Strong Interaction Dynamics and Fermi $\beta$ decay in the nucleon and the nucleus

Abstract

Nuclear super-allowed $\beta$ decay has been used to obtain tight limits on the value of the CKM matrix element $V_{ud}$ that is important for unitarity tests, and therefore important for tests of the standard model. Current requirements on precision are so intense that effects formerly thought too small to matter are now relevant. This article is a brief review of personal efforts to include the effects of strong interactions on Fermi $\beta $ decay. First I examine the role of isospin violation in the decay of the neutron. The size of the necessary correction depends upon detailed strong-interaction dynamics. The isospin violating parts of the nucleon wave function, important at the low energy of $\beta$ decay, can be constrained by data taken at much higher energies, via measurements, for example, of $ed\to e'\pi^\pm +\rm X $ reactions at Jefferson Laboratory. The next focus is on the role of nuclear short-ranged correlations, which affect the value of the correction needed to account for isospin violation in extracting the value of $V_{ud}$. The net result is that effects previously considered as irrelevant have become relevant for both neutron and nuclear $\beta$ decay.