The role of stangeness in hadronic matter (in)stability: from hypernuclei to compact stars

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1 The role of stangeness in hadronic matter (in)stability: from hypernuclei to compact stars James R. Torres (former Ph.D. student), Francesca Gulminelli and DPM Universidade Federal de Santa Catarina (Brazil) and EnsiCaen (France) INCT Adelaide

2 Are there strangeness driven phase transitions at low (liquid-gas) and high (stellar matter) densities? Motivation: low densities Many hypernuclei have been synthetized lately. To describe/understand their properties, hadronic matter must have strange degrees of freedom. What s the influence of strangeness in the liquid-gas phase transition? Is strangeness an order parameter of the transition? RMF models are parameter dependent. How can we choose the meson-hyperon couplings based on known phenomenology?

3 Motivation: high densities The hyperon puzzle: PSR J and PSR J (2 M ) require very stiff EOS at large densities but heavy ion collisions point in opposite direction for ρ < 5ρ. Hyperons are energetically favored, but soften the EoS; they are associated to first order phase transitions in many RMF models. Strange vector mesons mediating the hyperon-hyperon interaction increases the maximum mass, just pushing away the hyperon threshold. Meson-hyperon coupling constants are unknown: how to parametrize them in a less handwaving way as possible? Possible existence of instabilities in the strange sector are model dependent. How are they related to the values of the mesonhyperon couplings?

4 Formalism - RMF - (N)LWM L NLWM = j ψ j [ γ µ ( i µ g ωj ω µ g φj φ µ g ρj τ ρ µ ) ( mj g σj σ g σ jσ )] ψ j ( µ σ µ σ m 2 σ σ2) 1 3 bm N (g σn σ) c(g σnσ) 4 ( µ σ µ σ m 2 σ σ 2) 1 4 Ω µν Ω µν m2 ω ω µω µ 1 4 Φ µνφ µν m2 φ φµ φ µ 1 4 Rµν R µν m2 ρ ρ µ ρ µ (1) σ - strange scalar meson field, φ - strange vector meson field, b,c - non-linear terms, LWM - QHII, NLWM - GM1, g ij = χ ij g in, i = σ,ω,ρ,σ,φ.

5 Hyperon couplings in the literature SU(6): χ σλ = χ ωλ = 2/3, χ ρλ =, χ σ Λ = χ ΦΛ = 2/3 Glendenning conjecture: g Yσ g Nσ =.7, g Yω g Nω = χ ω g Yρ g Nρ = I 3B I 3N χ ρ, (2) the ρ meson always couples to the isospin projection I 3 ; the value of χ ρ is completely arbitrary: χ Yω = χ Yρ =.783 (GM1),.8 (GM3),.772 (NL3) so that U N Λ = 28 MeV. SU(3): Depends on the original parameter set: Luiz L. Lopes and Debora P. Menezes, Phys. Rev. C 89, 2585 (214)

6 Our prescription: U N Λ (n N) = 28MeV is the potential one Λ feels due to the nuclear symmetric mean field: Sym {}}{ U Λ ( n N,n Λ ) = χ ωλ (g ωn ω )+χ φλ (g ωn φ ) χ σλ (g σn σ ) χ σ Λ From the equations of motion, it becomes: ( gσn σ ). (3) UΛ N (n N) (4) ( ) gωn 2nN ( ) gσn 2[ρ = χ ωλ χ s σλ m ω m N (σ) bm n σ 2 cσ 3]. σ χ ωλ = χ σλ σ N=n 28 MeV ω N=n. (5)

7 U Λ Λ (n Λ) is the potential one Λ feels due to field generated by the other Λs in a pure Λ matter; U Λ Λ( n 5 ) =.67MeV U Λ Λ (n Λ) = 1+( χφλ χ ωλ ) 2 ( ) 2 mω m φ (χ ωλ )ω 1+( χσ Λ χ σλ ) 2 ( mσ m σ ) 2 (χ σλ )Σ (6) Σ = σ ( ) gσn 2 [ m σ ( χσ Λ χ σλ ) 2 ( 1+ ( χ σ Λ m σ m σ χ σλ ) 2 ( ) 2 ) ] 2 m σ m σ ( bmn σ 2 cσ 3). (7) χ φλ = ( ) mφ UΛ Λ m ω ( n 5 ) + [ 1+ ( χ σ Λ χ σλ ) 2 ( m σ m σ ) 2 ] χ σλ Σ χ ωλ ω χ ωλ ω χ ωλ. (8) Σ Σ nλ = n 5, ω ω nλ = n 5

8 χ ωλ is constrained by χ σλ and χ φλ is constrained by χ σ Λ. 5 4 LWM NLWM χ σλ =χ ωλ 3 χ ωλ χ σλ The increase of the χ σλ makes the potential more attractive at low densities AND more repulsive at high densities.

9 The increase of χ σ Λ increases the repulsion at high densities, but it is not the dominant feature.

10 Spinodals - Low densities 1 n Λ plane; 2 p Λ plane; 3 n p plane; 4 N Λ(Y p = Y n ) plane

11 (fm -3 ) n Y = χ σ Λ = χ φλ = LWM χ σλ NLWM χ σλ 3 ) n (fm NLWM χ σλ χ σ Λ n B (fm -3 ) Y Y = nn(fm -3 ) NLWM χ σλ χ σ Λ Y Λ n n (fm 3 ) 1.5 nλ(fm 3 ) n B (fm -3 ) n n (fm 3 )

12 High densities Non-relativistic ab-initio models: D, Lonardoni, A. Lovato, S. Gandolfi and F. Pederiva, PRL 114, 9231 (215).4 μ Λ =μ n.4 nb=6 fm -3 μ Λ =μ n.4 nb=6 fm Y Λ = 7 Y Λ = 7 Y Λ = 7 μ Λ =μ n n B =6 fm body interaction 3-body interaction (I) 3-body interaction (II)

13 5 4 χ ϕλ χ σ Λ Gray points = parameters for which there is no convergence in stellar matter; Λ effective mass becomes negative; χ ρ = 1.5 was fixed in such a way that Λ hyperons appear before Σ.

14 p - e NLWM χ σλ = χ σ Λ χ σλ = χ σ Λ Y 1.1 χ σλ = χ σ*λ = n Λ μ χ σ*λ= χ ϕλ= n p Λ e - μ n B (fm 3 ) If χ σλ > 1, no hyperons appear; χ σ Λ do not alter the onset of hyperons.

15 .6 LWM χ σλ = χ σ Λ =.6 NLWM χ σλ = χ σ Λ =.4 nb= fm -3.4 nb= fm No instabilities at high densities with RMF models!!!

16 Stellar Matter - 8 baryons included NLWM - χ σh =, χ ρh = χ σ H M max (M ) R (km) ǫ c (fm 4 ) n c (fm 3 ) YΛ c YH c n Λ Lim (fm 3 ) NLWM - χ σh =.8, χ ρh = χ σ H M max (M ) R (km) ǫ c (fm 4 ) n c (fm 3 ) YΛ c YH c.33 n Λ Lim (fm 3 ) The increase of the χ σλ (χ σ Λ) makes the potential U N Λ (UΛ Λ ) more repulsive at high densities and the EoS becomes stiffer. - M max < 1.44 (M )

17 Conclusions - Low densities At subsaturation densities, the existence of a n-λ liquid-gas phase transition is the result of a very clear hadronic matter instability. If n-p-λ matter is investigated, the instability is still present, strangeness being an order parameter of the phase transition, which means that dilute strange matter is expected to be unstable with respect to hyperclusters. Liquid-gas phase transition is slightly quenched by the inclusion of Λs.

18 Conclusions - High densities Once the meson-hyperon couplings are constrained to satisfy hypernuclear experimental potentials, no instability at supersaturation densities is found. Non-relativistic model produces pathological results. Hence, a strangeness driven phase transition only takes place in neutron star matter if quarks are present. Using our prescription, massive stars with small radii are obtained, in accordance with recent observational and theoretical results.

19 James R. Torres, Francesca Gulminelli and Debora P Menezes, PRC 93, 2436 (216); James R. Torres, Francesca Gulminelli and Debora P Menezes, arxiv: Thank you