Renormalization Approach to the Gribov Process: Numerical Evaluation of Critical Exponents in Two Subtraction Schemes

Abstract

We study universal quantities characterizing the second order phase transition in the Gribov process. To this end, we use numerical methods for the calculation of the renormalization group functions up to two-loop order in perturbation theory in the famous ε-expansion. Within this procedure the anomalous dimensions are evaluated using two different subtraction schemes: the minimal subtraction scheme and the null-momentum scheme. Numerical calculation of integrals was done on the HybriLIT cluster using the Vegas algorithm from the CUBA library. The comparison with existing analytic calculations shows that the minimal subtraction scheme yields more precise results.