Nuclei with strangeness. (From hypernuclei to kaonic nuclei) Nuclear Physics Institute, Rez/Prague

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1 Nuclei with strangeness. (From hypernuclei to kaonic nuclei) J. Mareš Nuclear Physics Institute, Rez/Prague RINGFEST - Advances in Nuclear Many-Body Physics Primošten, Croatia, 6 10 June, 2011

2 Hypernuclei Hypernuclei = nuclear systems containing nucleons + 1 or more hyperons. (M.Danysz, J. Pniewski, Bull. Pol. Acad.Sci. 1 (1953) 42.)

3 Hypernuclei Why to study hypernuclei? Test models of baryon-baryon and meson-baryon interactions (meson exchange models, quark models, chiral models,...) Test nuclear models (RMF,EDF, shell model,...) Test models of hadrons (SU(3)symmetry, quark models...) Hypernuclear production test reaction mechanisms Hypernuclear decays study of weak interaction Hyperon X Nucleon no Pauli blocking Hyperon can penetrate deep into the nuclear interior, probe the nuclear interior Implications for astrophysics (compact stars), HI collisions (strangeness production, medium modification od hadrons)

4 Λ hypernuclei > 30 Λ-hypernuclei:

5 Λ hypernuclei > 30 Λ-hypernuclei:

6 Λ hypernuclei (K, π ) reaction (emulsions, CERN, BNL, KEK, Frascati, JParc): a = a = (p 1 3/2, pλ 3/2 ) J=0 + B Λ(a) = 0 MeV, B Λ (a ) = 3.5 MeV b = b = (p 1 3/2, sλ 1/2 ) J=1 B Λ(b) = 11 MeV, B Λ (b ) = 7 MeV c = (p 1 1/2, pλ 1/2 ) J=0 + B Λ(c) = 2.5 MeV d = (p 1 1/2, sλ 1/2 ) J=1 B Λ(d) = 13 MeV B Λ (b ) B Λ (d) = 6 MeV (n SO splitting), B Λ (a ) B Λ (c) = 6 MeV (n + Λ SO splitting) (p1/2 Λ pλ ) 0.3 MeV 3/2

7 Λ hypernuclei (π +, K + ) reaction (BNL, KEK): Hotchi et al, PRC 64 (2001) Textbook example of single-particle structure Λ hyperon bound by 28 MeV in nuclear matter Negligible spin-orbit splitting

8 Λ hypernuclei RMF calculations (J.M., B.K. Jennings, PRC (1994): (+ quark model + Y ω tensor coupling f ωy 2M Y Ψ Y σ µν νv µψ Y )

9 Λ hypernuclei

10 Λ hypernuclei (K stop, π ) reaction (FINUDA, PLB 622 (2005) 35): (e, e K) reaction (JLab, PRL 99 (2007) ): Λ binding energy spectrum in 12 Λ C 12 Λ B excitation spectrum

11 Λ hypernuclei γ spectroscopy (BNL, KEK) spin dependence of the effective ΛN interaction in the nuclear p shell

12 Λ hypernuclei s-shell Λ hypernuclei Nemura et al, PRL 89 (2002) (including ΛN ΣN variational approach and ΛΛ ΞN mixings) Hiyama et al, PRC 65 (2002) (R) - Jacobi-coordinate Gaussian basis Nogga et al, PRL 88 (2002) Faddeev + Faddeev-Yakubovsky

13 Σ hypernuclei 9 Be(K, π ) 9 Σ Be (Bertini (80), CERN) + further narrow Σ-nuclear resonance states in the continuum (KEK, BNL): 4 Σ He, 6 Σ Li, 12 Σ C, 16 Σ O (limited statistics contradictory results) Narrow states X widths about MeV due to ΣN ΛN 80 s many attempts to produce Σ-hypernuclear states and to explain narrow widths

14 Σ hypernuclei Σ-nucleus interaction: (J.M., Friedman, Gal, Jennings, NPA 594 (1995) 311, E. Friedman, A. Gal, Phys. Rept. 452 (2007) 89) Σ hyperons are not bound in nuclei except for 4 Σ He Sawafta et al, PRL 83 (1999) 25; Noumi et al, PRL 89 (2002)

15 Σ hypernuclei DWIA calculations (Harada & Hirabayashi, NPA 759 (2005) 143) 28 Si(π, K + ) spectrum from KEK-E438, using 6 Σ-nucleus potentials, (a)-(c) with inner repulsion, (d)-(f) fully attractive

16 Ξ hypernuclei Ξ-nucleus interaction: no established yet QBS 12 C(K, K + ) spectra (KEK -E224, BNL-E885) V Ξ 14 MeV Calculations of light Ξ hypernuclei (Hiyama et al, PRC 78 (2008) ). Spectroscopic study of Ξ hypernucleus 12 Ξ B... (T. Nagae), A Day-1 experiment E05 at J-Parc

17 Multi-strange baryonic systems One can envisage bound many-body systems containing more baryons from the SU(3) octet: N, Λ, Σ, Ξ Multiply strange nuclear systems extension of conventional shell model picture to systems with larger number of hyperons of interest for astrophysics (neutron stars) of interest for HI collisions their study = source of information about B B interactions Unfortunately, only ΛΛ hypernuclei known (+ mutually contradictory info): 4 ΛΛ H (?), 6 ΛΛHe, 10 ΛΛBe, 13 ΛΛ B

18 ΛΛ hypernuclei 6 ΛΛ He (Prowse 66), 10 ΛΛ 13 Be (Danysz 63), ΛΛB (KEK-E176 91) B ΛΛ MeV Takahashi et al, PRL 87 (2001) B ΛΛ ( 6 ΛΛ He) = B ΛΛ( 6 ΛΛ He) 2B Λ( 5 ΛHe) 1 MeV

19 Multi-strange baryonic systems RMF calculations hidden-strangeness mesons introduced couple only to hyperons: scalar σ (975 MeV) and vector Φ (1020 MeV) (originally introduced to strengthen the ΛΛ interaction) RMF model predicts a possibility of forming bound systems with appreciable number of hyperons The dependence of E B /A, density distributions, r.m.s. radii, on the number of hyperons delicate interplay between the effect of Pauli blocking (Y, N distinquishable) and weaker YN interactions First calculations only mixtures of Λ and N E B /A 9 MeV, f s = S /A 0.2 ΣN ΛN ΞN ΛΛ ΩN ΛΞ (Q 78MeV) (Q 26MeV) (Q 178MeV)

20 Multi-strange baryonic systems HOWEVER!! For some critical number of Λ s in a system: ΛΛ ΞN energetically favorable due to Pauli blocking of Λ s It is necessary to include Ξ!! (Ξ-nucleus potential?) { N, Λ, Ξ} configurations ρ (2 3)ρ 0, f s = S /A 1, Z /A 1 E B /A (10 20) MeV

21 Multi-strange baryonic systems J. Schaffner, C.B. Dover, A. Gal, C. Greiner, H. Stöcker, PRL 71 (1993) ΞN ΛΛ ( 25 MeV in free space) is Pauli blocked

22 Strange hadronic matter neutron star structure Schaffner-Bielich, NPA 804 (2008) 309 Glendenning, Schaffner-Bielich, PRC 60 (1999) kaon condensation could occur at ρ 3ρ 0, l K + ν l (ω K 200 MeV)

23 K N interaction K N interaction strongly attractive I = 0 Λ(1405) πσ resonance, 27 MeV below K p threshold

24 K N interaction Scattering data

25 K N interaction K p atom Siddharta:

26 K N interaction Threshold branching ratios:

27 Kaonic nuclei K-nucleus interaction strongly attractive and absorptive kaonic atom level shifts and widths? optical potential depth: ReV opt ( ) MeV phenomenological models ReV opt (50 60) MeV chiral models of K-nuclear states? sufficiently narrow to allow identification by experiment

28 Motivation

29 Motivation (2N) K, (3N) K, (4N) K, (8N) K,... (Akaishi, Yamazaki, Doté et al.) large polarization effects ρ (4 8) ρ 0 B K 100 MeV, Γ K (20 35) MeV

30 Status Quo K capture in Li and 12 C (FINUDA, PRL (2005)): B = 115 ± 6 ± 4 MeV, Γ = 67 ± 14 ± 3 MeV K pn ΛN + FSI (Magas et al., PRC (2006)) K stopped in 6 Li K ppn cluster, B = 58 ± 6 MeV, Γ 30 MeV vs. vs. (FINUDA, PLB (2007) vs. Magas et al., arxiv: ) p annihilation on 4 He (Obelix, LEAR) K pp : B 160 MeV, Γ 24 MeV K ppn: B = 121±15 MeV,Γ<60MeV (Bendiscioli et al., NPA (2007)) pp K + Λp (DISTO) K pp : B = 105±118 MeV (T. Yamazaki et al EXA08, arxiv: [nucl-ex])??

31 K pp quasibound state Coupled-channel calculations of a KNN πσn system (Shevchenko, Gal, JM, PRL 98 (2007) ) 3-body Faddeev equations (in AGS form): U 11 = + T 2 G 0 U 21 + T 3 G 0 U 31 U 21 = G T 1 G 0 U 11 + T 3 G 0 U 31 U 31 = G T 1 G 0 U 11 + T 2 G 0 U 21, U ij describe elastic and re-arrangement processes: U 11 : 1 + (23) 1 + (23) U 21 : 1 + (23) 2 + (31) U 31 : 1 + (23) 3 + (12) KN strongly coupled with πσ via Λ(1405) πσ channel included particle channels α: 1 : ( KNN) 2 : (πσn) 3 : (πnσ) i = 1 NN ΣN ΣN i = 2 KN πn πσ i = 3 KN πσ πn

32 K pp quasibound state Table: Calculated K pp binding energies and widths (in MeV) single channel coupled channel AY DHW SGM IS WG B Γ

33 Status Quo MFG (πσ,ρ) DISTO Γ K - (MeV) SGM WG08 AY02 YS07 FINUDA05 OBELIX? GFGM (πσ,πλ,ρ 2 ) DHW08 FINUDA07 WG08 OBELIX B - K (MeV)

34 RMF Methodology Larger K -nuclear systems Relativistic mean field model for a system of nucleons, K mesons, and hyperons interacting through the exchange of σ, σ, ω, ρ, φ and photon fields: L = L RMF + L K + L Y where L RMF = standard relativistic mean field lagrangian density L K = (D µk) (D µ K) mk 2 K K g σk m K σ K K g σ K m K σ K K, L Y = ψ Y [id/ (m Y g σy σ g σ Y σ )]ψ Y, with covariant derivative: D µ = µ + i g ωk ω µ + i g ρk I ρµ + i g φk φ µ + i e (I Y )Aµ.

35 RMF Methodology + antikaons: ( 2 E 2 K + m 2 K + Π K )K = 0 Re Π K = g σ K m K σ g σk m K σ 2 E K (g ωk ω + g ρk ρ + g φk φ + e A) (g ωk ω + g ρk ρ + g φk φ + e A) 2 Im Π K = (0.7 f 1Σ f 1Λ )W 0 ρ N (r) f 2Σ W 0 ρ 2 N (r)/ ρ 0 f iy Absorption through: kinematical suppression factors ( reduced phase space) W 0 constrained by kaonic atom data pionic conversion modes ρ N (r) KN πσ+90 MeV, πλ+170 MeV (70%, 10%) nonmesonic modes ρ 2 N (r) KNN YN+240 MeV (20%) Γ K width phase space suppression x density enhancement

36 Single-K nuclei Γ K follows the dependence sf(b K ) 200 Γ K - (MeV) C O Ca Pb B - K (MeV) The K decay widths Γ K in K C, K O, K Ca, and K Pb as function of the K binding energy B K. The dashed line indicates a static nuclear matter calculation.

37 Single-K nuclei C ρ _ (fm -3 ) Ca O Pb B K - (MeV) Average nuclear density ρ as function of the K binding energy.

38 Multi- K nuclei O + κk B K (MeV) K - K κ The K binding energies as functions of the number κ of antikaons. saturation observed across the periodic table B K << m K + m N m Λ 320 MeV, far away from kaon condensation

39 Multi- K nuclei O+ κk B K - (MeV) σ, ω σ, ω, φ σ, ω, φ, ρ σ, ω, φ, ρ, Coul σ, ω, φ, ρ, Coul, ImV opt saturation occurs for any boson-field composition (when ω-field present repulsion) 60 σ, ω, φ, ρ, σ, Coul, ImV opt κ The K binding energy as a function of the number κ of antikaons.

40 Multi- K nuclei ρ N (fm -3 ) O + κk ρ N (fm -3 ) Pb + κk ρ K (fm -3 ) no K 2K 4K 6K 8K 10K ρ K - (fm -3 ) no K - 2K - 4K - 6K - 8K - 10K - 12K - 14K - 16K r (fm) r (fm) Nuclear (ρ N ) and K (ρ K ) density distributions for various numbers κ of antikaons.

41 Multi- K hypernuclei Fig. 17 The K binding energy B K in 208 Pb as a function of the number κ of antikaons and η of Λ hyperons.

42 Multi- K hypernuclei B K - (MeV) Ca+20Λ+2Ξ 0 +κk O+8Λ+K - 90 Zr+40Λ+2Ξ 0 +2Ξ +κk - 90 Zr+40Λ+2Ξ 0 +2Ξ +κk - ; VΞ -=-25 MeV 208 Pb+106Λ + 2Ξ 0 +18Ξ +κk κ The K binding energy B K in A Z + ηλ + µ 0 Ξ 0 + µ Ξ + κk as a function of the number κ of antikaons.

43 Summary Λ hyperon bound by 28 MeV in nuclear matter, spin-orbit splitting 0 Few-body Λ (and ΛΛ) hypernuclei - ΣN ΛN important p-shell hypernuclei - effective ΛN interaction determined (exp. JLab, FINUDA, planned JParc, GSI (FAIR)) more data on ΛΛ hypernuclei needed PANDA@GSI Σ hyperons are not bound in nuclei except for 4 Σ He Ξ hyperons perhaps bound by 14 MeV in nuclear matter (planned exp. JParc) K nuclei the issue is far from being resolved (searches for K pp are underway in GSI and JParc) kaon condensation is unlikely to occur in strong-interaction self-bound strange hadronic matter