Isospin breaking in neutron<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>β</mml:mi></mml:math>decay and SU(3) violation in semileptonic hyperon decays

Abstract

Present precision measurements of the neutron lifetime lead to a CKM matrix element $|{V}_{\mathrm{ud}}|,$ which is 3 standard deviations off the value inferred from heavy quark decays, etc. We investigate the possibility whether isospin-breaking effects in the neutron-to-proton vector current transition matrix element $〈p|{V}_{0}^{+}|n〉=1+\ensuremath{\delta}{g}_{V}$ could eventually close this gap. For that we calculate in chiral perturbation theory the effect of pion and kaon loops on the matrix element $〈p|{V}_{0}^{+}|n〉$ taking into account the mass differences of the charged and neutral mesons. We find a negligibly small isospin-breaking effect of $\ensuremath{\delta}{g}_{V}\ensuremath{\simeq}\ensuremath{-}4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}.$ The crucial quantity in the analysis of neutron $\ensuremath{\beta}$-decay precision measurements is thus the radiative correction term ${\ensuremath{\Delta}}_{R}.$ Furthermore, we calculate in heavy baryon chiral perturbation theory the SU(3) breaking effects on the vector transition charges of weak semileptonic hyperon decays. We find for these quantities channel-dependent relative deviations from the SU(3) limit which range from -10% to +1%.