Thermodynamic Free Energy Calculation with One Loop Correction at Finite Chemical Potential

Abstract

The thermodynamic free energy of quark gluon plasma (QGP) under one loop correction is calculated in presence of finite chemical potential to create bubble/droplet formation of QGP. The forming of bubble/droplet is affected by the presence of the chemical potential in the loop factor and the equilibrium/ stable and unstable droplets are formed at the parametrization values of quarks and gluons at the range of γ_q = 1/8 and 22γ_q ≤γ_g ≤ 30γ_q.  However, the energy equilibration/stable of the droplet is obtained at the parametrization range of quark and gluon as γ_q = 1/8 and 26γ_q ≤γ_g ≤ 28γ_q. It implies that the existence of droplet is dependent on quark anti-quark and gluon parameters with the equilibrium/stable and non-equilibrium/unstable droplets. It means that the phenomenological parameters introduced which is similar to the Reynolds number, boost in forming the droplet of QGP and enhance the free energy amplitude with the equilibrium droplet depending on their values. However, the effect of the stable droplet size after the incorporation of chemical potential at one loop correction factor is visible with smaller size.