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

Alejandro Ayala; L. A. Hernández; M. Loewe; Juan Cristobal Rojas; R. Zamora

doi:10.1140/epja/s10050-020-00086-z

2023 Impact factor 2.6

Hadrons and Nuclei

Eur. Phys. J. A (2020) 56: 71
https://doi.org/10.1140/epja/s10050-020-00086-z

Regular Article - Theoretical Physics

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

Alejandro Ayala¹^,2, L. A. Hernández¹^,2^*, M. Loewe²^,3^,4, Juan Cristobal Rojas⁵ and R. Zamora⁶^,7

¹ Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, 04510, Mexico, CDMX, Mexico
² Centre for Theoretical and Mathematical Physics, and Department of Physics, University of Cape Town, Rondebosch, 7700, South Africa
³ Instituto de Física, Pontificia Universidad Católica de Chile, Casilla 306, Santiago 22, Chile
⁴ Centro Científico-Tecnológico de Valparaíso CCTVAL, Universidad Técnica Federico Santa María, Casilla 110-V, Valaparaíso, Chile
⁵ Departamento de Física, Universidad Católica del Norte, Casilla 1280, Antofagasta, Chile
⁶ Instituto de Ciencias Básicas, Universidad Diego Portales, Casilla 298-V, Santiago, Chile
⁷ Centro de Investigación y Desarrollo en Ciencias Aeroespaciales (CIDCA), Fuerza Aérea de Chile, Santiago, Chile

^* e-mail: luis.hernandezr@correo.nucleares.unam.mx

Received: 14 August 2019
Accepted: 8 February 2020
Published online: 27 February 2020

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 mass-parameter, 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 $5.02<\mu _B^{\tiny {\text{ CEP }}}/T_c<5.18$ , $0.14<T^{\tiny {\text{ CEP }}}/T_c<0.23$ , where $$T_c$$ is the critical transition temperature at zero baryon chemical potential.