LAMBDA - NUCLEAR INTERACTION and HYPERON PUZZLE in NEUTRON STARS - PowerPoint PPT Presentation

Kyoto, 17 May 2017 LAMBDA - NUCLEAR INTERACTION and HYPERON PUZZLE in NEUTRON STARS Wolfram Weise T echnische U niversität M ünchen PHYSIK DEPARTMENT Equation of State of dense baryonic matter : constraints from massive neutron stars Hyperon-nucleon interactions from SU(3) chiral effective field theory Hyperon-NN three-body forces Emerging repulsions : suppression of hyperons in dense neutron matter Stefan Petschauer, Johann Haidenbauer, et al. : Eur. Phys. J. A (2017) (arXiv: 1612.03758 [nucl-th]); Nucl. Phys. A 957 (2017) 347; Phys. Rev. C93 (2016) 014001; Eur. Phys. J. A52 (2016)15; Nucl. Phys. A915 (2013) 24 1

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Part I: Prologue Cons ts aints on Equa tj ons of Sta tf fs om massive Neu ts on Stars 3

NEUTRON STARS and the EQUATION OF STATE of DENSE BARYONIC MATTER J. Lattimer, M. Prakash Phys. Reports 621(2016) 127 Phys. Reports 442 (2007) 109 Mass - Radius Relation quark matter ?? T olman- O ppenheimer- V olkov Equations NUCLEONIC MATTER ( M + 4 π Pr 3 )( E + P ) STRANGE dP dr = − G QUARK c 2 r ( r − GM / c 2 ) MATTER dM dr = 4 π r 2 E c 2 4

Constraints from massive NEUTRON STARS P .B. Demorest et al. J. Antoniadis et al. Nature 467 (2010) 1081 Science 340 (2013) 6131 Shapiro delay measurement M M PSR J1614+2230 PSR J0348+0432 . 8 M ⇥ M = 1 . 97 ± 0 . 04 M = 2 . 01 ± 0 . 04 . 8 M ⇥ conditions conditions 5

Population of MILLISECOND PULSARS J. Antoniadis et al. arXiv:1605.01665 0 . 5 1 . 0 1 . 5 2 . 0 ms pulsars in binaries 0 . 0 mass [ M � ] e.g. with white dwarfs double neutron stars Note: about 25% of population are mass [ M � ] massive n-stars ( M > 1 . 5 M � ) 6

CONSTRAINTS from NEUTRON STARS (contd.) Atmosphere model fits of Comprehensive analysis of X-ray bursts 12 selected neutron stars SAX J1810.8-2609 R = ( 11 . 5 − 13 . 0 ) km ( M = 1 . 3 − 1 . 8 M solar ) J. Nättilä et al. : Astron. Astroph. 591 (2016) A25 F. Özel, D. Psaltis, T. Güver, G. Baym, C. Heinke, S. Guillot V.F. Suleimanov et al. : arXiv:1611.09885 Astroph. J. 820 (2016) 28 7

CONSTRAINTS from NEUTRON STARS F. Özil, D. Psaltis: Phys. Rev. D80 (2009) 103003 F. Özil, G. Baym, T. Güver: Phys. Rev. D82 (2010)101301 3 Mass - 10 purely “ nuclear ” EoS ! 2.5 A. Akmal, V.R. Pandharipande, D.G. Ravenhall Radius 180 Phys. Rev. C 58 (1998) 1804 Relation 160 2 140 K. Hebeler, ) J. Lattimer, 120 M (M Ch. Pethick, 1.5 A. Schwenk: 100 Phys. Rev. Lett. kaon 105 (2010) 161102 80 condensate 1 60 r >>R ph A.W. Steiner, quark 40 J. Lattimer, E.F. Brown Astroph. J. 722 (2010) 33 matter 0.5 20 0 6 8 10 12 14 16 18 R (km) “ Exotic ” equations of state ruled out ? 8

NEUTRON STAR MATTER from Chiral EFT and FRG Symmetry energy range: 30 - 35 MeV Crust: SLy EoS M. Drews, W. W. 2 . 0 Phys. Rev. C91 (2015) 035802 Chiral T. Hell, W. W. Prog. Part. Nucl. Phys. 1 . 5 ChEFT Phys. Rev. FRG 93 (2017) 69 C90 (2014) 045801 M / M � 1 . 0 Central Radius core density window 0 . 5 ρ c . 5 ρ 0 A.W. Steiner, J.M. Lattimer, E.F. Brown EPJ A52 (2016) 18 0 16 8 12 14 10 R ( km ) Chiral many-body dynamics using “conventional” (pion & nucleon) degrees of freedom is consistent with neutron star constraints 9

… and extrapolation NEUTRON STAR MATTER to PQCD limit Equation of State A. Kurkela et al. Astroph. J. 789 (2014) 127 10000 10 2-tropes w/o neutron star mass constraint core region P 1000 1 pQCD . pQCD [ GeV / fm 3 ] 3-tropes w/o mass constraint 10 − 1 100 Polytropes ( with 2 M � mass constraint ) 2-tropes with mass constraint 10 − 2 10 Chiral NM − FRG Chiral EFT − FRG M. Drews, W. W. HLPS Phys. Rev. C91 (2015) 035802 . Neutron matter Neutron matter K. Hebeler et al. 10 − 3 1 APJ 773 (2013) 11 100 1000 10000 0 . 1 10 1 ε [ GeV / fm 3 ] 10

NEUTRON STAR MATTER Equation of State In-medium C hiral E ffective F ield T heory up to 3 loops (reproducing thermodynamics of normal nuclear matter) 3-flavor PNJL (chiral quark) model at high densities (incl. strange quarks) PNJL, G v ⇥ 0.5 G Th. Hell, W. W. conventional Phys. Rev. C90 (2014) 045801 ( hadronic ) 200 PNJL, G v ⇥ 0 equation of state neutron star 100 P � MeV fm � 3 ⇥ seems to work quark - nuclear constraints quark - nuclear coexistence coexistence 20 can occur at baryon densities 10 ChEFT ρ > 5 ρ 0 realistic 5 pressure “ conventional ” EoS ( ρ 0 = 0 . 16 fm − 3 ) ( nucleons & pions ) see also: 1 K. Masuda, T. Hatsuda, T. Takatsuka 50 100 200 300 500 1000 2000 PTEP (2013) 7, 073D01 ⇤ � MeV fm � 3 ⇥ energy density 11

NEUTRON STAR MATTER including HYPERONS In-medium C hiral E ffective F ield T heory (3-loops) plus hyperons (incl. potential consistent with hypernuclei) Λ 3-flavor PNJL model at high densities (incl. strange quarks) 1.0 T. Hell, W. W. Phys. Rev. C90 (2014) 045801 M max . 1 . 5 M � Particle n neutrons 0.8 composition: occurrence of 0.6 hyperons Λ r i ê r tot ρ i Fraction of quarks ρ d quarks µ n = µ Λ particle species 0.4 d u s u quarks L hyperons Λ as function of baryon density 0.2 s quarks protons p 0.0 0 2 4 6 8 10 ρ / ρ 0 r ê r 0 Equation of state too soft : maximum neutron star mass too low 12

NEUTRON STAR MATTER including HYPERONS 1 3 n NN " EFT600 n NSC97a N NSC97c 2.5 NSC97f p NSC89 0.1 p J04 ! EFT600 e 2 K 0 =300 MeV a t =32 MeV M [M 0 ] 0.01 1.5 N + Λ K 0 =200 MeV H. Djapo, a t =32 MeV 1 B.-J. Schaefer, 0.001 µ J. Wambach Λ Phys. Rev. C81 # 0.5 (2010) 035803 0.0001 0 1 2 3 4 5 6 10 12 14 16 ! B [ ! 0 ] R [km] Adding hyperons : equation of state far too soft “Hyperon Puzzle” 13

NEUTRON STAR MATTER including HYPERONS Q uantum M onte C arlo calculations using phenomenological hyperon-nucleon and hyperon-NN three-body interactions constrained by hypernuclei 2.8 QMC ChEFT PNM QMC 2.4 computations n − matter calculations PSR J0348+0432 (hyper-neutron matter): 2.0 “conventional” M Λ N + PSR J1614-2230 . � N + � NN (II) n-star matter M O Λ NN ( 2 ) 1.6 D. Lonardoni, ChEFT M [M 0 ] A. Lovato, Λ N + 1.2 S. Gandolfi, Λ NN ( 1 ) � N + � NN (I) T. Hell, W.W. F. Pederiva PRC90 (2014) 045801 0.8 Phys. Rev. Lett. 114 (2015) 092301 Λ N 0.4 � N 0.0 11 12 13 14 15 R [ km ] R [km] Inclusion of hyperons : EoS too soft to support 2-solar-mass n-stars unless: strong repulsion in YN and YNN … interactions 14

Part II Hyperon - Nucle0n In tf rac tj ons fs om Chiral SU ( 3 ) E ff ec tj ve Field Ti eory 15

Hierarchy of QUARK MASSES in QCD - Separation of Scales - 1 10 GeV 100 100 MeV 0 “ heavy ” quarks t b “ light ” quarks c u , d s PDG 2016 Basic principles of LOW - ENERGY QCD : Confinement of quarks & gluons in hadrons Chiral Symmetry SU ( 3 ) L × SU ( 3 ) R Spontaneously Explicitly broken broken by non - zero ( QCD dynamics ) quark masses 16

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 Order parameter : a (0) | φ b ( p ) ⟩ = i δ ab p µ f b ⟨ 0 | A µ 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 17

Chiral Effective Field Theory SU ( 3 ) L × SU ( 3 ) R Realization of Low-Energy QCD for energies / momenta Q < 4 π f ∼ 1 GeV based on SU(3) Non-Linear Sigma Model plus (heavy) baryons Pseudoscalar meson octet of SU ( 3 ) L × SU ( 3 ) R Nambu-Goldstone bosons coupled to baryon octet × Σ 0 π 0 2 + Λ Σ + η  π + K +  p   2 + √ √ √ √ 6 6 − Σ 0 − π 0 η 2 + Λ   K 0 Σ − , B = π − n P =   2 + √ √ √ √     6 6   − 2 η − 2 Λ Ξ 0 K 0 ¯ − Ξ − K − √ √ 6 6 (15) short distance meson-baryon + + + . . . dynamics: interaction contact terms vertices [ 8 ] [ 8 ] [ 8 ] [ 8 ] [ 8 ] [ 8 ] 18

Chiral Effective Field Theory SU ( 3 ) L × SU ( 3 ) R Starting point: Meson-Baryon Lagrangian (chiral limit) � ¯ � ¯ � ¯ − D − F � � � � � L MB = tr B i γ µ D µ − M 0 B 2 tr B γ µ γ 5 { u µ , B } 2 tr B γ µ γ 5 [ u µ , B ] × π 0 Σ 0 η   2 + Λ π + K + Σ + 2 + p   √ √ √ √ 6 6 − π 0 − Σ 0 η   K 0 2 + Λ π − P = , B = Σ − 2 +  n  √ √ √ √   6  6    − 2 η − 2 Λ K 0 ¯ Ξ 0 K − − Ξ − √ √ 6 6 (15) Chiral covariant derivative: with D µ B = ∂ µ B + [ Γ µ , B ], space. The constant M 0 de B ], Γ µ = 1 2 ( u † ∂ µ u + u ∂ µ u † ) a ) and u µ = i( u † ∂ µ u − u ∂ µ u † ), denotes the baryon mass i n the three-flavor chiral lim Chiral (pseudoscalar Nambu-Goldstone boson) field : ! √ 2 P ( x ) transforms as U → R U L † U ( x ) = u 2 ( x ) = exp i f R ∈ SU (3) R L ∈ SU (3) L 19