Finite volume effects on chiral phase transition and pseudoscalar mesons properties from the Polyakov-Nambu-Jona-Lasinio model

Abstract: Within the framework of Polyakov-Nambu-Jona-Lasinio model and by means of Multiple Reflection Expansion, we study the finite volume effects on chiral phase transition, especially its influence on the location of the possible critical end point (CEP) and masses of mesons. Our result shows that as the radius of spherical volume decreases, the location of CEP shifts toward smaller temperature while changes little in chemical potential. As for the finite volume effects on the masses of mesons, the masses of $\pi$ and $K$ increase with decreasing volume, while for $\sigma$, $\eta$ and $\eta '$ the situation is the opposite. Especially, the masses of chiral parters $\pi$ and $\sigma$ get closer as the volume decreases, indicating that the dynamical chiral symmetry breaking effect reduces with decreasing volume.