2021 journal article

Standard model O(Ξ±) renormalization of gA and its impact on new physics searches

Physical Review D.

By: L. Hayen n 

co-author countries: Belgium πŸ‡§πŸ‡ͺ United States of America πŸ‡ΊπŸ‡Έ
Source: ORCID
Added: June 3, 2021

We present an $\mathcal{O}(\ensuremath{\alpha})$ Standard Model calculation of the inner radiative corrections to Gamow-Teller $\ensuremath{\beta}$ decays. We find that a priori contributions arise from the photonic vertex correction and $\ensuremath{\gamma}W$ box diagram. Upon evaluation most elastic contributions vanish due to crossing symmetry or cancellation between isoscalar and isovector photonic contributions, leaving only the polarized parity-odd contribution, i.e., the Gamow-Teller equivalent of the well-known axial $\ensuremath{\gamma}W$ box contribution for Fermi decays. We show that weak magnetism contributes significantly to the Born amplitude, and consider additional hadronic contributions at low energy using a holomorphic continuation of the polarized Bjorken sum rule constrained by experimental data. We perform the same procedure for the Fermi inner radiative correction through a combination of the running of Bjorken and Gross-Llewellyn Smith sum rules. We discuss heavy flavor, higher-twist, and target mass corrections and find a significant increase at low momentum from the latter. We find ${\mathrm{\ensuremath{\Delta}}}_{R}^{A}=0.02532(22)$ and ${\mathrm{\ensuremath{\Delta}}}_{R}^{V}=0.02473(27)$ for axial and vector inner radiative corrections, respectively, resulting in ${\mathrm{\ensuremath{\Delta}}}_{R}^{A}\ensuremath{-}{\mathrm{\ensuremath{\Delta}}}_{R}^{V}=0.60(5)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, which allows us to extract ${g}_{A}^{0}$ for the first time to our knowledge. We discuss consequences for comparing experimental data to lattice calculations in beyond Standard Model fits. Further, we show how some traditional $\ensuremath{\beta}$ decay calculations contain part of this effect but fail to account for cancellations in the full $\mathcal{O}(\ensuremath{\alpha})$ result. Finally, we correct for a double-counting instance in the isospin $T=1/2$ mirror decay extraction of $|{V}_{ud}|$, the up-down matrix element of the Cabibbo-Kobayashi-Maskawa matrix element, resolving a long-standing tension and leading to increased precision.