Nuclei with Antikaons

Transcription

1 Nuclei with Antikaons Daniel Gazda Nuclear Physics Institute, Řež/Prague Czech Technical University in Prague Czech Republic together with A. Cieplý, E. Friedman, A. Gal, J. Mareš INT Program 12-3, Seattle, Oct 16, 2012

2 Outline Introduction and motivation Relativistic mean-field model for K nuclei Single- K nuclei Multi- K (hyper)nuclei Chiral approach for K nuclei Summary D. Gazda: Nuclei with Antikaons Page 2 of 50

3 Motivation Study of K mesons in medium attracts considerable attention. Related topical questions include: Free-space and in-medium KN interaction: chiral model tests, nature of Λ(1405) Possible existence of (narrow) deeply bound K nuclear states Heavy ion collision: strangeness production, medium modifications Neutron stars: kaon condensation D. Gazda: Nuclei with Antikaons Page 3 of 50

4 Motivation Motivation Kaon condensation in neutron stars? neutron star structure weak interaction operative, strangeness changing processes: e K ν e for µ K = µ e 200 MeV Glendenning, Schaffner-Bielich, Glendenning, Schaffner-Bielich, PRC 60 (1999) PRC 60 (1999) kaon condensation could occur at ρ 3ρ 0 Schaffner-Bielich, NPA 804 (2008) 309 Schaffner-Bielich, NPA 804 (2008) 309 D. Gazda: Nuclei with Antikaons Page 4 of 50

5 Motivation Heavy ion collisions medium effects? strong interaction operative Li, Lee, Brown, NPA 625 (1997) 372 p+c, p+au collisions KaoS Scheinast et al., PRL 96 (2006) medium effects, V K 80 MeV D. Gazda: Nuclei with Antikaons Page 5 of 50

6 Motivation Deeply bound and narrow K nuclear states? phenomenological extrapolation from K atoms (density-dependent optical potentials, RMF approach) ReV K ( ) MeV Mareš, Friedman, Gal, NPA 770 (2006) 84 D. Gazda: Nuclei with Antikaons Page 6 of 50

7 Motivation Deeply bound and narrow K nuclear states? early calculations: D. Gazda: Nuclei with Antikaons Page 7 of 50

8 Motivation Deeply bound and narrow K nuclear states? microscopic approaches based on chiral models constrained by low-energy KN data (scattering, kaonic 1 H, branching ratios) KN interaction Λ(1405) resonance χpt not applicable nonpertubartive approaches L. Sch./B.-S. equation importace of KN πσ coupled channel dynamics well understood near KN threshold,? subtreshold extrapolations K nucleus interaction strongly attractive and absorptive K nucleus interaction L. Sch./B.-S. T =T +VGT, V K T ρ ReV K 100 ± 20 MeV D. Gazda: Nuclei with Antikaons Page 8 of 50

9 Current status Deeply bound and narrow K nuclear states? Theory few-body systems variational approaches, Akaishi, Yamazaki, Doté,... : KNN, KNNN,... : B K 100 MeV, Γ K 30 MeV Faddeev calculations, Shevchenko, Gal, Mareš: K pp: B=50 70 MeV, Γ= MeV heavier systems phenomenology, RMF, K atom data analysis: ReV K MeV chiraly motivated approaches LO Tomozawa-Weinberg interaction: V K = 3/(8 f 2 π )ρ ρ0 55 MeV coupled channel calculations, Weise, Härtle: ReV K 100 MeV + K selfenergies, Lutz, Ramos and Oset: ReV K 50 MeV D. Gazda: Nuclei with Antikaons Page 9 of 50

10 Current status Deeply bound and narrow K nuclear states? Experiment (candidate K bound states) KEK-PS, E471, 4 He(K stop, p/n) BNL-AGS, parasite E930, 16 O(K, n) FINUDA, K capture in Li, C: PRL 2005, PRC 2006, NPA 2006, PLB 2007 Magas et al., Shevchenko et al., Ikeda & Sato LEAR, p annihilation on 4 He SATURNE, pp collisions none of them conclusive dedicated experiments comming: J-PARC, GSI, Frascati, Jülich,... D. Gazda: Nuclei with Antikaons Page 10 of 50

11 RMF model for K nuclei Relativistic mean field model for a system of nucleons, hyperons, and K mesons interacting through the exchange of σ, σ, ω, ρ, φ and photon fields: where L = L N +L Y +L K, L N = ψ( id/ m N ) ψ µ σ µ σ 1 2 m2 σσ g 2σ g 3σ ΩµνΩµν m2 ωω µω µ d (ωµωµ ) 2 1 P µν P µν m2 ρ ρ µ ρ µ 1 µν FµνF 4 L Y = ψ Y [id/ (m Y g σy σ g σ Y σ )]ψ Y L K = (D µk) (D µ K) m 2 K K K g σk m K σ K K g σ K m K σ K K, with D µ given by: D µ = µ + i g ωi ω µ + i g ρi I ρµ + i g φi φ µ + i e (I Y )Aµ. D. Gazda: Nuclei with Antikaons Page 11 of 50

12 baryons (nucleons, hyperons): [ iα j j +(m B g σb σ g σ B σ )β +g ωb ω+g ρb I 3 ρ+g φb φ+e(i Y )A]ψ B = εψ B mesons: ( 2 + mσ)σ 2 = g σn ρ s + g 2 σ 2 g 3 σ 3 + g σk m K K K+g σy ρ sy ( 2 +mσ)σ 2 = g σ K m K K K+g σ Y ρ sy ( 2 + mω)ω 2 = g ωn ρ N g ωk ρ K +g ωy ρ Y ( 2 + mρ 2 )ρ = g ρn ρ 3 g ρk ρ K +g ρn ρ 3Y ( 2 + mφ 2 )φ = g φk ρ K +g φy ρ Y 2 A = e ρ p e ρ K +e ρ cy where ρ K = 2(E K + g ωk ω + g ρk ρ + g φk φ + e A)K K D. Gazda: Nuclei with Antikaons Page 12 of 50

13 + 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 g VK SU(3) relations: 2g ωk = 2g φk = 2g ρk = g ρπ = 6.04 g σk kaonic atom data / scaled Absorption through: 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 kinematical suppression factors (phase space considerations) 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%) D. Gazda: Nuclei with Antikaons Page 13 of 50

14 + 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 g VK SU(3) relations: 2g ωk = 2g φk = 2g ρk = g ρπ = 6.04 g σk kaonic atom data / scaled Absorption through: 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 kinematical suppression factors (phase space considerations) 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%) D. Gazda: Nuclei with Antikaons Page 13 of 50

15 Single- K nuclei Aims: dynamical effects in nuclei due to the presence of K core nucleus polarization g σk scaled wide range of B K covered widths Γ K =Γ K (B K ) of K nuclear states states sufficiently narrow for large B K? Phys. Rev. C 77 (2007) D. Gazda: Nuclei with Antikaons Page 14 of 50

16 Single- K nuclei Dynamical core polarization Fig. 1: Average nuclear density ρ (left) and nuclear density distribution ρ(r) (right) for several values of K binding energy B K. D. Gazda: Nuclei with Antikaons Page 15 of 50

17 Single- K nuclei Widths of K nuclear states Absorption through: KN πσ (100%) Fig. 2: Widths of K nuclear states as a function of K binding energy.. D. Gazda: Nuclei with Antikaons Page 16 of 50

18 Single- K nuclei Widths of K nuclear states Absorption through: KN πσ (80%), KNN ΣN (20%) ρ Fig. 3: Widths of K nuclear states as a function of K binding energy.. D. Gazda: Nuclei with Antikaons Page 17 of 50

19 Single- K nuclei Widths of K nuclear states Absorption through: KN πσ, πλ (70%, 10%), KNN ΣN (20%) ρ Fig. 4: Widths of K nuclear states as a function of K binding energy.. D. Gazda: Nuclei with Antikaons Page 18 of 50

20 Single- K nuclei Widths of K nuclear states Absorption through: KN πσ, πλ (70%, 10%), KNN ΣN (20%) ρ 2 Fig. 5: Widths of K nuclear states as a function of K binding energy.. D. Gazda: Nuclei with Antikaons Page 19 of 50

21 Single- K nuclei Widths of K nuclear states Absorption through: KN πσ, πλ (70%, 10%), KNN ΣN (20%) ρ 2 Fig. 6: Widths of K nuclear states as a function of K binding energy.. D. Gazda: Nuclei with Antikaons Page 20 of 50

22 Multi- K (hyper)nuclei Aims: K condensation in finite self-bound nuclear systems behavior of K binding energies with increasing number of K s B K 320 MeV m K + m N M Λ all K decay channels kinematicaly blocked K mesons relevant degrees of freedom B K 240 MeV m K + m N M Σ decay widths fairly weak KNN ΛN behavior of baryon densities with increasing number of K s exotic nuclear systems {n, K 0 }, {N, Y, K, K + } Phys. Rev. C 76 (2007) , 77 (2008) D. Gazda: Nuclei with Antikaons Page 21 of 50

23 Multi- K nuclei B K = B K (# of K s) O + κk B K (MeV) κ Fig. 7: K binding energies B K as a function of the number κ of embedded antikaons. D. Gazda: Nuclei with Antikaons Page 22 of 50

24 Multi- K nuclei B K = B K (# of K s) O + κk B K (MeV) κ Fig. 8: K binding energies B K as a function of the number κ of embedded antikaons. D. Gazda: Nuclei with Antikaons Page 23 of 50

25 Multi- K nuclei B K = B K (# of K s) O + κk B K (MeV) κ Fig. 9: K binding energies B K as a function of the number κ of embedded antikaons. D. Gazda: Nuclei with Antikaons Page 24 of 50

26 Multi- K nuclei B K = B K (# of K s) O + κk B K (MeV) κ Fig. 10: K binding energies B K as a function of the number κ of embedded antikaons. D. Gazda: Nuclei with Antikaons Page 25 of 50

27 Multi- K nuclei B K = B K (# of K s) O + κk B K (MeV) κ Fig. 11: K binding energies B K as a function of the number κ of embedded antikaons. D. Gazda: Nuclei with Antikaons Page 26 of 50

28 Multi- K nuclei B K = B K (# of K s) O + κk B K (MeV) K - K κ Fig. 12: K binding energies B K as a function of the number κ of embedded antikaons. D. Gazda: Nuclei with Antikaons Page 27 of 50

29 Multi- K nuclei σ, ω, φ, ρ, Coul, ImV opt O+ κk B K - (MeV) σ, ω σ, ω, φ σ, ω, φ, ρ σ, ω, φ, ρ, Coul saturation observed for any field composition containing ω-meson σ, ω, φ, ρ, σ, Coul, ImV opt no saturation for purely scalar interaction κ substantial effect of ImΠ K for B K 100 MeV Fig. 13: K binding energies as a function of the number κ of antikaons for different mean field compositions. D. Gazda: Nuclei with Antikaons Page 28 of 50

30 Multi- K nuclei B K - (MeV) Ca + κk - NL-SH NL-TM1 NL-TM κ Fig. 14: K binding energies as a function of the number κ of antikaons for different RMF models. saturation qualitatively independent of RMF model used D. Gazda: Nuclei with Antikaons Page 29 of 50

31 Multi- K nuclei Baryon and antikaon density distributions O + κk Pb + κk - ρ N (fm -3 ) ρ N (fm -3 ) 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) Fig. 15: r (fm) Nucleon ρ N and antikaon ρ K density distributions in 16 O and 208 Pb. D. Gazda: Nuclei with Antikaons Page 30 of 50

32 Multi- K nuclei instabilities of traditional nonlinear RMF models at high densities Dirac-Brueckner calculations of nuclear matter suggest g φ = g φ (ρ) g φ = g φ (ρ 0 )a φ 1 + b φ (ρ/ρ 0 + d φ ) c φ (ρ/ρ 0 + d φ ) 2, φ = σ, ω gρ = gρ(ρ 0)e aρρ/ρ g σn g ωn g ρn g ρ / ρ 0 Fig. 16: Density dependence of the meson-nucleon coupling constants. D. Gazda: Nuclei with Antikaons Page 31 of 50

33 Multi- K nuclei B K = B K (# of K s) Fig. 17: K binding energies B K as a function of the number κ of embedded antikaons for density dependent RMF model. D. Gazda: Nuclei with Antikaons Page 32 of 50

34 Multi- K exotic systems O + κk O + κk n+6p B K (MeV) n + κk 0 16n + κk 0 B[A,Z,κK] (MeV) n+4p 14n+2p 16n + κk n + κk MeV 50 MeV κ κ Fig. 18: K binding energies B K (left) and total binding energies B (right) as functions of the number κ of embedded antikaons. D. Gazda: Nuclei with Antikaons Page 33 of 50

35 Multi- K hypernuclei Adding hyperons We considered self-bound systems consisting of SU(3) octet baryons {N, Λ, Σ, Ξ}. Only Ξ p ΛΛ and Ξ 0 n ΛΛ (Q 26 MeV) can be overcome by binding effects {N, Λ, Ξ} configurations. filling up Λ single-particle states up to the Λ Fermi level adding Ξ hyperons (Ξ 0, Ξ ) as long as both reactions: [AN, ηλ, µξ] [(A 1)N, ηλ, (µ 1)Ξ] + 2Λ [AN, ηλ, µξ] [(A + 1)N, (η 2)Λ, (µ + 1)Ξ] are kinemalically blocked particle-stable configurations with highest S /B ratio for given core nucleus Phys. Rev. C 80 (2009) D. Gazda: Nuclei with Antikaons Page 34 of 50

36 Multi- K nuclei B K = B K (# of K s, # of Y s) B K (MeV) Pb + ηλ + κk Λ 20Λ 50Λ 70Λ 100Λ κ Fig. 19: K binding energy B K in 208 Pb as a function of the number κ of antikaons and η of Λ hyperons. D. Gazda: Nuclei with Antikaons Page 35 of 50

37 Multi- K nuclei Zr + 40Λ + 2Ξ 0 + 2Ξ + 0K no Ξ (open symbols) 110 ρ (fm 3 ) 0.1 Y N 100 B K - (MeV) K Ca+20Λ+2Ξ 0 +κk - ρ (fm 3 ) 0.2 N ρ N ρ Y ρ K O+8Λ+K Zr+40Λ+2Ξ +2Ξ +κk Zr+40Λ+2Ξ +2Ξ +κk ; VΞ -=-25 MeV 0.1 Y Fig. 20: 208 Pb+106Λ+2Ξ 0 +18Ξ +κk κ 0 K r (fm) K binding energies (left) and nuclear density distributions (right) in hypernuclear systems with maximal S /B ratio. D. Gazda: Nuclei with Antikaons Page 36 of 50

38 Chiral approach for K nuclei K nuclear bound states studied by solving in-mediun K. G. equation: h ω K 2 + i 2 mk 2 Π K ( p K, ω K, ρ) φ K = 0 complex energy ω K = ω K iγ K /2 V C selfenergy operator Π K ( p K, ω K, ρ) constructed from chiral model = V K = 2π 1 + ω K F ω k m KN ( s, ρ) ρ N Π K 2ω K ω K = K energy in lab. frame F KN = KN scattering amplitude, s = KN energy in c.m. frame ρ = nuclear density (RMF calculations) KN c.m. frame K nucleus c.m. frame s Eth B K B N m N m K +m N T N m K m K +m N T K T N = 23(ρ/ρ 0 ) 2/3 MeV, T K = B K Re V K selfconsistent solution Π K = Π K (ω K ) D. Gazda: Nuclei with Antikaons Page 37 of 50

39 Model INT Program 12-3, Seattle, Oct 16, 2012 Chiral model for KN scattering amplitude (A. Cieplý, J. Smejkal, Eur. Phys. J A 43 (2010) 191.) SU(3) L SU(3) R chiral EFT for {π, K, η} + {N, Λ, Σ, Ξ} Λ(1405) resonance nonperturbative approach required multichannel L. Sch. equation T ij = V ij + V ik G kl T lj V ij separable form, G = 1 E H 0 Π( s, ρ) parameters of V ij parameters of L χ meson(baryon) selfenergies Π m(b) in G ij selfconsistency in V K D. Gazda: Nuclei with Antikaons Page 38 of 50

40 Model INT Program 12-3, Seattle, Oct 16, 2012 p-wave interaction Π P K = 4π 1 ω K m N 1 CKN ( s)ρ C KN p-wave amplitude parametrization of Weise and Härtle, NPA 804 (2008) 173 2N absorption modes nonmesonic KNN YN (20%) conversion modes from phenomenology: Im Π 2N K = 0.2 f 2Y W 0 ρ 2 f 2Y kinematical factor (phase space suppression) W 0 constrained by kaonic atom data dynamical core nucleus polarization selfconsistent RMF calculations nuclear core polarized (compressed) by presence of K meson D. Gazda: Nuclei with Antikaons Page 39 of 50

41 Chiral approach for K nuclear states Aims: study in detail energy and density dependencies of K nuclear interaction calculate binding energies and widths of K nuclear states analyze kaonic atom data deep phenomenological shallow chiral potentials Phys. Lett. B 702 (2011) 402, Phys. Rev. C 84 (2011) , Nucl. Phys. A (2012) D. Gazda: Nuclei with Antikaons Page 40 of 50

42 Results KN scattering amplitude Fig. 21: Energy dependence of the effective KN scattering amplitude, f KN = 1/2(f Kp + f Kn ), E th = m K + m N. D. Gazda: Nuclei with Antikaons Page 41 of 50

43 Results KN scattering amplitude Fig. 22: Energy dependence of the effective KN scattering amplitude, f KN = 1/2(f Kp + f Kn ), E th = m K + m N. D. Gazda: Nuclei with Antikaons Page 42 of 50

44 Results KN scattering amplitude Fig. 23: Energy dependence of the effective KN scattering amplitude, f KN = 1/2(f Kp + f Kn ), E th = m K + m N. D. Gazda: Nuclei with Antikaons Page 43 of 50

45 Results K nuclear potentials: amplitude at threshold: s=eth Table 1: K binding energies and widths of K states (in MeV). 12 C 16 O 40 Ca 90 Zr 208 Pb B K Γ K Fig. 24: K nuclear potentials in 40 Ca. D. Gazda: Nuclei with Antikaons Page 44 of 50

46 Results K nuclear potentials: amplitude at threshold: s=eth selfenergies in amplitude: F KN = F KN (Π K ) Table 2: K binding energies and widths of K states (in MeV). 12 C 16 O 40 Ca 90 Zr 208 Pb B K Γ K Fig. 25: K nuclear potentials in 40 Ca. D. Gazda: Nuclei with Antikaons Page 45 of 50

47 Results K nuclear potentials amplitude below threshold: s=eth B K V C B N T K T N K. G. eq. selfconsistent: ω K V K ( s) Table 3: k binding energies and widths of K states (in MeV). 12 C 16 O 40 Ca 90 Zr 208 Pb B K Γ K Fig. 26: K nuclear potentials in 40 Ca. D. Gazda: Nuclei with Antikaons Page 46 of 50

48 Results K nuclear potentials amplitude below threshold: s=eth B K V C B N T K T N K. G. eq. selfconsistent: ω K V K ( s) selfenergies in amplitude: F KN = F KN (Π K ) Table 4: k binding energies and widths of K states (in MeV). 12 C 16 O 40 Ca 90 Zr 208 Pb B K Γ K Fig. 27: K nuclear potentials in 40 Ca. D. Gazda: Nuclei with Antikaons Page 47 of 50

49 Results Binding energies and widths of K nuclear states B K (MeV) Li O C 1s 1p Ca 1d 2s Zr 1f 2p 1g Pb 2d 3s 1h 2f 3p 1i Γ K (MeV) C O Li 1p 1s Ca 2s 1d Zr 1g 2p 1f Pb 1i 3p 1h 2f 3s 2d A 2/ A 2/3 Fig. 28: Binding energies B K (left) and widths Γ K (right) of K nuclear states. D. Gazda: Nuclei with Antikaons Page 48 of 50

50 Results Binding energies and widths of K nuclear states Table 5: Binding energies B K and widths Γ K of K nuclear states in 40 Ca (in MeV). 1s 1p 1d 2s static calculation B K Γ K dynamical calculation B K Γ K p-wave interaction B K Γ K N absorption B K Γ K D. Gazda: Nuclei with Antikaons Page 49 of 50

51 Summary Dynamical calculations of K nuclear states within RMF approach considerable core polarization for light nuclei substantial widths of K nuclear states even for B K πσ threshold (Hyper)nuclear systems containing several antikaons K binding energies and nuclear densities saturate with number of K mesons saturation occurs also in the presence of hyperons Chiral approach for K nuclei chiral models results in relatively deeply bound K nuclear states B K (50 100) MeV substantial absorption widths of K nuclear states for B K near πσ threshold dominated by two-nucleon absorption Γ K 10 MeV ( KN YN) + 40 MeV ( KNN YN) D. Gazda: Nuclei with Antikaons Page 50 of 50