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

arXiv commentMatches journal version. Small typos fixed

References in corpus (23)

• Reduced hadronic uncertainty in the determination of $V_{ud}$
• New physics searches in nuclear and neutron $\beta$ decay
• Radiative Corrections to Neutron and Nuclear Beta Decays Revisited
• Beta Decays and Non-Standard Interactions in the LHC Era
• Dispersive Evaluation of the Inner Radiative Correction in Neutron and Nuclear $\beta$-decay
• Joint lattice QCD - dispersion theory analysis confirms the quark-mixing top-row unitarity deficit
• Global Fit to Modified Neutrino Couplings and the Cabibbo-Angle Anomaly
• High precision analytical description of the allowed $\beta$ spectrum shape
• Beta decays as sensitive probes of lepton flavor universality
• Standard Model $\mathcal{O}(\alpha )$ renormalization of $g_A$ and its impact on new physics searches
• Comprehensive analysis of beta decays within and beyond the Standard Model
• Global Electroweak Fit and Vector-Like Leptons in Light of the Cabibbo Angle Anomaly
• Three-loop anomalous dimension of the heavy-light quark current in HQET
• Electroweak axial structure functions and improved extraction of the $V_{ud}$ CKM matrix element
• Scrutinizing CKM unitarity with a new measurement of the $K_{\mu 3}/K_{\mu 2}$ branching fraction
• Neutron beta decay in effective field theory
• The Fermi constant from muon decay versus electroweak fits and CKM unitarity
• Pion-induced radiative corrections to neutron beta-decay
• Dispersion relation analysis of the radiative corrections to $g_A$ in the neutron $\beta$-decay
• The Nab Experiment: A Precision Measurement of Unpolarized Neutron Beta Decay
• Beta spectrum of unique first-forbidden decays as a novel test for fundamental symmetries
• All orders factorization and the Coulomb problem
• Constraints on subleading interactions in beta decay Lagrangian

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