In-medium K & mesons Mesic Nuclei, JU Krakow, Sept. 2013 - PowerPoint PPT Presentation

In-medium ¯ K & η mesons Mesic Nuclei, JU Krakow, Sept. 2013 Hadrons in Nuclei, YITP Kyoto, Oct. 2013 Avraham Gal Racah Institute of Physics, Hebrew University, Jerusalem ¯ • KN − πY chiral dynamics and its consequences ¯ • K nuclear few-body systems K -nucleus potentials from K − atoms ¯ • A.Gal in HYP2012 Proc., NPA 914 (2013) 270 • Quest for η nuclear quasibound states E.Friedman, A.Gal, J.Mareˇ s, PLB 725 (2013) 334 1

¯ KN − πY Chiral Dynamics 2

K − p scattering amplitude from NLO chiral SU(3) dynamics Y. Ikeda, T. Hyodo, W. Weise (IHW), PLB 706 (2011) 63; NPA 881 (2012) 98 Strong subthreshold K − p attraction; Λ(1405) physics Consequences for kaonic atoms and K − nuclear quasibound states K − absorption might be governed by out-of-model K − NN → Y N 3

K − p subthreshold ambiguity Two NLO chiral-model fits by Guo-Oller, PRC 87 (2013) 035202 • Fit I: one value of meson weak-decay constant f = 125 . 7 ± 1 . 1 MeV. • Fit II: separate fixed values for f π , f K , f η . Fit II will create problems when confronted with kaonic-atom data. 4

K − p → π ± Σ ∓ reaction data fitted by LEC of NLO scheme for ¯ KN − πY coupled channels ( Y = Λ , Σ) Y. Ikeda, T. Hyodo, W. Weise, NPA 881 (2012) 98 Large difference in cross sections ⇒ Strong isospin dependence 5

1.5 4 πΣ (I=0) KN(I=0) 1.0 2 0.5 F KN [fm] F πΣ [fm] 0.0 0 -0.5 Re F , 2ch Im F , 2ch -2 Re F , full Im F , full -1.0 1320 1360 1400 1440 1320 1360 1400 1440 s 1/2 [MeV] s 1/2 [MeV] T. Hyodo, W. Weise, PRC 77 (2008) 035204 I = 0 coupled-channel amplitudes Location of ‘resonances’: ¯ KN ≈ 1420 MeV, π Σ ≈ 1405 MeV Are there two distinct ‘Λ(1405)’ resonances? 6

K nuclear few-body systems 7

Energy dependence in ¯ K nuclear few-body systems • Λ(1405) induces strong energy dependence of the KN ( √ s ) and the underlying scattering amplitudes f ¯ KN ( √ s ). effective single-channel input potentials v ¯ • s = ( √ s th − B K − B N ) 2 − ( � p N ) 2 ≤ s th p K + � • Expanding nonrelativistically near √ s th ≡ m K + m N : δ √ s = − B � 2 � T K � , A − A − 1 A B K − ξ N A − 1 � A − 1 A � T N : N � − ξ K A δ √ s ≡ √ s − √ s th , B K = − E K , ξ N ( K ) ≡ m N ( K ) ( m N + m K ) . • Self-consistency: output √ s from solving the Schroedinger equation identical with input √ s . 8

3– & 4–body B & Γ calculated self-consistently 160 0 ¯ KNN I = 1 KNN I = 1 ¯ 2 2 K ¯ ¯ KNN I = 0 K ¯ ¯ 140 KNN I = 0 ¯ − 5 KNNN I = 0 ¯ ¯ KNNN I = 0 KNNN I = 1 120 ¯ KNNN I = 1 − 10 100 E g.s. [MeV] − 15 Γ [MeV] 80 − 20 60 − 25 40 − 30 20 0 − 35 -80 -70 -60 -50 -40 -30 -20 -10 0 0 5 10 15 20 25 30 35 40 δ √ s [MeV] K max N. Barnea, A. Gal, E.Z. Liverts, PLB 712 (2012) • Variational calculation in hyperspherical basis controlled by K max • ¯ KN energy dependence [Hyodo–Weise, PRC 77 (2008) 035204] restrains B & Γ by treating δ √ s ¯ KN self-consistently • B (4-body) small w.r.t. non-chiral estimates of over 100 MeV 9

• ¯ KNN : is there an excited I = 1 / 2 quasibound state ( ¯ Kd , dominantly I NN = 0) on top of “ K − pp ” g.s. ? • Bayar & Oset [NPA 881 (2012) 127]: YES , bound by KNN | 2 calculated in a about 9 MeV, from a peak in | T ¯ fixed-scatterer approximation to Faddeev equations. • Shevchenko [NPA 890-1 (2012) 50]: UNLIKELY , judging from the K − d scattering length and effective range deduced from a ¯ KNN Faddeev calculation. • Barnea, Gal & Liverts do not find such a bound state below the Λ ∗ N threshold at B = 11 . 4 MeV. 10

K − pp calculated binding energies & widths (in MeV) chiral, energy dependent non-chiral, static calculations var. [1] var. [2] Fad. [3] var. [4] Fad. [5] Fad. [6] var. [7] B 16 17–23 9–16 48 50–70 60–95 40–80 Γ 41 40–70 34–46 61 90–110 45–80 40–85 1. N. Barnea, A. Gal, E.Z. Liverts, PLB 712 (2012) 2. A. Dot´ e, T. Hyodo, W. Weise, NPA 804 (2008) 197, PRC 79 (2009) 014003 3. Y. Ikeda, H. Kamano, T. Sato, PTP 124 (2010) 533 4. T. Yamazaki, Y. Akaishi, PLB 535 (2002) 70 5. N.V. Shevchenko, A. Gal, J. Mareˇ s, PRL 98 (2007) 082301 6. Y. Ikeda, T. Sato, PRC 76 (2007) 035203, PRC 79 (2009) 035201 7. S. Wycech, A.M. Green, PRC 79 (2009) 014001 (including p waves) Robust binding & large widths; chiral models give weak binding 11

Yamazaki et al. PRL 104 (2010) 132502, DISTO data reanalysis at 2.85 GeV Broad K − pp structure in pp → Λ pK + at πN Σ threshold pp → ( K − pp ) + K + at GSI Forthcoming experiments: π + d → ( K − pp ) + K + (E27) at J-PARC K − 3 He → ( K − pp ) + n (E15) & 12

RMF quasibound spectra calculated self-consistently (NLO30 ‘+ SE’) 100 Pb Zr Pb 1i Zr C Ca 80 3p 40 2f He 1h Ca O O 60 C 1g 1s Γ K (MeV) B K (MeV) 1f 30 2s 1d Li 1p Li 3s 2d 40 2p 2d 3s 1p 2p 1h 1d 2s 1f 1g 20 2f He 3p 20 1i 1s 10 0 10 20 30 40 0 10 20 30 40 A 2/3 A 2/3 D. Gazda, J. Mareˇ s, NPA 881 (2012) 159 • NLO30 is a chirally motivated coupled channel separable model with in-medium versions [A. Ciepl´ y, J. Smejkal, NPA 881 (2012) 115] • Γ K due only to K − N → πY (no K − NN → Y N ) decay modes • Self consistency: deep K − levels are narrower than shallow ones 13

What do K − atoms tell us? 14

kaonic atoms F model 1 10 3 n=2 5 6 7 4 0 10 −1 10 width (keV) n=8 −2 10 −3 10 −4 10 −5 10 0 10 20 30 40 50 60 70 80 90 100 Z K − atom widths across the periodic table in model F (deep pot.) Lowest χ 2 phenom. model, χ 2 = 84 per 65 data points, J. Mareˇ s, E. Friedman, A. Gal, NPA 770 (2006) 84. 15

0.4 2.0 − overlap Ni +4f K normalized formation rates 6 |R| 2 ρ m DD model 10 0.3 1.5 −4 6 |R| 2 ρ m ‘t ρ ’ model 3 10 R(1s Λ ) x10 −3 or fm 0.2 1.0 ρ m SH (shallow) fm DD (deep) 0.1 0.5 0 0.0 0 1 2 3 4 5 6 7 8 9 10 6 8 10 12 14 16 18 r (fm) mass number Left: K − -Ni 4f atomic wavefunction overlap with nuclear density for deep potential, revealing a nuclear ℓ = 3 quasibound state. Right: FINUDA 1 s Λ formation rates in K − stop capture in nuclei [Ciepl´ y-Friedman-Gal-Krejˇ ciˇ r´ ık, PLB 698 (2011) 226]. Deep K − nuclear potential is favored. 16

Self-consistency requirement imposed in recent K − atom calculations [Ciepl´ y-Friedman-Gal-Gazda-Mareˇ s, PLB 702 (2011) 402]: p 2 p 2 √ s K − N → E th − B N − B K − ξ N N K − ξ K 2 m N 2 m K p 2 m N ( K ) K ∼ − V K − ≈ 100 MeV ξ N ( K ) = ( m N + m K ) 2 m K E vs. ρ K − is not at rest! −10 E−E th (MeV) −30 Ni Friedman-Gal, NPA 899 (2013) 60 −50 K − N subthreshold energy vs Pb −70 nuclear density in K − atoms. −90 A dominant in-medium effect 0 0.2 0.4 0.6 0.8 1 ρ / ρ 0 17

1.2 − Ni F eff K 1.4 IHW average amplitude Imag. 1.0 1.2 Real average f (fm) 0.8 1.0 0.6 eff (fm) 0.8 Real 0.4 F 0.6 0.2 1N only 0.4 Imag. 0.0 1N only 0.2 −0.2 0.0 1340 1360 1380 1400 1420 1440 0 0.2 0.4 0.6 0.8 1 s 1/2 (MeV) ρ / ρ 0 Right: atomic-fit output F eff Left: IHW free-space input f K − N tot • Subthreshold energy shift is applied self consistently to in-medium 1N amplitude plus (2+...)N phenomenological amplitude. • Multiple-scattering inclusion of in-medium correlations. • K − -atom best-fit: χ 2 / N data = 118 / 65 [Friedman-Gal, NPA 899 (2013) 60]. 18

0 0 − Ni potentials K − Ni potentials − (MeV) − (MeV) K −40 −40 1N −80 −80 IHW Re V K Re V K IHW −120 −120 mN −160 −160 NLO30 −200 −200 − (MeV) − (MeV) −20 −20 1N IHW IHW Im V K Im V K −60 −60 NLO30 mN −100 −100 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 r (fm) r (fm) Kaonic-atom best-fit V K − for Ni & its non-additive breakdown into in-medium 1N and phenomenological m(any)N contributions. NLO30: A. Cieply, J. Smejkal, NPA 881 (2012) 115 (in-medium). IHW: Y. Ikeda, T. Hyodo, W. Weise, NPA 881 (2012) 98. Figures taken from Friedman-Gal, NPA 899 (2013) 60. 19

0 0 -20 -10 -40 -20 Im V one [MeV] Im V two [MeV] -60 -30 Mesonic Nonmesonic -80 -40 p K = 0 MeV/ c p K = 0 MeV/ c p K = 50 MeV/ c p K = 50 MeV/ c -100 -50 p K = 100 MeV/ c p K = 100 MeV/ c p K = 150 MeV/ c p K = 150 MeV/ c -120 -60 p K = 200 MeV/ c p K = 200 MeV/ c p K = 250 MeV/ c A bound state p K = 250 MeV/ c A bound state -140 -70 0 0.05 0.1 0.15 0.2 0 0.05 0.1 0.15 0.2 ρ N [fm –3 ] ρ N [fm –3 ] K − nuclear 1N (left) and 2N (right) absorptive potentials, both calculated in a chiral unitary approach [PRC 86 (2012) 065205] by Sekihara, Yamagata-Sekihara, Jido, Kanada-En’yo. Note: empirical 25% 2N:1N BR is reached at too high density. 20

η nuclear quasibound states 21