Effective field theory for radiative corrections to charged-current processes I: Vector coupling

Abstract

We study radiative corrections to low-energy charged-current processes involving nucleons, such as neutron beta decay and (anti)neutrino-nucleon scattering within a top-down effective-field-theory approach. We first match the Standard Model to the low-energy effective theory valid below the weak scale and, using renormalization group equations with anomalous dimensions of $\mathcal{O}(\alpha ,\alpha {\alpha }_s,{\alpha }^2)$, evolve the resulting effective coupling down to the hadronic scale. Here, we first match to heavy-baryon chiral perturbation theory and subsequently, below the pion-mass scale, to a pionless effective theory, evolving the effective vector coupling with anomalous dimensions of $\mathcal{O}(\alpha ,{\alpha }^2)$ all the way down to the scale of the electron mass, relevant for beta decays. We thus provide a new evaluation of the ``inner" radiative corrections to the vector coupling constant and to the neutron decay rate, discussing differences with the previous literature. Using our new result for the radiative corrections, we update the extraction of the Cabibbo-Kobayashi-Maskawa matrix element $V_{ud}$ from the neutron decay.

40 pages, 3 figures

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• All orders factorization and the Coulomb problem
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• Field Theory of the Fermi Function
• Data-driven reevaluation of $ft$-values in superallowed $\beta$ decays
• Opportunities and open questions in modern $\beta$ decay
• Isospin breaking corrections in $2\pi$ production in tau decays and $e^{+}{e}^{-}$ annihilation: consequences for the muon $g-2$ and CVC tests
• Pseudo-neutrino versus recoil formalism for 4-body phase space and applications to nuclear decay
• Hybrid analysis of radiative corrections to neutron decay with current algebra and effective field theory
• Unique forbidden beta decays at zero momentum transfer
• Radiative Corrections and the Renormalization Group for the Two-Nucleon Interaction in Effective Field Theory
• The Role of Ab Initio Beta-Decay Calculations in Light Nuclei for Probes of Physics Beyond the Standard Model
• Most general neutron decay correlations: Standard Model recoil and radiative corrections
• Reducing Hadronic Uncertainty in Low-Energy Neutral-Current Processes
• Testing effective field theory with the most general neutron decay correlations
• Tau data-driven evaluation of the Hadronic Vacuum Polarization
• Parity violation in Møller scattering within low-energy effective field theory
• Hadronic contributions to $a_{\mu }$ within Resonance Chiral Theory
• Pion $\beta$ decay and $\tau \to \pi \pi {\nu }_{\tau }$ beyond leading logarithms