  The anomalous dimension for heavy-heavy-light effective theory operators
describing nuclear beta decay is computed through three-loop order in the
static limit. The result at order $Z^2\alpha^3$ corrects a previous result in
the literature. An all-orders symmetry is shown to relate the anomalous
dimensions at leading and subleading powers of $Z$ at a given order of
$\alpha$. The first unknown coefficient for the anomalous dimension now appears
at $O(Z^2\alpha^4)$.
