Two loop calculation of the anomalous dimension of the axial current with static heavy quarks

A method to perform two loop calculations in Eichten's effective field theory for heavy quarks is developed. The anomalous dimension of the axial current for static heavy quarks is calculated at two loops. For N = 3, (gamma(sub A))(sup 2) = -1/36(127/2 + 94(xi)2 - 5N(sub f)). The result is very important to understand the physical significance of the lattice measurement of the decay constant of the B meson. The two loop correction generated by the second coefficient of (gamma(sub A))(sup 2) turns out to be small, less than 1.5 percent for four quark flavors, so that the value of the decay constant of the B meson does not need in practice renormalization group improvement. The self energy renormalization constant at two loop level for a heavy static quark and that for the coupling of a heavy quark to a gluon are obtained.