Mesonic screening mass at zero and finite chemical potential

Abstract

The finite temperature analysis of QCD is challenging since perturbation theory is not applicable in that regime. A non-perturbative method like lattice QCD is thus required to obtain an estimate of the necessary observables. In this Ph.D. thesis, we study the symmetries of the chiral phase transition and its transition temperature. This is undertaken by measuring the screening masses of those mesons that rotate amongst themselves under the symmetries.

Firstly, we discuss the regime of zero chemical potential where it is easy to obtain the correlators using which we calculate the meson screening masses. We discuss the different computational techniques used for calculating the screening masses on lattice following which we do their continuum extrapolate, to obtain their physical values. Using them, we notice the temperatures at which the symmetries get restored.

Finally, we expand our analysis to finite chemical potential. Including the non-zero value of chemical potential to the action makes it imaginary resulting in what is called the sign problem. This imaginary action cannot be used to simulate the system on a lattice. We avoid this problem by expanding the screening correlators in a Taylor series expansion in our analysis. Thus, this gives us an estimate of the screening mass at a small finite chemical potential.