Renormalization of beta decay at three loops and beyond

Abstract

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 $O(Z^2{\alpha }^4)$.

Matches journal version. Small typos fixed

References in corpus (2)

• Dispersion relation analysis of the radiative corrections to $g_A$ in the neutron $\beta$-decay
• All orders factorization and the Coulomb problem

Cited by in corpus (5)

• Ab-initio electroweak corrections to superallowed $\beta$ decays and their impact on $V_{ud}$
• Radiative corrections to superallowed $\beta$ decays in effective field theory
• Unique forbidden beta decays at zero momentum transfer
• Generalized eikonal identities for charged currents
• Pion $\beta$ decay and $\tau \to \pi \pi {\nu }_{\tau }$ beyond leading logarithms