Electroweak axial structure functions and improved extraction of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><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> CKM matrix element
Kyle Shiells, P. G. Blunden, Wally Melnitchouk
Abstract
We present a comprehensive analysis of the $\ensuremath{\gamma}W$ interference radiative correction to the neutron $\ensuremath{\beta}$-decay matrix element. Within a dispersion relations approach, we compute the axial-vector part of the $\ensuremath{\gamma}W$ box amplitude ${\ensuremath{\square}}_{A}^{\ensuremath{\gamma}W}$ in terms of the isoscalar part of the ${F}_{3}^{\ensuremath{\gamma}W}$ interference structure function. Using the latest available phenomenology for ${F}_{3}^{\ensuremath{\gamma}W}$ from the nucleon elastic, resonance, deep-inelastic, and Regge regions, we find the real part of the box correction to be ${\ensuremath{\square}}_{A}^{\ensuremath{\gamma}W}=3.90(9)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$. This improved correction gives a theoretical estimate of the CKM matrix element $|{V}_{ud}{|}^{2}=0.94805(26)$, which represents a $4\ensuremath{\sigma}$ violation of unitarity.