A Quantum Monte Carlo study of the Hyperon-Nucleon interaction

Transcription

1 A Quantum Monte Carlo study of the Hyperon-ucleon interaction Diego Lonardoni Physics Department & I..F.., University of Trento, via Sommarive 14, Povo (T), Italy Collaborators: F. Pederiva (Trento, Italy) P. Armani (Trento, Italy) S. Gandolfi (LAL, US-M) K. E. Schmidt (ASU, US-AZ) G. Co (Lecce, Italy) HYP2012, Barcelona - October 4, 2012

2 Outline Motivations International Conference on Hypernuclear XIand Strange Particle Physics The idea M. Danysz and J. Pniewski, Philosophical Magazine 44, 348 (1953) The method: AFDMC The interaction October 1-5, 2012 Barcelona, Spain Conference Topics Production, structure and decay of hypernuclei Multistrange systems Production of strangeness Interactions of mesons and baryons with strangeness Strangeness in hadron structure Kaonic nuclear systems and strange mesons in nuclei Strangeness in astrophysics and in extreme forms of matter Baryonic heavy flavor systems Present and future facilities Results Conclusions Organizing Committee: Bruno Juliá-Díaz U Barcelona and ICC Volodymyr Magas U Barcelona and ICC Eulogio Oset U València and IFIC Assumpta Parreño U Barcelona and ICC Artur Polls U Barcelona and ICC Àngels Ramos U Barcelona and ICC (chair) Laura Tolós Institut de Ciències de l'espai, CSIC Isaac Vidaña U of Coimbra Contact: hyp2012@icc.ub.edu International Advisory Committee: R. Bertini (Torino) H.C. Bhang (Seoul) T. Bressani (Torino) D.H. Davis (London) F.L. Fabbri (Frascati) V.. Fetisov (Moscow) T. Fukuda (Osaka) A. Gal (Jerusalem) B.F. Gibson (Los Alamos) C. Guaraldo (Frascati) O. Hashimoto (Tohoku) Ed V. Hungerford (Houston) K. Imai (J-PARC) K. Kilian (Julich) T. Kishimoto (Osaka) H. Lenske (Giessen) J. LeRose (JLab) Yu-Gang Ma (Shanghai) J. Mares (Rez) D.J. Millener (BL) T. Motoba (Osaka) T. agae (Kyoto) M. Oka (Tokyo I. T.) E. Oset (Valencia) J. Pochodzalla (Mainz) A. Ramos (Barcelona) R. Schumacher (CMU) L. Tang (Hampton) R.G.E. Timmermans (Groningen) T. Yamazaki (Tokyo) Shi-Lin Zhu (Peking) U UIVERSITAT DE BARCELOA B Design by Mikel ELorduy

3 Motivations I. Vidaña, D. Logoteta, C. Providência, A. Polls, I. Bombaci, EPL 94 (2011) Gravitational Mass [M ] PSR J PSR J Hulse-Taylor H. Ðapo, B.-J. Schaefer, J. Wambach, Phys. Rev. C, 81(2010) Radius R [km] PSR J PSR J Mass MC1-H/ MC1-HF/ MC3-HF/ MC1-H/Y MC1-HF/Y MC2-HF/Y MC3-HF/Y MC4-HF/Y QMC Radius É. Massot, J. Margueron, G. Chanfray, EPL 97 (2012) M/M O R [km] V18+TBF V18+UIX V18+TBF+ESC08 V18+UIX +ESC08 V18+TBF+SC89 V18+UIX +SC ρ c [fm -3 ] H.-J. Schulze, T. Rijken, Phys. Rev. C 84 (2011) T. Miyatsu, T. Katayama, K. Saito, Phys. Lett. B 709 (2012) see I. Vidaña s talk, Tuesday 2, October 2012

4 Motivations I. Vidaña, D. Logoteta, C. Providência, A. Polls, I. Bombaci, EPL 94 (2011) Gravitational Mass [M ] PSR J PSR J Hulse-Taylor H. Ðapo, B.-J. Schaefer, J. Wambach, Phys. Rev. C, 81(2010) Radius R [km] PSR J PSR J hyperon-nucleon interaction? 2 Mass MC1-H/ MC1-HF/ MC3-HF/ MC1-H/Y MC1-HF/Y MC2-HF/Y MC3-HF/Y MC4-HF/Y QMC Radius É. Massot, J. Margueron, G. Chanfray, EPL 97 (2012) M/M O R [km] V18+TBF V18+UIX V18+TBF+ESC08 V18+UIX +ESC08 V18+TBF+SC89 V18+UIX +SC ρ c [fm -3 ] H.-J. Schulze, T. Rijken, Phys. Rev. C 84 (2011) T. Miyatsu, T. Katayama, K. Saito, Phys. Lett. B 709 (2012) see I. Vidaña s talk, Tuesday 2, October 2012

5 The idea n p p n n p p n nucleus -hypernucleus exact method BE nuc = h nuc H nuc i h nuc nuc i BE hyp = h hyp H + hyp i h hyp hyp i B = BE nuc BE hyp H + H Hyp. : nuclear effects cancel at most information about the hyperon-nucleon interaction

6 The method: Auxiliary Field DMC stochastic ab-initio method with microscopic interaction Auxiliary Field Diffusion Monte Carlo (AFDMC) = (R, S, ) =H (R, S, ) (R, S, + d ) = Z walkers hsr e (H E 0)d R 0 S 0 ihs 0 R 0 ( )i dr 0 ds 0 d kinetic term potential term problem d d

7 The method: Auxiliary Field DMC P e 1 2 d O2 X 2 A A! (A Z)!Z! terms high computational cost GFMC: A apple 12 Idea: Hubbard-Stratonovich transformation e 1 2 d O2 = 1 p 2 Z dx e x2 2 +p d xo auxiliary field rotation over spin-isospin configurations computational cost: A! A 3

8 The interaction need of local interaction in coordinate space nuclear potentials - Argonne V4, V6, V8 (6) - Minnesota hypernuclear potential - Usmani interaction diagrammatic contributions due to pion exchange 2-body and 3-body terms A. Bodmer, Q.. Usmani, J. Carlson, Phys. Rev. C 29 (1984) A. Bodmer, Q.. Usmani, ucl. Phys. A 477 (1988) A. A. Usmani, S. C. Pieper, Q.. Usmani, Phys. Rev. C 51 (1995) A. A. Usmani, Phys. Rev. C 52 (1995) A. A. Usmani, S. Murtaza, Phys. Rev. C 68 (2003) A. A. Usmani, Phys. Rev. C 73 (2006) A. A. Usmani, F. C. Khanna, J. Phys. G: ucl. Part. Phys. 35 (2008)

9 The interaction 1 2-body 2 forbidden K, K

10 3-body dispersive 2 3 forbidden The interaction

11 The interaction Usmani potential: 2-body K, K v i (r) =v 0 (r)+v 0 (r)"(p x 1) v T 2 (m r) i 8 >< >: v 0 (r) = v c (r) v 2 (r) h v c (r) = W c 1+e r r a v 2 (r) = vt 2 (m r) i 1 8 < : v = v s v t v = 1 4 (v s +3v t )

12 The interaction Usmani potential: 3-body 8 >< >: v PW ij = v SW v ij = v ij 2 + v ij D = v ij PW 1 6 CP {X i,x j } i j + v SW ij + v D ij ij = C S Z (m r i ) Z (m r j )( i ˆr i j ˆr j ) i j apple v ij D = W D T 2 (m r i ) T 2 (m r j ) ( i + j )

13 Results He -separation energy B [MeV] W D =0.015 MeV C P =0.6 MeV exp AFDMC V (V 4 ) + V AFDMC V (V 6 ) + V AFDMC V (V 4 ) + V + V AFDMC V (V 6 ) + V + V e+00 2e-05 4e-05 6e-05 8e-05 1e-04 d [MeV -1 ]

14 Results separation energy Ca B [MeV] O 91 Zr preliminary!! He exp AFDMC V (V 4 ) + V A

15 Results separation energy 80.0 B [MeV] preliminary!! 91 Zr Ca O He exp AFDMC V (V 4 ) + V AFDMC V (V 4 ) + V + V A

16 Results separation energy exp AFDMC V (V 4 ) + V AFDMC V (V 4 ) + V + V 60.0 A!1 B [MeV] Zr Ca 17 O A -2/3 5 He

17 Results separation energy exp 30.0 AFDMC V (V 4 ) + V AFDMC V (V 4 ) + V + V Ca B [MeV] C 16 O 17 O He 7 He 6 He H H, 4 He A

18 Results separation energy exp 30.0 AFDMC V (V 4 ) + V AFDMC V (V 4 ) + V + V Ca B [MeV] C 16 O 17 O He 6 He 7 He 3 6 H H preliminary!! (??) 4 H, 4 He A

19 Results 0.45 density: 4 He vs 5 He He V (v4 ) 5 He V (v4 )+V 5 He V (v4 )+V 0.30 [fm -3 ] x r [fm]

20 Results density: 4 He vs 5 He 4 He V (v4 ) 5 He V (v4 )+V +V 5 He V (v4 )+V +V 0.30 [fm -3 ] x r [fm]

21 Results 0.45 density: 16 O vs 17 O preliminary 16 O V (v4 ) 17 O V (v4 )+V +V 17 O V (v4 )+V +V 0.30 [fm -3 ] x r [fm]

22 Results 0.45 density: 40 Ca vs 41 Ca preliminary 40 Ca V (v4 ) 41 Ca V (v4 )+V +V 41 Ca V (v4 )+V +V 0.30 [fm -3 ] x r [fm]

23 Results 0.45 density: 90 Zr vs 91 Zr preliminary!! 90 Zr V (v4 ) 91 Zr V (v4 )+V +V 91 Zr V (v4 )+V +V 0.30 [fm -3 ] x r [fm]

24 Conclusions AFDMC algorithm can be used to study hypernuclear systems: information about the hyperon-nucleon interaction the 3-body interaction is fundamental for the computation of the hyperon separation energy, but a fine tuning of the parameters is needed the 3-body interaction is repulsive in hypernuclei: extrapolation for nuclear matter could lead to more realistic hyperon-nucleon interaction for S EOS ( the inclusion of a 2-body interaction in the AFDMC algorithm is also possible: deeper investigation of the -hypernuclear potentials ) ( E. Hiyama, M. Kamimura, T. Motoba, T. Yamada, Y. Yamamoto, Prog. Theor. Phys. 97 (1997) )