Two-Loop Anomalous Dimension of the Chromo-Magnetic Moment of a Heavy Quark

Abstract

We find that the anomalous dimension (in the $\overline{MS}$ scheme) of the chromo-magnetic operator $g_s{\bar{h}}_v{\sigma }_{\mu \nu }{G}^{\mu \nu }{h}_v$ 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.

Comments: 13 pages, 4 figures