Anomalous dimension of the heavy-light quark current in HQET up to four loops

Abstract

The anomalous dimension of the heavy-light quark current in HQET is calculated up to four loops. The N${}^3$LL perturbative correction to $f_B/f_D$ is obtained.

Comments: 12 pages, no figures; v2: some info on $1/m$ corrections included, 5 new references; v3: some info on the large ${\beta }_0$ limit and summing divergent perturbative series included, very slight changes of some numbers, 8 new references