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 $g_s{\bar{h}}_v\ddot{I}{ƒ}_{\hat{I}¼\hat{I}½}{G}^{\hat{I}¼\hat{I}½}{h}_v$ in the heavy-quark effective theory is γ_{mag} = (C_Aα_s / 2π) [1 + ( 17/18 C_A - 13/18 T_F n_f)α_s/π+ O(α_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.

13 pages, 4 figures