Current theoretical topics on K - pp quasi-bound state

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1 SNP J-PARC August 3, 215 Current theoretical toics on K - quasi-bound state Yoshinori AKAISHI and Toshimitsu YAMAZAKI

2 "Λ(145) Ansatz" A. Dote et al. nucl U K MeV -5 Σ+π Λ+π -2 K r fm Λ(145) E Γ K -27 MeV 4 MeV nucl U K MeV -5 Σ+π Λ+π -2 K r fm E K Γ 2 KH -48 MeV 61MeV nucl U K MeV -5 Σ+π Λ+π -2 K He 1 2 3r fm 3 KH E -18 MeV K Γ 2 MeV Shrinkage! N.V. Shevchenko, A. Gal & J. Mares, Phys. Rev. Lett. 98 (27) 8231 E -55~-7 MeV, Γ 9~11 MeV Y. Ikeda & T. Sato, Phys. Rev. C 76 (27) 3523 E -8 MeV, Γ 73 MeV A. Dote, T. Hyodo & W. Weise, Phys. Rev. C 79 (29) E MeV, Γ 4~7 MeV -5-5 DAΦNE Conf. (1999), HYP Conf. (2) ; rejected from Proc. Y. Akaishi & T. Yamazaki, Phys. Rev. C 65 (22) 445 T. Yamazaki & Y. Akaishi, Phys. Lett. B 535 (22) 7

3 K - J-PARC E31 : D (K -, n)

4 K bar N scattering amlitude T. Hyodo and W. Weise, Phys. Rev. C 77 (28) 3524 Chiral SU(3) dynamics Akaishi-Yamazaki Chiral The most relevant issue is: 145 or 142? s "ORB": E. Oset, A. Ramos & C. Bennhold, Phys. Lett. B 527 (22) 99 "HNJH": T. Hyodo, S.I. Nam, D. Jido & A. Hosaka, Phys. Rev. C 68 (23) 1821 "BNW": B. Borasoy, R. Nissler & W. Weise, Eur. Phys. J. A 25 (25) 79 "BMN": B. Borasoy, U.G. Meissner & R. Nissler, Phys. Rev. C 74 (26) 5521 "JOORM": D. Jido, J.A. Oller, E. Oset, A. Ramos & U.G. Meissner, Nucl. Phys. A 725 (23) 181

5 Σπ invariant mass from stoed K - on 4 He J. Esmaili, Y. Akaishi & T. Yamazaki, Phys. Lett. B686 (21) 23 Data : B. Riley et al., Phys. Rev. D 11 (1975) 365 χ 2 as a function of 1 st ole s M and Γ.

6 Λ(145) from HADES G. Agakishiev et al., Phys. Rev. C 87 (213) 2521 M. Hassanvand et al., Phys. Rev. C 87 (213) 5522 PDG 14

7 Interretation of the Λ(145) shift in HADES data J. Siebenson & L. Fabbietti, Phys. Rev. C 88 (213) 5521 T 2 iφ 2 Λ( 145) C.s. BW1 m) e + BW2( m) BW ( m) i Coherent sum ( 1 q 1 Ai 2 2 m mi + im Γ i i c.m. Best fit Interference between double oles!

8 215

9 D(K -, n) missing mass sectrum calculation n K - 1. GeV/c n J-PARC K - I 1 E31 QF-K Useful information for n K - 1. GeV/c QF-K E15 QF-Λ* n K - Λ(145) PDG I MM(n) MeV

10 D(K -, n) missing mass sectrum P K- 1. GeV/c I only o θ n E(Λ*) MeV I I I I I I I MM(n) MeV/c 2 react-ki/d_kn_ls1.f

11 MM MeV/c 2 I I 1 QF-K - IM(Σπ) o θ n Missing-mass sectrum of ( ) m π Σ n K D - ±, I I 1 IM(Σπ) MeV/c 2 Inclusive I Σπ I 1 Σπ, Λπ π Σ π Σ π Σ I I I I I I I I

12 Missing and invariant mass sectra n K - n Missing mass Eigenstate of H(K-Σπ) iε H E G + 1 On-shell Green s function Singularities aear above threshold. Moon-shaed singularity ε.1 MeV with Δcosθ ) ( ) ( G TG G G G TG G VG G G G G G G VG TG TG G T V G G TG V TG V V T V H H G G Identity ε ε ε i H E i + lim ( ) E E E H E, Ψ Ψ Ψ Non-eigenstate of H + Quasi-free K : Invariant mass (Σπ,..) G TG iε H E G + 1 Off-shell Σ π

13 Σπ invariant-mass sectrum I only o θ n K - 1. GeV/c n Peak shift Formation weight n D Λ* π Σ E(Λ*) MeV + 1. I I I ( K n) Σ π D, I main, no I IM(Σπ) MeV/c 2

14 Σπ invariant-mass sectrum Deuteron-size deendence P K- 1. GeV/c ψ ( r d ) 2 1 ex( 4 ar ), a a f a fm 2 Free N f IM(Σπ) MeV/c 2

15 Shevchenko s interaction Phys. Rev. C. 85 (212) 341

16 Missing-mass sectrum of ( ) m D K -, n Σ ± π o θ n Shevchenko interaction Phys. Rev. C 85 (212) 341 M 2 c. Λ * i25 MeV Total I 1 Deviation sectrum I IM(Σπ) MeV/c 2

17 Missing-mass sectrum of ( ) m D K -, n Σ ± π o θ n AMY interaction M 2 c. Λ * 145. i25 MeV Total I 1 Deviation sectrum I IM(Σπ) MeV/c 2

18 Missing-mass sectrum of ( ) m D K -, n Σ ± π o θ n AMY interaction M 2 c. Λ * 142. i25 MeV Total I 1 Deviation sectrum I IM(Σπ) MeV/c 2 react-ki/d_kn_ls2d.f

19 Missing-mass sectrum of ( ) m D K -, n Σ ± π θ n Shev147 o K - + threshold AMY145 AMY142 Χ 2 -fitting must be done! IM(Σπ) MeV/c 2

20 K - J-PARC E15 : 3 He (K -, n)

21 Semi-inclusive neutron sectrum T. Hashimoto et al., Prog. Theor. Ex. Phys. 215, 61D1 K - 1. GeV/c n n K -

22 Theoretical works KH : T. Koike & T. Harada, Phys. Lett. B 652 (27) 262 Phys. Rev. C 8 (29) 5528 Phase sace suression factor (Mares-Friedman-Gal) for Im V ot (E) YJNH: J. Yamagata-Sekihara, D. Jido, H. Nagahiro & S. Hirenzaki, Phys. Rev. C 8 (29) 4524 [MeV] E-inde. E E-1 MeV E-5 MeV V ot ( E) t K ( E) ρ N E-de. real art BE (Width) N V ot r [fm] v eff. KN ρ N E-de. imaginary art

23 Variational wave function of K - ATMS Amalgamation of Two-body correlations into Multile Scattering rocess Ψ I [{ ˆ I I 1 ˆ I 1 I ( ) ( ) } ( ) ( ) ( ) ( ){ ( ) ˆ I I 1 ( ) ˆ I 1 f r P + f r P f r f r + f r f r f r P + f r P }] T 1/ 2 N 2 K N T NN NN r r r r ˆ I 1τKτ N ˆ I τkτ N P12, P / 2 3, 1 1 1, 2 1,1 ( K1N 2) 3 + K1N K1N 2 n Λ* [ ] ( ) ( ) v T 2 KN ( r ) { 595 i83} MeV ex{ ( r /.66fm) } T 1 { } { fm 2 KN ( r ) 175 i15 MeV ex ( r /.66 ) } 2 2 { ( r /.447 ) } 27 ex{ ( r /.942 ) } 5 ex{ ( / } v v Euler-Lagrange equation δ f { Ψ H Ψ λ Ψ Ψ } NN ( r ) 2MeV ex fm MeV fm MeV r fm)

24 Density distributions of K bar -N T. Yamazaki and Y. Akaishi, Phys. Rev. C 76 (27) r ρ( r ) K bar -N in Λ(145) K I N Λ* N.4.3 x.625 I K bar -N in K - I ;.25 I 1;.75 N K I N Λ*.2 I :.5x(1+.25).625 I 1:.5x I 1 Dynamically favored r fm

25 Adiabatic - otential in K - K - [MeV fm 2 ] R 2 V(R) 1 Normal nuclear force : virtual meson exchange 5 R [fm] Suer strong / Normal ~ 4.1 volume integral ratio Suer-strong nuclear force : real K bar migration

26 Λ*N system with meson exchange A. Arai, M. Oka & S. Yasui, Prog. Theor. Phys. 119 (28) 13 T. Yamazaki & Y. Akaishi, Proc. Jaan Academy, B 83 (27) 144

27 K - quasi-bound state 1.36 fm K - 1. GeV/c n 22 K fm rms distance n K - K - n 27 n Λ*

28 Quasi-freeY s in E15 missing mass sectrum T. Hashimoto 2N absortion n 1494 MeV/c n 1254 MeV/c n 1 MeV/c QF-Λ QF-Σ QF-Λ 145 π Δ π MM GeV/c 2 "n-knockout window" 2812 MeV for n n-sectator window K - Y 1 MeV/c - n M miss c ( Ein En) (1 MeV - nc) E 2 K + M3Hec 3924 MeV

29 Missing mass sectrum of Λ*- system o θ n Σ +π + Λ*+ K Without Λ* width With Λ* width of 5 MeV YA int. QF -Λ* QF- K X 1/5 K + "n" K + K + "" K + n n DISTO int. No Λ* int MM MeV/c 2

30 Semi-inclusive neutron sectrum K E15" E31"

31 Semi-inclusive neutron sectrum Preliminary!

32 3N absortion K - n n Y observed seudoqf-y θ n Pseudo-QF Λ* θ o n ~ 2 sqf Λ* is obtained by 3N absortion calculation! Σ +π + o Λ*+ o θ n K o θ n 2 Without Λ* width o 4 o 6 All the integrated sectra are normalized to unity. With Λ* width of 5 MeV DISTO int MM MeV/c 2 o 6 o 4 θ o n

33 Pseudo-QF Λ* and K - sqf Λ* K - n n θ n o Λ Λ* width. Λ* width DISTO int. DISTO int. K - sqf Λ* react-ki/h_kn_mod5b.f IM. [MeV/c 2 ] IM. [MeV/c 2 ]

34 K - J-PARC E27 : D (π +, K + )

35 Inclusive sectrum Y. Ichikawa et al., Proc. Science (Nara Conf. 213) o θ 8 o θ 12 K -?

36 Y. Ichikawa et al., Prog. Theor. Ex. Phys. 215, 21D1 Theor. Yamazaki-Akaishi E K Γ -48 MeV 61MeV 17% enhanced K bar N interaction E Γ K -13 MeV 118 MeV DISTO T. Yamazaki et al., Phys. Rev. Lett. 14 (21) 13252

37 Missing mass sectrum of Λ*- system for Λ + π, 1.5 MeV / c YA 17 % DISTO S. Maeda, Y. Akaishi & T. Yamazaki, Proc. Jn. Acad. B 89 (213) 418 Σ +π + Λ*+ Σ K Σ + + DISTO + π, Λ +, Λ +, 189. MeV / c MeV / c ΣΝ-ΛΝ conversion 476. MeV / c "K - " Λ*- QBS Coincidence by T. Nagae et al. Γ Λ 5 MeV YA int. Γ Λ 5 MeV DISTO int. Γ Λ 5 MeV No int. Γ Λ No Λ* int MM [MeV/c 2 ]

38 Y. Ichikawa et al., Prog. Theor. Ex. Phys. 215, 21D1 K - Λ*- with real K bar migration (17% enhanced int.) Preliminary! K + K + π + K - Λ* K - n Which is of ground? Λ*- structure K - structure

39 QF-Σ θ 8.3 A stable article with Lorentzian mass distribution S δ ( E An unstable article with decay width X 1 H ) Im π E H H Σ + H * QF Σ* Σ* H ( E Σ* + iw X Σ* 1 H + iε ) + T Σ* Simulation by Y. Ichikawa No width

40 QF-Λ 7.7 θ 8.3 Decay width HADES fit ~15 MeV Decay width Simulation by Y. Ichikawa Mass distribution

41 K - quasi-bound state 22 K fm 1.9 fm rms distance -4-8 Stronger KN attraction K Λ*+ Λ*- L1 excited state K - - L1 excited state DISTO [MeV] K - L ground state (Λ*- or K - -) -24

42 Angular-mom. decomosition of the Λ*- air π GeV/c Λ* K + L 12 n L Σ +π + Λ*+ L 8 L 4 L 2 QF Λ* No Λ* int. ~4 MeV DISTO Λ* int. L 1 L L react-ik/d_ik_mod1b.f MM [MeV/c 2 ]

43 Concluding remarks The Λ* Λ(145) lays an essential role in forming "anti-kaonic Nuclear Clusters", the simlest one of which is K - (K - ) Λ*. The Λ* structure interacting with "suer-strong force" due to K bar migration rovides a ossible exlanation of recent J-PARC data on K -. K - Λ *

44 Strangelet

45 A new aradigm of nuclear hysics Swan Nuclear Physics Yamazaki diagram Excitation energy (MeV) Nuclei of 2 nd generation The s quark combined with u bar lays a leading role in forming a dense and cold nucleus A1 Ξ [ Z ] - 1 Ξ A [ Z + 1] ΛΛ A2 [ Z ] K K Σ + - A A A1 A1 [ Z ] [ Z + 1] [ Z 1] [ Z ] 2 1 Σ [ ] ( K -,K + ) (K, π ),( π,k ) ( K -, π ),( π +,K + ) ( K -,N), (,K + ) Nuclei of 1 st generation Σ - Λ A 1 Z A1 [ Z ] + 1 π - A [ Z + 1] S-2 S-1 A [ Z ] A A [ Z + 1] [ Z + 2 ] S nuclei

46 Thank you very much!