Kaon and strangeness production in an effective relativistic mean field model

Abstract

Abstract. We investigate the strangeness production at finite temperature and baryon density by means of an effective relativistic mean-field model with the inclusion of the full octet of baryons and kaon mesons. Kaons are considered taking into account of an effective chemical potential depending on the self-consistent interaction between baryons. In this context, we study the influence of the kaon-nucleon interaction in the determination of the kaon to anti-kaon ratio and in the strangeness production. The results are then compared with a minimal coupling scheme, calculated for different values of the antikaon optical potential.We investigate the nuclear medium in the context of relativistic mean field approach, where the nuclear force is mediated by the exchange of isoscalar-scalar (σ), isoscalar-vector (ω) and isovectorvector (ρ) mesons fields [1,2]. The hadronic lagrangian can be expressed as:where L octet stands for the full octet of baryons in the quantum hadrodynamics model with the GM3 parameters set [1] and L K for kaon mesons (see below for details). Hyperon degrees of freedom are included taking into account of the determination of the corresponding meson-hyperon coupling constants that have been fitted to hypernuclear properties [3,4].Because we are going to describe finite temperature and density nuclear matter with respect to strong interaction, we have to require the conservation of three "charges": baryon number, electric charge and strangeness number. Therefore, the chemical potential of particle of index i can be written aswhere b i , c i and s i are, respectively, the baryon, the electric charge and the strangeness quantum numbers of the i-th hadrons and the effective chemical potential µ * i of the i-th baryon is given byIn this work, we are going to study the kaon degrees of freedom using two different approaches. At this scope, for simplicity, other strangeless mesons (mainly pions) are not considered in our analysis, assuming that they do not sensibly affect the strangeness production but contribute essentially to the total pressure and energy density. Heavier strange meson degrees of freedom have been also neglected.In the first approach, we consider the interaction between kaons and baryons by means of a direct minimal coupling scheme with the meson fields [4][5][6][7]. In this scheme the kaon lagrangian density can be written aswhere D µ = ∂ µ + ig ωK ω µ + ig ρK τ 3K ρ µ is the covariant derivative of the meson field, m * K = m K − g σK σ is the effective kaon mass and τ 3K is the third component of the isospin operator.The kaons vector and iso-vector coupling constant, are obtained from the quark model and the isospin counting rules and set equal to g ωK = g ωN /3 and g ρK = g ρN . Whereas the scalar g σK coupling constant is determined from the study of the real part of the anti-kaon optical potential by setting U K − = −g σK σ − g ωK ω at the saturation nuclear density and in a symmetric nuclear matter. EPJ Web of Conferences

Role of the Chiral Phase Transition in Modelling the Kaon-to-Pion Ratio

“…The chemical potential for pions is a phenomenological parameter and in this work it was chosen as a constant µ π = 0.135 GeV, following the works [21][22][23]. The chemical potential for kaons can be defined (see, for example, [23,24]) from µ q = B q µ B + S q µ s + I q µ q , and in the isospin symmetry case (I q = 0), the result is µ K = µ u − µ s .…”

Strange matter and kaon to pion ratio in the SU(3) Polyakov–Nambu–Jona-Lasinio model

“…The chemical potential for kaons can be defined (see, for example, Refs. [39,40]) from μ q = B q μ B + S q μ s + I q μ q , and in the isospin-symmetry case (I q = 0), the result is μ K = μ u − μ s . If all experimental data are taken from various experiments, it is shown in the statistical model that for each experiment the temperature and the baryon chemical potential of freeze-out [41] can be found by using the parametrization suggested by Cleymans et al It turned out to be possible to rescale the experimental data in the variable T /μ B (see Fig.…”

Using the Beth–Uhlenbeck Approach to Describe the Kaon to Pion Ratio in a 2 + 1 Flavor PNJL Model

“…The chemical potential for kaons can be defined (see for example [16,17]) from µ M = B q µ B + S q µ s + I q µ q , and in the isospin symmetry case (I q = 0), the result is µ K = µ u − µ s . The chemical potential for pions also is a phenomenological parameter, but it has its origin in the nonequilibrium nature of the distribution function of the pions for which, in contrast to the equilibrium case, the pion number is a quasi conserved quantity, see also [18].…”