Vortical effects and the critical end point in the linear sigma model coupled to quark

In this paper, we study the effects of vorticity on the QCD phase transition using the linear sigma model coupled to quarks. By going beyond the mean-field approximation and incorporating screening effects via ring diagrams, we explore the chiral symmetry restoration in extreme conditions, such as high temperatures, high densities, and large angular velocities. Our analysis reveals how the critical temperature decreases as the angular velocity increases, suggesting that vorticity catalyzes the symmetry restoration. Additionally, we observe a shift in the critical end point (CEP) in the effective QCD phase diagram, where higher angular velocities move the CEP to lower quark chemical potentials and higher temperatures. Moreover, we analyze the baryon number fluctuations through the normalized fourth moment <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>κ</a:mi><a:msup><a:mi>σ</a:mi><a:mn>2</a:mn></a:msup><a:mo>=</a:mo><a:msub><a:mi>c</a:mi><a:mn>4</a:mn></a:msub><a:mo>/</a:mo><a:msub><a:mi>c</a:mi><a:mn>2</a:mn></a:msub></a:math> as a function of the collision energy in heavy-ion reactions <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msqrt><c:msub><c:mi>s</c:mi><c:mrow><c:mi>N</c:mi><c:mi>N</c:mi></c:mrow></c:msub></c:msqrt></c:math>, which serves as a key observable to identify the CEP. Our study reveals that, for high collision energies, <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>κ</e:mi><e:msup><e:mi>σ</e:mi><e:mn>2</e:mn></e:msup></e:math> remains nearly constant; however, as the system approaches the CEP, the ratio increases sharply, indicating the proximity of the critical region. This rise is influenced by the presence of vorticity, which causes the CEP to shift to higher collision energies. These findings provide insight into the role of vorticity in heavy-ion collisions.