The Lambert W Function, Laguerre Polynomials, and the Zeros of the QCD Partition Function

Abstract

We study solutions of a transcendental equation for the complex chemical potential at which a random-matrix QCD model can undergo a phase transition at zero mass. An explicit solution is obtained in terms of the Lambert W function. We also provide a closed form expression for a QCD random matrix model partition function, as a sum of Laguerre polynomials, for complex chemical potential and non-zero mass.

Comments: 7 pages, 1 figure. Resubmitted 28-Oct-2014 to correct typographical errors in equations (9) and (11). Also reformatted as single column, and provided article titles in the references. No other changes to content