + Γ p +...+FSI,

14 The11 th International Conference on Hypernuclear and Strange Particle Physics (Hyp-XI), Barcelona, Spain. October 2, 2012 p. 8/1 Microscopic model forn N andn NN N n = 2 Γ n + Γ p +3 Γ nn +2 Γ np + Γ pp + N p = Γ p + Γ np +2 Γ pp + i,i ;j N nn = Γ n +3 Γ nn + Γ np + i,i ;j N np = Γ p +2 Γ np +2 Γ pp + N pp = Γ pp + i,i ;j i,i ;j N j(pp) Γi,i j. i,i ;j N j(p) Γi,i j, N j(nn) Γ i,i j, N j(np) Γi,i j, N j(n) Γi,i j, where, Γ Γ/Γ NM From E.B. Nucl. Phys. A796 (2007) 11

15 The11 th International Conference on Hypernuclear and Strange Particle Physics (Hyp-XI), Barcelona, Spain. October 2, 2012 p. 9/1 Employed Feynman diagrams Without FSI f = 2p1h D E With FSI f = 2p1h or f = 3p2h pp pp hh hh ph ph

16 The11 th International Conference on Hypernuclear and Strange Particle Physics (Hyp-XI), Barcelona, Spain. October 2, 2012 p. 10/1 Thepp-Feynman diagram, expressed in terms of it sum of Goldstone diagrams: pp Γ 1,1 2 Γ 2 Γ 1, Γ2,1 2 +

17 The11 th International Conference on Hypernuclear and Strange Particle Physics (Hyp-XI), Barcelona, Spain. October 2, 2012 p. 11/1 FSI from theδ(1232), These are Goldstone diagrams, (a) (b) (c) (d) (e) (f)

18 The11 th International Conference on Hypernuclear and Strange Particle Physics (Hyp-XI), Barcelona, Spain. October 2, 2012 p. 12/1 Results & Comparison with Data V ΛN NN is represented by the exchange of the π, η, K, ρ, ω and K mesons, with the coupling constants and cut off parameters deduced from the Nijmegen soft core interaction NSC97f of V. G. J. Stoks and Th. A. Rijken, Phys. Rev. C 59 (1999) 3009; Th. A. Rijken, V. G. J. Stoks and Y. Yamamoto, ibid. 59 (1999) 21. For V NN NN we adopt the Bonn potential (with the exchange of π, ρ, σ and ω mesons), R. Machleidt, K. Holinde and Ch. Elster; Phys. Rep. 149 (1987) 1. For V NN ΔN we have used a V π+ρ -potential with the addition of a g ΔN -Landau-Migdal parameter. (See for instance, E. Oset, H. Toki and W. Weise, Phys. Rept. 83 (1982) 281). We have used, g ΔN = 0.4.

19 The11 th International Conference on Hypernuclear and Strange Particle Physics (Hyp-XI), Barcelona, Spain. October 2, 2012 p. 13/1 Single nucleon spectra N with FSI 1N + 2N without FSI 1N+2N+ with FSI KEK-E508 KEK-E N without FSI 1N+2N with FSI 1N+2N+ with FSI KEK-E508 FINUDA BNL-CERN N n 0.15 N p T n (MeV) T p (MeV) KEK-E508: J.H. Kim et al., Phys. Rev. C 68 (2003) ; KEK-E369: S. Okada et al., Phys. Lett. B 597 (2004) 249. FINUDA: M. Agnello et al. (FINUDA Collaboration), Phys. Lett. B 685 (2010) 247. BNL-CERN: A. Montwill et al., Nucl. Phys. A 234 (1974) 413.

20 The11 th International Conference on Hypernuclear and Strange Particle Physics (Hyp-XI), Barcelona, Spain. October 2, 2012 p. 14/1 Opening angle distribution ofnn andnp pairs N without FSI 1N+2N with FSI and T N th =30 MeV 1N without FSI 1N+2N with FSI and T N th =30 MeV N+2N+ with FSI and T N th =30 MeV KEK-E N+2N+ with FSI and T N th =30 MeV KEK-E508 N nn N np cos θ nn cos θ np KEK-E508: M. J. Kim et al., Phys. Lett. B 641 (2006) 28.

21 The11 th International Conference on Hypernuclear and Strange Particle Physics (Hyp-XI), Barcelona, Spain. October 2, 2012 p. 15/1 Momentum correlation spectra,p NN p N + p N N without FSI 1N+2N with FSI 1N+2N+ with FSI KEK-E N without FSI 1N+2N with FSI 1N+2N+ with FSI KEK-E508 N nn p nn (MeV/c) N np p np (MeV/c) KEK-E508: M. Kim et al., Phys. Rev. Lett. 103 (2009)

22 The11 th International Conference on Hypernuclear and Strange Particle Physics (Hyp-XI), Barcelona, Spain. October 2, 2012 p. 16/1 Momentum correlation spectra 0.1 back-to-back without back-to-back with non back-to-back without non back-to-back with KEK-E508 back-to-back KEK-E508 non back-to-back N nn +N np p NN (MeV/c) Momentum correlation spectra for the sum of the nn and np pair numbers for the back to back (cosθ NN < 0.7) and non back to back kinematics (cosθ NN > 0.7). KEK-E508: H. Bhang and M. Kim, private communication.

23 The11 th International Conference on Hypernuclear and Strange Particle Physics (Hyp-XI), Barcelona, Spain. October 2, 2012 p. 17/1 Conclusions A microscopic approach including GSC and FSI on the same footing is used to evaluate the nucleon emission spectra in non mesonic weak decay of hypernuclei.

24 The11 th International Conference on Hypernuclear and Strange Particle Physics (Hyp-XI), Barcelona, Spain. October 2, 2012 p. 17/1 Conclusions A microscopic approach including GSC and FSI on the same footing is used to evaluate the nucleon emission spectra in non mesonic weak decay of hypernuclei. The approach includes for the first time many body terms introduced by the nucleonic resonance Δ(1232).

25 The11 th International Conference on Hypernuclear and Strange Particle Physics (Hyp-XI), Barcelona, Spain. October 2, 2012 p. 17/1 Conclusions A microscopic approach including GSC and FSI on the same footing is used to evaluate the nucleon emission spectra in non mesonic weak decay of hypernuclei. The approach includes for the first time many body terms introduced by the nucleonic resonance Δ(1232). QIT play a key role: in the single nucleon emission spectra they are responsible for moving intensity from the high energy region to the low energy region, while in the opening angle distribution of nucleon pairs the strong reduction of the back to back peak is entirely due to QIT.

26 The11 th International Conference on Hypernuclear and Strange Particle Physics (Hyp-XI), Barcelona, Spain. October 2, 2012 p. 17/1 Conclusions A microscopic approach including GSC and FSI on the same footing is used to evaluate the nucleon emission spectra in non mesonic weak decay of hypernuclei. The approach includes for the first time many body terms introduced by the nucleonic resonance Δ(1232). QIT play a key role: in the single nucleon emission spectra they are responsible for moving intensity from the high energy region to the low energy region, while in the opening angle distribution of nucleon pairs the strong reduction of the back to back peak is entirely due to QIT. Among the Goldstone diagrams incorporating the Δ, the relevant ones are QIT and turn out to produce a sensitive reduction of the spectra.

27 The11 th International Conference on Hypernuclear and Strange Particle Physics (Hyp-XI), Barcelona, Spain. October 2, 2012 p. 17/1 Conclusions A microscopic approach including GSC and FSI on the same footing is used to evaluate the nucleon emission spectra in non mesonic weak decay of hypernuclei. The approach includes for the first time many body terms introduced by the nucleonic resonance Δ(1232). QIT play a key role: in the single nucleon emission spectra they are responsible for moving intensity from the high energy region to the low energy region, while in the opening angle distribution of nucleon pairs the strong reduction of the back to back peak is entirely due to QIT. Among the Goldstone diagrams incorporating the Δ, the relevant ones are QIT and turn out to produce a sensitive reduction of the spectra. Discrepancies with experiment remain, but are relegated to spectra involving protons.

28 The11 th International Conference on Hypernuclear and Strange Particle Physics (Hyp-XI), Barcelona, Spain. October 2, 2012 p. 18/1 The next steps: In M. Agnello et al. (FINUDA Collaboration) Nucl. Phys. A881 (2012) 322, the first triple coincidence measurement has been reported.

29 The11 th International Conference on Hypernuclear and Strange Particle Physics (Hyp-XI), Barcelona, Spain. October 2, 2012 p. 18/1 The next steps: In M. Agnello et al. (FINUDA Collaboration) Nucl. Phys. A881 (2012) 322, the first triple coincidence measurement has been reported. Evaluation of Γ 3 Γ(ΛN 1 N 2 N 3 nn 1 N 2 N 3 ) to get some insight on the importance of four particles emission.

30 The11 th International Conference on Hypernuclear and Strange Particle Physics (Hyp-XI), Barcelona, Spain. October 2, 2012 p. 18/1 The next steps: In M. Agnello et al. (FINUDA Collaboration) Nucl. Phys. A881 (2012) 322, the first triple coincidence measurement has been reported. Evaluation of Γ 3 Γ(ΛN 1 N 2 N 3 nn 1 N 2 N 3 ) to get some insight on the importance of four particles emission. Evaluation of the three particle coincidence spectra.

31 The11 th International Conference on Hypernuclear and Strange Particle Physics (Hyp-XI), Barcelona, Spain. October 2, 2012 p. 19/1 Asymmetry Parameter from Λp np TABLE I: Asymmetry parameter for 12 Λ C. Nijmegen89 Nijmegen97f E th (MeV) Asymmetry OME OME+2π OME OME+2π 0 a 1N Λ a 1N+2N Λ a 1N+FSI Λ a 1N+2N+FSI Λ a 1N+2N Λ a 1N+FSI Λ a 1N+2N+FSI Λ a 1N+2N Λ a 1N+FSI Λ a 1N+2N+FSI Λ KEK E ± KEK-E508: T. Maruta et al., Eur. Phys. J. A 33 (2007) 255.