hyperon puzzle RMF nucleonic parametrization hyperonic parametrization results summary Role of hyperon–scalar-meson couplings on the EoS Giuseppe Colucci1 1Institut für Theoretische Physik, Goethe Universität, Frankfurt am Main Yerevan, September 19th, 2013 GC and A. Sedrakian, Phys. Rev. C 87, 055806 (2013) HGS-HIRe Helmholtz Graduate School for Hadron and Ion Research hyperon puzzle RMF nucleonic parametrization hyperonic parametrization results summary outline 1 hyperon puzzle 2 RMF 3 nucleonic parametrization 4 hyperonic parametrization 5 results 6 summary hyperon puzzle RMF nucleonic parametrization hyperonic parametrization results summary hyperon puzzle 1 hyperon puzzle 2 RMF 3 nucleonic parametrization 4 hyperonic parametrization 5 results 6 summary hyperon puzzle RMF nucleonic parametrization hyperonic parametrization results summary PSR J1614-2230: M = 1:97 ± 0:04 M pulsar 30 20 10 0 -10 -20 -30 -40 30 20 10 s) µ 0 -10 Timing residual ( -20 -30 -40 30 20 10 0 -10 -20 -30 -40 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Orbital Phase (turns) *Here we present radio timing observations of the binary millisecond pulsar J1614-2230 that show a strong Shapiro delay signature. We calculate the pulsars mass to be 1:97 ± 0:04 solar masses which rules out almost all currently proposed hyperon or boson condensate equations of state.* (Demorest et al, 2010, Nature 467, 1081) hyperon puzzle RMF nucleonic parametrization hyperonic parametrization results summary onset of hyperons in neutron star matter 1800 µ 0 µ B = n µ - µ µ 1600 B = n+ e µ + µ µ Page and Reddy (2006) B = n- e thin lines: free gas 1400 thick lines: with mean-field NN − + Σ Σ potential 1200 Λ horizontal lines are hyperon vacuum masses 1000 Baryon chemical potential (MeV) 800 0 1 2 3 4 5 6 7 8 nB/n0 hyperons appear, when its in-medium energy equals its chemical potential: µ(Y ) = !(Y ) = mY + UY (n); with µ(Y ) = B(Y ) · µn − Q(Y ) · µe onset in several models: RMF, DBHF, DDMF, ξ with SU(3) symmetry HIC? hyperon puzzle RMF nucleonic parametrization hyperonic parametrization results summary consequences of hyperons on the maximum mass of neutron stars Glendenning and Moszkowski (1991) neutron star with nucleons and leptons only: M ≈ 2:3M substantial decrease of the maximum mass due to hyperons maximum mass for "giant hypernuclei": M ≈ 1:7M noninteracting hyperons result in a too low mass: M ≈ 1:4M hyperon coupling constants: gσY Y = gρY Y = 0:6gρNN and g!Y Y = 0:658gρNN At a given density, the presence of hyperons increases the number of Fermi spheres to be occupied leading to a lower pressure what is an effective model? full model effective model d.o.f.: observable particles (hadrons) instead of quarks and gluons hyperon puzzle RMF nucleonic parametrization hyperonic parametrization results summary how can we study this problem? analytical, first-principle treatment of QCD is currently a cherished dream. extremely high energies/densities ! perturbative QCD very low energies/densities ! well defined nuclear physics based on NN potentials intermediate energies/densities ! many effective models - astrophysical applications: supernovae compact objects (white dwarfs, neutron stars, black holes) hyperon puzzle RMF nucleonic parametrization hyperonic parametrization results summary how can we study this problem? analytical, first-principle treatment of QCD is currently a cherished dream. extremely high energies/densities ! perturbative QCD very low energies/densities ! well defined nuclear physics based on NN potentials intermediate energies/densities ! many effective models - astrophysical applications: supernovae compact objects (white dwarfs, neutron stars, black holes) what is an effective model? full model effective model d.o.f.: observable particles (hadrons) instead of quarks and gluons hyperon puzzle RMF nucleonic parametrization hyperonic parametrization results summary RMF 1 hyperon puzzle 2 RMF 3 nucleonic parametrization 4 hyperonic parametrization 5 results 6 summary hyperon puzzle RMF nucleonic parametrization hyperonic parametrization results summary relativistic mean-field (RMF) model basic assumptions and features for describing nuclear (and hypernuclear) properties: nucleons (and hyperons) interact through meson exchange assume that only low spin, isospin is needed (from OBEP) only Hartree diagrams σ–meson: mimics attractive potential nonlinearities of the σ–meson–field: needed for a correct compression modulus of nuclear matter (not always) !–meson: repulsive part of the potential ρ–meson: isospin dependent part of the potential hyperon puzzle RMF nucleonic parametrization hyperonic parametrization results summary RMF Lagrangian full Lagrangian X ¯ µ 1 LB = B [γ (i@µ − g!BB !µ − gρBB τ · ρµ) − (mB − gσBB σ)] B 2 B 1 µ 1 2 2 1 2 µ 1 µν 1 2 µ + @ σ@µσ − m σ + m ! !µ − ρ · ρµν + m ρ · ρµ 2 2 σ 2 ! 4 2 ρ X ¯ µ + λ(iγ @µ − mλ) λ e−,µ− 1 µν − F Fµν 4 baryon octet: p; n; Λ; Σ’s and Ξ’s mesons: σ; ! and ρ leptons: e−; µ− (and neutrinos at finite-temperature) photons hyperon puzzle RMF nucleonic parametrization hyperonic parametrization results summary nucleonic parametrization 1 hyperon puzzle 2 RMF 3 nucleonic parametrization 4 hyperonic parametrization 5 results 6 summary hyperon puzzle RMF nucleonic parametrization hyperonic parametrization results summary meson-nucleon coupling constants - DD-ME2 parametrization ansatz: giNN (ρ) = giNN (ρsat)fi(x) for i = σ; ! where 2 1 + bi(x + di) f (x) = a x = ρ/ρ i i 2 sat 1 + ci(x + di) and gρNN (ρ) = gρNN (ρsat) exp[−aρ(x − 1)] in total 8 parameters to be adjusted to reproduce the properties of symmetric and asymmetric nuclear matter, binding energies, charge radii, and neutron radii of spherical nuclei 18 g_sigma(x) 16 g_omega(x) g_rho(x) 14 12 10 8 6 (i = sigma,omega,rho) i 4 g 2 0 0 0.5 1 1.5 2 2.5 3 x = rho/rhosat (Niksic et al., 2008) hyperon puzzle RMF nucleonic parametrization hyperonic parametrization results summary rearrangement self-energy contributions 1 1 1 P = − m2 σ2 + m2 !2 + m2ρ2 2 σ 2 ! 0 2 ρ 03 Z 1 4 1 X 2JB + 1 k dk ∗ ∗ + [f(Ek − µ ) + f(Ek + µ )] 3 2π2 (k2 + m∗2)1=2 B B B 0 B 1 X 1 Z 1 k4 dk + [f(E − µ ) + f(E + µ )] 2 2 2 1=2 k l k l 3 π 0 (k + m ) l=e−,µ− l +ρB Σr; where Σr is the rearrangement self-energy: @gNN! @gNNσ Σr = !0ρB − σρS ; @ρB @ρB thermodynamic consistency 2 @ P = ρB @ρB ρB hyperon puzzle RMF nucleonic parametrization hyperonic parametrization results summary hyperonic parametrization 1 hyperon puzzle 2 RMF 3 nucleonic parametrization 4 hyperonic parametrization 5 results 6 summary hyperon puzzle RMF nucleonic parametrization hyperonic parametrization results summary choice of hyperon couplings - vector mesons VDM: universal coupling of ρ to the isospin current 1 gΞΞρ = gNNρ = gΣΣρ; gΛΛρ = 0 2 quark model and ideal mixing: mesons 1 ! ∼ p uu¯ + dd¯ 2 φ ∼ ss¯ simple strangeness-content counting 2 gΣΣ! = gΛΛ! = 2gΞΞ! = gNN! 3 hyperon puzzle RMF nucleonic parametrization hyperonic parametrization results summary choice of hyperon couplings - scalar mesons for the scalar octet (de Swart, 1955): 1 gNNa = gS ; gNNσ = p gS (4αS − 1) 0 8 3 2 gΣΣa = 2gS αS ; gΣΣσ = p gS (1 − αS ) 0 8 3 2 gΛΛa = 0; gΛΛσ = − p gS (1 − αS ) 0 8 3 1 gΞΞa = −gS (1 − 2αS ); gΞΞσ = − p gS (1 + 2αS ) 0 8 3 nonet mixing: g = cos θ g + sin θ g BBσ S 1 S BBσ8 relation independent on θS ; αS ; g1 and gS ! 2(gNNσ + gΞΞσ) = 3gΛΛσ + gΣΣσ parameter study by fixing one of the couplings to NSC89 hyperon puzzle RMF nucleonic parametrization hyperonic parametrization results summary results 1 hyperon puzzle 2 RMF 3 nucleonic parametrization 4 hyperonic parametrization 5 results 6 summary hyperon puzzle RMF nucleonic parametrization hyperonic parametrization results summary results for zero-temperature hyperon coupling constants fixed by NSC89 300 = 0.26 = 0.52 xΣΣσ xΛΛσ = 0.46 = 0.59 xΣΣσ xΛΛσ = 0.66 = 0.66 xΣΣσ xΛΛσ SU(6) SU(6) N N 200 ] 3 P [MeV fm 100 0 0 1 2 3 4 5 0 1 2 3 4 5 6 ρ /ρ ρ /ρ B 0 B 0 xΛΛσ = 0:58 xΣΣσ = 0:448 hyperon puzzle RMF nucleonic parametrization hyperonic parametrization results summary mass-radius relation 2.5 2.5 2 2 O 1.5 O 1.5 M/M 1 M/M 1 0.5 xΣΣσ = 0.26, xΛΛσ = 0.58 0.5 xΣΣσ = 0.66, xΛΛσ = 0.58 xΣΣσ = 0.66, xΛΛσ = 0.58 xΣΣσ = 0.26, xΛΛσ = 0.58 2.5 2.5 2 2 O 1.5 O 1.5 M/M 1 M/M 1 0.5 xΛΛσ = 0.52, xΣΣσ = 0.448 xΛΛσ = 0.52, xΣΣσ = 0.448 x = 0.66, x = 0.448 0.5 ΛΛσ ΣΣσ x = 0.66, x = 0.448 0 ΛΛσ ΣΣσ 0.5 1 1.5 2 0 10 12 14 16 18 ρ 15 -3 B [10 g cm ] R [km] hyperon puzzle RMF nucleonic parametrization hyperonic parametrization results summary particle fractions: zero temperature 1 n n 0.1 − Σ Λ p B p 0 /n Σ − i n − e e + Σ − 0.01 µ Ξ− µ− 0 − Ξ 0 Σ Λ Σ 1 2 3 4 5 1 2 3 4 5 6 ρ ρ ρ ρ B/ 0 B/ 0 symmetric case stiffest (hyp) case deleptonization due to negative hyperon onset shift of hyperon onset in case of small *attractive* couplings (gY σ) hyperon puzzle RMF nucleonic parametrization hyperonic parametrization results summary finite-temperature and neutrino trapping new dof (neutrinos) ! new constraint: fixed lepton fraction 400 YL = 0.4 YL = 0.4 YL = 0.1 YL = 0.1 = 0 = 0 Yν Yν 300 ] 3 200 P [MeV fm 100 0 0 1 2 3 4 5 0 1 2 3 4 5 6 ρ /ρ ρ /ρ B 0 B 0 (T = 30 MeV) hyperon puzzle RMF nucleonic parametrization hyperonic parametrization results summary particle fractions: finite temperature 1 n p n − e − ν p µ µ Σ− ν B e /n i 0.1 0 n Λ Σ Σ+ − Λ − Ξ e 0 Σ0 Ξ − µ + 0 Σ Ξ Σ− Ξ− 0.01 1 2 3 4 5 1 2 3 4 5 6 ρ ρ ρ ρ B/ 0 B/ 0 Yν = 0 Yν = 0:4 no deleptonization due to fixed lepton fraction positive charged hyperons favoured due to the presence of electrons inversion of charged hyperon onset hyperon puzzle RMF nucleonic parametrization hyperonic parametrization results summary summary 1 hyperon puzzle 2 RMF 3 nucleonic parametrization 4 hyperonic parametrization 5 results 6 summary hyperon puzzle RMF nucleonic parametrization hyperonic parametrization results summary summary summary recent data (2M NS) and hyperon puzzle realistic meson-nucleon interaction at finite density choice of hyperon couplings: parameter study for scalar-hyperon interaction finte temperature and neutrino trapping outlook effect of pions from chiral lagrangians strong magnetic field contribution hyperon puzzle RMF nucleonic parametrization hyperonic parametrization results summary thanks for your attention!.