$\gamma W$-box Inside-Out: Nuclear Polarizabilities Distort the Beta Decay Spectrum

Abstract

I consider the $\gamma W$-box correction to superallowed nuclear $\beta$-decays in the framework of dispersion relations. I address a novel effect of a distortion of the emitted electron energy spectrum by nuclear polarizabilities and show that this effect, while neglected in the literature, is sizable. I estimate its size in the approximation of a linear energy dependence, and using two models that are expected to give the lower and the upper bound. The respective correction to the ${\beta }^{+}$ spectrum is estimated to be ${\Delta }_R(E)=(1.6\pm 1.6)\times 10^{-4}E/\mathrm{MeV}$ assuming a conservative 100\% uncertainty. The effect is positive-definite and can be observed if a high-precision measurement of the positron spectrum is viable. If only the full rate is observed, it should be included in the calculated $\mathcal{F}t$-values of nuclear decays. I argue that this novel effect should be evaluated in state-of-the-art nuclear models and included in the analyses of nuclear beta decay experiments to ensure the correct extraction of $V_{ud}$ from decay rates, and of the Fierz interference term from precision measurements of decay spectra.

5 pages, 2 figures, 1 table; version accepted to Phys.Rev.Lett

References in corpus (2)

• Reduced hadronic uncertainty in the determination of $V_{ud}$
• Dispersive Evaluation of the Inner Radiative Correction in Neutron and Nuclear $\beta$-decay

Cited by in corpus (67)

• FLAG Review 2021
• 50 Years of Quantum Chromodynamics
• Radiative Corrections to Neutron and Nuclear Beta Decays Revisited
• 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
• Constraints on Sterile Neutrinos in the MeV to GeV Mass Range
• Beta decays as sensitive probes of lepton flavor universality
• Comprehensive analysis of beta decays within and beyond the Standard Model
• Standard Model $\mathcal{O}(\alpha )$ renormalization of $g_A$ and its impact on new physics searches
• Electroweak axial structure functions and improved extraction of the $V_{ud}$ CKM matrix element
• FLAG Review 2024
• Scrutinizing CKM unitarity with a new measurement of the $K_{\mu 3}/K_{\mu 2}$ branching fraction
• First-principles calculation of electroweak box diagrams from lattice QCD
• The Fermi constant from muon decay versus electroweak fits and CKM unitarity
• On the Statistical Treatment of the Cabibbo Angle Anomaly
• Searching for Lepton Flavour (Universality) Violation and Collider Signals from a Singly-Charged Scalar Singlet
• Combined Constraints on First Generation Leptoquarks
• First-Generation New Physics in Simplified Models: From Low-Energy Parity Violation to the LHC
• Unveiling Hidden Physics at the LHC
• Global Analysis of Leptophilic Z' Bosons
• Pion-induced radiative corrections to neutron beta-decay
• Combined Explanation of the $Z\to b\bar{b}$ Forward-Backward Asymmetry, the Cabibbo Angle Anomaly, $\tau \to \mu \nu \nu$ and $b\to s{\ell }^{+}{\ell }^{-}$ Data
• Dispersion relation analysis of the radiative corrections to $g_A$ in the neutron $\beta$-decay
• Global Fit of Modified Quark Couplings to EW Gauge Bosons and Vector-Like Quarks in Light of the Cabibbo Angle Anomaly
• Lattice QCD calculation of the electroweak box diagrams for the kaon semileptonic decays
• Particle Physics at the European Spallation Source
• Muon $g-2$ and CKM Unitarity in Extra Lepton Models
• Testing Lepton Flavor Universality with Pion, Kaon, Tau, and Beta Decays
• Update on $|V_{us}|$ and $|V_{us}/V_{ud}|$ from semileptonic kaon and pion decays
• Complete theory of radiative corrections to $K_{\ell 3}$ decays and the $V_{us}$ update
• Precise Measurements of the Decay of Free Neutrons
• Electroweak nuclear radii constrain the isospin breaking correction to $V_{ud}$
• High-precision determination of the $K_{e3}$ radiative corrections
• D-meson semileptonic decays to pseudoscalars from four-flavor lattice QCD
• Ab-initio electroweak corrections to superallowed $\beta$ decays and their impact on $V_{ud}$
• Dispersive formalism for the nuclear structure correction ${\delta }_{\mathrm{NS}}$ to the $\beta$ decay rate
• $\mathcal{F}t$ values of the mirror $\beta$ transitions and the weak magnetism induced current in allowed nuclear $\beta$ decay
• Radiative corrections to superallowed $\beta$ decays in effective field theory
• An $\text{ab initio}$ strategy for taming nuclear-structure dependence of $V_{ud}$ extractions: the ${}^{10}\mathrm{C}\to {}^{10}\mathrm{B}$ superallowed transition
• A New Theory Framework for the Electroweak Radiative Corrections in $K_{l3}$ Decays
• Radiative corrections to semileptonic beta decays: Progress and challenges
• Superallowed nuclear beta decays and precision tests of the Standard Model
• Correlating Non-Resonant Di-Electron Searches at the LHC to the Cabibbo-Angle Anomaly and Lepton Flavour Universality Violation
• Measurement of the neutron lifetime and inverse quantum Zeno effect
• Data-driven reevaluation of $ft$-values in superallowed $\beta$ decays
• Constraints on subleading interactions in beta decay Lagrangian
• Nuclear charge radius of ${}^{26m}$Al and its implication for V${}_{ud}$ in the quark-mixing matrix
• Towards $ab$-$initio$ nuclear theory calculations of ${\delta }_{\mathrm{C}}$
• The role of non-universal $Z$ couplings in explaining the $V_{us}$ anomaly
• Opportunities and open questions in modern $\beta$ decay
• Study of Two-Photon Exchange via the Beam Transverse Single Spin Asymmetry in Electron-Proton Elastic Scattering at Forward Angles over a Wide Energy Range
• High-Precision Branching Ratio Measurement and Spin Assignment Implications for ${}^{62}$Ga Superallowed $\beta$ Decay
• Influence of the recoil-order and radiative correction on the beta decay correlation coefficients in mirror decays
• Towards a discovery of BSM physics from the Cabibbo angle anomaly
• Parity-Violating Inelastic Electron-Proton Scattering at Low $Q^2$ Above the Resonance Region
• Branching ratio of the super-allowed beta decay of 10C
• Quark flavor physics and lattice QCD
• Theoretical point of view on Cabibbo angle anomaly
• Modified lepton couplings and the Cabibbo-angle anomaly
• Vector-like quark doublets, weak-basis invariants and CP violation
• Improved $K_{e3}$ radiative corrections sharpen the $K_{\mu 2}$--$K_{l3}$ discrepancy
• Muon capture on the deuteron in chiral effective field theory
• Cabibbo angle anomalies and a global fit to vector-like quarks
• The Role of Ab Initio Beta-Decay Calculations in Light Nuclei for Probes of Physics Beyond the Standard Model
• Electron Mass Singularities in Semileptonic Kaon Decays
• Pion $\beta$ decay and $\tau \to \pi \pi {\nu }_{\tau }$ beyond leading logarithms
• (Semi)leptonic kaon decays and neutral kaon mixing from lattice QCD