Two-Loop Anomalous Dimension of the Chromo-Magnetic Moment of a Heavy Quark
Abstract
We find that the anomalous dimension (in the
MS
¯
scheme) of the chromo-magnetic operator
g
s
h
¯
v
σ
μν
G
μν
h
v
in the heavy-quark effective theory is \gamma_{mag} = (C_A\alpha_s / 2\pi) [1 + ( 17/18 C_A - 13/18 T_F n_f)\alpha_s/\pi + O(\alpha_s^2)] generalizing the one-loop expression known previously. To derive the two-loop result, we use the reparametrization invariance and the virial theorem. After performing infrared subtractions, all two-loop integrals are of propagator type and are evaluated by a recurrence relation for tensor integrals.