<i>Ab initio</i> electroweak corrections to superallowed <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>β</mml:mi> </mml:math> decays and their impact on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>V</mml:mi> <mml:mrow> <mml:mi>u</mml:mi> <mml:mi>d</mml:mi> </mml:mrow> </mml:msub> </mml:math>
Vincenzo Cirigliano, Wouter Dekens, Jordy de Vries, Stefano Gandolfi, Martin Hoferichter, Emanuele Mereghetti
Abstract
The authors propose a new approach for the calculation of nuclear-dependent corrections to superallowed $\ensuremath{\beta}$ decays based on effective field theory (EFT). The calculation is timely given the observation in recent years of a 2--3 $\ensuremath{\sigma}$ anomaly in the test of the first row of the Cabibbo-Kobayashi-Maskawa matrix. Within a comprehensive assessment, the authors methodically develop a master formula for superallowed $\ensuremath{\beta}$ decays, paving the way for $a\phantom{\rule{0}{0ex}}b$-$i\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}o$ nuclear many-body computations of nuclear-structure-dependent corrections. The results show promise for state-of-the-art extractions of ${V}_{u\phantom{\rule{0}{0ex}}d}$ from nuclear processes with controlled uncertainty quantification, and for using precision $\ensuremath{\beta}$-decay experiments to search for physics beyond the standard model.