31st Reimei Workshop ASRC Tokai, Japan 18 January 2016 TOPICS in LOW - ENERGY QCD with STRANGE QUARKS Wolfram Weise T echnische U niversität M ünchen PHYSIK DEPARTMENT Symmetry breaking patterns in low - energy QCD : Chiral SU (3) effective field theory Antikaon - nucleon interactions and status of Λ ( 1405 ) ¯ systems: KNN K − d Kaonic deuterium and reactions In-medium meson spectral function and implications φ Hyperon - nucleon interactions: Chiral EFT and Lattice QCD Strangeness in dense baryonic matter Constraints from two-solar-mass neutron stars 1
Hierarchy of QUARK MASSES in QCD - separation of scales - 1 10 GeV 100 100 MeV 0 t b “ heavy ” quarks “ light ” quarks c u , d s PDG 2014 Basic principles of LOW - ENERGY QCD : Confinement of quarks & gluons in hadrons Chiral Symmetry explicitly broken spontaneously broken by non - zero ( QCD dynamics ) quark masses special role of STRANGE QUARKS 2 own
Spontaneously Broken CHIRAL SYMMETRY SU ( 3 ) L × SU ( 3 ) R NAMBU - GOLDSTONE BOSONS : Pseudoscalar SU(3) meson octet { φ a } = { π , K , ¯ K , η 8 } DECAY CONSTANTS : Chiral limit: f = 86 . 2 MeV a (0) | φ b ( p ) ⟩ = i δ ab p µ f b ⟨ 0 | A µ Order parameter : 4 π f ∼ 1 GeV µ f π = 92 . 21 ± 0 . 16 MeV π axial current f K = 110 . 5 ± 0 . 5 MeV K ν π = − m u + m d G ell-Mann, uu + ¯ m 2 π f 2 ⟨ ¯ dd ⟩ 2 + higher order O akes, corrections R enner K = − m u + m s m 2 K f 2 ⟨ ¯ ss ⟩ uu + ¯ relations 2 3
Spontaneously Broken CHIRAL SYMMETRY GOLDSTONE ’s Theorem : Massless Nambu-Goldstone bosons do not interact in the limit of zero momentum (long-wavelength limit) S - wave interactions of NG bosons T ∼ E scattering p m 2 + k 2 E = amplitude f 2 explicit chiral symmetry breaking meson decay constant Tomozawa - Weinberg order parameter of spontaneous low-energy theorem chiral symmetry breaking 4
CHIRAL SU ( 3 ) EFFECTIVE FIELD THEORY ordered hierarchy of driving interactions pseudoscalar [8] meson octet Leading order terms ( W einberg & T omozawa) baryon [8] octet ¯ Examples: (S = -1) and (S = +1) threshold (s wave) amplitudes : KN KN T ( K + p ) thr = 2 T ( K + n ) thr = − m K repulsive f 2 T ( K − p ) thr = 2 T ( K − n ) thr = m K attractive f 2 + + (d) next-to-leading order ( NLO ) O ( p 2 ) input : several low-energy constants 5
PART I Antikaon - Nucleon Interactions and the K (1405) - brief status report - 6
Low - Energy Interactions KN Framework: Chiral SU (3) Effective Field Theory . . . but : Chiral Perturbation Theory NOT applicable: N. Kaiser, P . Siegel, W. W. (1995) E. Oset, A. Ramos (1998) Λ (1405) resonance 27 MeV below threshold K − p * (1405) * (1385) L Non-perturbative S 1500 Coupled Channels ** (1520) L approach based on √ s [ MeV ] _ Chiral SU ( 3 ) Dynamics Lp Sp KN ` KN th Leading s-wave I = 0 meson-baryon interactions (Weinberg-Tomozawa) orld of antikaon-nucleon scattering ¯ Σ K N π π Σ ¯ KN π Σ ¯ ¯ K N Σ K π N channel coupling Recent Review : T. Hyodo, D. Jido Prog. Part. Nucl. Phys. 67 (2012) 55 7
CONSTRAINTS from SIDDHARTA Strong interaction Kaonic hydrogen 1s energy shift and width precision data Hydrogen EM value K-p K � spectrum Kaonic hydrogen K � K � higher SIDDHARTA KC54 KC65 Ti K � KO65 Ti K � KC75 KN65 KO76 KAl87 Cu M. Bazzi et al. (SIDDHARTA collaboration) Phys. Lett. B 704 (2011) 113 ∆ E = 283 ± 36 ( stat ) ± 6 ( syst ) eV − ε 1s = Γ = 541 ± 89 ( stat ) ± 22 ( syst ) eV 8
SCATTERING AMPLITUDE from K − p CHIRAL SU (3) COUPLED CHANNELS DYNAMICS Y. Ikeda, T. Hyodo, W. W. f ( K − p ) = 1 � � KN ( I = 0 ) + f ¯ KN ( I = 1 ) f ¯ PLB 706 (2011) 63 2 NPA881 (2012) 98 KN ( I = 0 ) quasibound state embedded in the π Σ continuum : ¯ Λ ( 1405 ) Prototype example for emergence of resonant structure close to a threshold 1.5 2.5 [ fm ] [ fm ] Im f ( K − p → K − p ) 1 2 Re f ( K − p → K − p ) 0.5 1.5 Re a ( K − p ) Λ ( 1405 ) 0 1 incl. SIDDHARTA -0.5 0.5 constraints Im a ( K − p ) -1 0 1340 1360 1380 1400 1420 1440 1340 1360 1380 1400 1420 1440 √ s [ MeV ] √ s [ MeV ] E (MeV) E (MeV) Complex scattering length (including Coulomb corrections) Im a ( K − p ) = 0 . 81 ± 0 . 15 fm Re a ( K − p ) = − 0 . 65 ± 0 . 10 fm 9
CHIRAL SU ( 3 ) COUPLED CHANNELS DYNAMICS Predicted antikaon - neutron amplitudes at and below threshold Y. Ikeda, T. Hyodo, W. Weise : Phys. Lett. B 706 (2011) 63 , Nucl. Phys. A 881 (2012) 98 0.8 0.8 real part imaginary part [ fm ] Re f ( K − n → K − n ) [ fm ] Im f ( K − n → K − n ) 0.6 TW 0.6 WT TW + Born 0.4 WTB NLO NLO 0.2 0.4 TW 0.0 WT TW + Born 0.2 WTB NLO -0.2 NLO -0.4 0.0 1360 1380 1400 1420 1440 1360 1380 1400 1420 1440 √ s [ MeV ] √ s [ MeV ] a ( K − n ) = 0 . 57 + 0 . 04 − 0 . 21 + i 0 . 72 + 0 . 26 − 0 . 41 fm Needed : accurate constraints from antikaon - deuteron threshold measurements complete information for both isospin I = 0 and channels ¯ I = 1 KN plus potentially important information about K - NN absorption 10
ANTIKAON - DEUTERON SCATTERING LENGTH Calculations using SIDDHARTA - constrained input Im a ( K − d ) [ fm ] excluded Looking Three-body forward to: Faddeev calculation multiple scattering separable “chiral” using I keda H yodo W KAONIC amplitudes ( c ) scattering lengths DEUTERIUM ( b ) N.V. Shevchenko measurements S. Ohnishi, T. Hyodo, NPA 890-891 (2012) 50 Y. Ikeda, W. W. (2014) ( a ) SIDDHARTA2 and Non-relativistic J-PARC E57 effective field theory excluded M. Döring, U.-G. Meißner Phys. Lett. B 704 (2011) 663 Re a ( K − d ) [ fm ] 11
Λ ( 1405 ) : RECENT NEWS γ p → K + π − Σ + @ CLAS / JLab ) (1405) Λ data 2 counts /(5 MeV/c 1000 * (1520) + Λ K Σ * 0 (1385) Y (1670) Σ K. Moriya et al. (CLAS collaboration) 500 Phys. Rev. D88 (2013) 045201 (a) 0 1.35 1.4 1.45 1.5 1.55 + - 2 M( ) (GeV/c ) Σ π Detailed analysis of distribution Σ + π − 1.8 40 ) 2 and polarization confirms Σ + ) (GeV/c 1.7 30 J P = 1 1.6 − of Λ ( 1405 ) 20 2 1.5 - � + � 10 (b) K. Moriya et al. (CLAS collaboration) 1.4 M( � Phys. Rev. Lett. 112 (2014) 068103 � 1.3 0 1 1.5 + - 2 M(K ) (GeV/c ) � 12 �
Recent Structure of Λ ( 1405 ) from Lattice QCD � developments: | Λ ∗ ⟩ = a | uds ⟩ + b | ( udu )( ¯ us ) ⟩ + . . . � | � Λ ∗ | n � | 2 | � | � Λ ∗ | n � | 2 constituent � 8 0.8 0.8 quark ¯ dominated KN 0.6 quasi 0.6 qqq molecular � “heavier” quarks ¯ 0.4 0.4 KN m π ≃ 0 . 6 GeV structure π Σ π Σ Σ ¯ ¯ KN 0.2 KN 0.2 “light” quarks qqq m π ≃ 0 . 3 GeV 570 570 ] [ MeV ] m m 296 J.M.M. Hall et al. ; Phys. Rev. Lett. 114 (2015) 132002 Note: qualitative structural change depending on quark mass (interplay of spontaneous & explicit chiral symmetry breaking) 13
Structure of Λ ( 1405 ) from Lattice QCD (contd.) Strangeness magnetic form factor of Λ ( 1405 ) Quasi-molecular state: s-quark localised in Kbar subcluster strange quark does not contribute to magnetic structure � 1.0 light sector strange sector � 0.8 J.M.M. Hall et al. � Phys. Rev. Lett. + 1 114 (2015) 132002 G M @ Μ N D 0.6 0 − 2 0.4 � 0.2 0.0 0.0 0.1 0.2 0.3 0.4 2 @ GeV ê c 2 D m Π 14
The TWO POLES scenario Characteristic feature of Chiral SU (3) Dynamics : Energy dependent driving interactions D. Jido et al. � !"#$%& ¯ KN π Σ Nucl. Phys. A723 (2003) 205 #(' T. Hyodo, W. W. Phys. Rev. C 77 (2008) 03524 #(% +,+&#-.'"(% #(" T. Hyodo, D. Jido #(' Prog. Part. Nucl. Phys. 67 (2012) 55 #($ #(% d o m i n a n t l y #(" dominantly &'# Σ #($ π ¯ &%# KN &"# )*#$%&#'"(% !"%# !""# &$# !"$# !"## !"#$%&#'"(% Pole positions from chiral SU ( 3 ) coupled - channels calculation T. Hyodo, D. Jido, arXiv:1104.4474 with SIDDHARTA threshold constraints: E 2 = 1381 ± 15 MeV E 1 = 1424 ± 15 MeV Y. Ikeda, T. Hyodo, W. W. : Nucl. Phys. A 881 (2012) 98 Γ 2 = 162 ± 15 MeV Γ 1 = 52 ± 10 MeV Note: phenomenological potential approach is qualitatively different: Y. Akaishi, T. Yamazaki energy- independent interaction, single pole Λ ( 1405 ) 15
Scenarios : TWO - POLES ENERGY - DEPENDENT vs. SINGLE - POLE ENERGY - INDEPENDENT �� � Three-body coupled channels (Faddeev) calculations Neutron energy spectrum mass distributions → π Σ (J-PARC E31) E-dependent - two poles E-independent - one pole K − d → n π − Σ + (a) E-dep. d σ /dM πΣ ( µ b/MeV) p lab (b) E-indep. = 1 GeV 0.3 0.3 K π + Σ - π - Σ + π 0 Σ 0 0.2 0.2 0.1 0.1 K − d → n π + Σ − 0 0 K − d → n π 0 Σ 0 1350 1400 1450 1500 1350 1400 1450 1500 M πΣ (MeV) M πΣ (MeV) S. Ohnishi, Y. Ikeda, T. Hyodo, W. W. : arXiv:1512.00123, Phys. Rev. C (2016) 16
Present status of K − d → n π Σ experiment 𝑒 𝐿 − , 𝑜 𝑌 𝜌 ± Σ ∓ E 31 @ J-PARC 𝜌 + Σ − /𝜌 − Σ + 𝑒 𝐿 − , 𝑜 𝑌 𝜌 ± Σ ∓ S Neutron detected in forward direction s resol . ~ 10 MeV 𝐿 − 𝑞 Focus on: possible structure around missing mass 1.42 GeV ? separation of and modes π + Σ − π − Σ + spectra above threshold KN 17
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