Two-loop renormalization of the effective field theory of a static quark

TL;DR

This paper derives exact two-loop results for the propagator and vertex function of a static heavy quark in effective field theory, providing new corrections to anomalous dimensions and extending previous calculations.

Contribution

It introduces a recurrence relation for two-loop integrals in the effective field theory of a static quark, enabling exact calculations in any dimension and gauge.

Findings

Exact two-loop propagator results obtained.

Anomalous dimension of the heavy-light current calculated.

New two-loop correction to previous results provided.

Abstract

We give a recurrence relation for two-loop integrals encountered in the effective field theory of an infinitely heavy quark, Q, interacting with gluons and Nl massless quarks, q, from which we obtain exact two-loop results, in any dimension and covariant gauge, for the propagator of Q and the vertex function of the heavy-light current J = Q Gamma q, at zero q momentum. The anomalous dimension of the Q field agrees with the recent result of Broadhurst, Gray and Schilcher. The anomalous dimension of the current is gamma_J = d log Z_J / d log mu = - alpha_s/pi (1 + (127 + 56 zeta(2) - 10 Nl)/72) alpha_s/pi + O(alpha_s^2)) which gives the new two-loop correction to the result of Voloshin and Shifman.