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hyperon puzzle RMF nucleonic parametrization hyperonic parametrization results summary

Role of –scalar- 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 and Ion Research hyperon puzzle RMF nucleonic parametrization hyperonic parametrization results summary outline

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PSR J1614-2230: M = 1.97 ± 0.04 M pulsar

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-10 Timing residual ( -20

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-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 condensate equations of state.* (Demorest et al, 2010, Nature 467, 1081) hyperon puzzle RMF nucleonic parametrization hyperonic parametrization results summary onset of in star

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 (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 ) = ω(Y ) = mY + UY (n), with µ(Y ) = B(Y ) · µn − Q(Y ) · µe

onset in several models: RMF, DBHF, DDMF, ξ with SU(3) 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 and 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 gωY 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 () instead of and

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 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

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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 , 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) ω–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 = ψB [γ (i∂µ − gωBB ωµ − gρBB τ · ρµ) − (mB − gσBB σ)]ψB 2 B

1 µ 1 2 2 1 2 µ 1 µν 1 2 µ + ∂ σ∂µσ − m σ + m ω ωµ − ρ · ρµν + m ρ · ρµ 2 2 σ 2 ω 4 2 ρ X ¯ µ + ψλ(iγ ∂µ − mλ)ψλ e−,µ−

1 µν − F Fµν 4

baryon octet: p, n, Λ, Σ’s and Ξ’s : σ, ω and ρ leptons: e−, µ− (and at finite-) hyperon puzzle RMF nucleonic parametrization hyperonic parametrization results summary nucleonic parametrization

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6 summary hyperon puzzle RMF nucleonic parametrization hyperonic parametrization results summary meson- coupling constants - DD-ME2 parametrization

ansatz: giNN (ρ) = giNN (ρsat)fi(x) for i = σ, ω 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, 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 ω2 + m2ρ2 2 σ 2 ω 0 2 ρ 03 Z ∞ 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 ∞ 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:

∂gNNω ∂gNNσ Σr = ω0ρB − σρS , ∂ρB ∂ρB thermodynamic consistency   2 ∂  P = ρB ∂ρB ρB hyperon puzzle RMF nucleonic parametrization hyperonic parametrization results summary hyperonic parametrization

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VDM: universal coupling of ρ to the isospin current 1 gΞΞρ = gNNρ = gΣΣρ, gΛΛρ = 0 2 model and ideal mixing: mesons 1 ω ∼ √ uu¯ + dd¯  2 φ ∼ ss¯

simple -content counting 2 gΣΣω = gΛΛω = 2gΞΞω = gNNω 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 = √ gS (4αS − 1) 0 8 3 2 gΣΣa = 2gS αS , gΣΣσ = √ gS (1 − αS ) 0 8 3 2 gΛΛa = 0, gΛΛσ = − √ gS (1 − αS ) 0 8 3 1 gΞΞa = −gS (1 − 2αS ), gΞΞσ = − √ 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

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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 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 trapping

new dof (neutrinos) → new constraint: fixed 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 inversion of charged hyperon onset hyperon puzzle RMF nucleonic parametrization hyperonic parametrization results summary summary

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summary

recent data (2M NS) and hyperon puzzle realistic meson-nucleon at finite density choice of hyperon couplings: parameter study for scalar-hyperon interaction finte temperature and neutrino trapping outlook effect of from chiral lagrangians strong magnetic field contribution hyperon puzzle RMF nucleonic parametrization hyperonic parametrization results summary

thanks for your attention!