Charge-symmetry-breaking effects on neutron β decay in nonrelativistic quark models

Abstract

A formalism for the study of charge-symmetry-breaking (CSB) effects is discussed and used to analyze the effects of charge-symmetry breaking on neutron $\ensuremath{\beta}$ decay. The effect of including CSB reduces the $\ensuremath{\beta}$-decay matrix element by an amount on the order of ${10}^{\ensuremath{-}4}$, a value much larger than the previous estimate. The earlier calculation used the neutron-proton mass difference as the CSB operator instead of the matrix element of the sum of the individual terms between the ground and excited states. The electromagnetic and dynamic effects of the up-down quark mass difference oppose the up-down quark mass difference leading to a small $n\ensuremath{-}p$ mass difference, but add coherently in computing the excitation matrix elements causing large enhancements. The current uncertainty in the value of ${V}_{ud}$ is also on the order of ${10}^{\ensuremath{-}4}$. An improvement of that uncertainty by an order of magnitude would require that charge-symmetry-breaking effects should be included in future analyses.