On the critical end point in a two-flavor linear sigma model coupled to quarks

Abstract

We use the linear sigma model coupled to quarks to explore the location of the phase transition lines in the QCD phase diagram from the point of view of chiral symmetry restoration at high temperature and baryon chemical potential. We compute analytically the effective potential in the high-and low-temperature approximations up to sixth order, including the contribution of the ring diagrams to account for the plasma screening properties. We determine the model parameters, namely, the couplings and massparameter, from conditions valid at the first order phase transition at vanishing temperature and, using the Hagedorn limiting temperature concept applied to finite baryon density, for a critical baryochemical potential of order of the nucleon mass. We show that when using the set of parameters thus determined, the second order phase transition line (our proxy for the crossover transition) that starts at finite temperature and zero baryon chemical potential converges to the line of first order phase transitions that starts at zero temperature and finite baryon chemical potential to determine the critical end point to lie in the region 5.02 < µ CEP B /T c < 5.18, 0.14 < T CEP /T c < 0.23, where T c is the critical transition temperature at zero baryon chemical potential.

Catalysis and inverse electric catalysis in a scalar theory

“…However, the rate of this diminishing becomes smaller when the electric field starts to grow, showing a damped behavior. This behavior is analogous to what happens in the pure magnetic case [35][36][37][38][39][40][41]. However,when going into the strong field regime, Fig.…”

QCD phase diagram in a magnetized medium from the chiral symmetry perspective: The linear sigma model with quarks and the Nambu--Jona-Lasinio model effective descriptions

“…Different ways to try fixing the parameters λ and g have been previously discussed but the conclusions are unclear. It is however important to mention that when conditions to fix the latter contain the possibility of a first order phase transition for T = 0 and µ = m B /3, where m B ∼ 1 GeV is the typical baryon mass, the CEP turns out to be located at low values of T and high values of µ [49,50].…”

“…Although for the explored parameter space, the transition lines at B = 0 do not show a CEP, we have shown that the presence of a finite and even small magnetic field produces a CEP for smaller values of µ. For lower temperatures one needs to resort to a low-T expansion to make a thorough exploration of the phase diagram [50,49].…”

Collision energy dependence of the critical end point from baryon number fluctuations in the Linear Sigma Model with quarks

“…Calculations using Lattice QCD (LQCD) have found that for finite temperature and vanishing baryon chemical potential , the transition between the confined/chiral symmetry broken and the deconfined/partially restored chirally symmetric phases, is a crossover that happens at a pseudocritical temperature ( = 0) ≃ 158 MeV [5][6][7]. However, using effective model calculations [8][9][10][11][12] it can be shown that this transition becomes first order for low and high . Thus, when the temperature is increased, the end of this first order phase transition line in the vs.…”

“…In this work we study the evolution of cumulant ratios describing baryon number fluctuations as a function of the collision energy, in the context of relativistic heavyion collisions, using the Linear Sigma Model with quarks (LSMq) [8,10,29]. The model incorporates a crucial feature of plasmas near transition lines, namely, the plasma screening effects.…”