High precision corrections to the neutron beta decay rate and electron asymmetry and current determination of Vud

Abstract

The goal of the present analysis is to find, in the free neutron beta decay, the expressions for the decay rate and the electron asymmetry that contain all the theoretical effects at the 10−4 level. This accuracy is better than the current experimental precision that modern experiments allow. For this aim it is necessary to study the strong interaction effects, the radiative corrections and the recoil of the proton. A conceptual problem that we discuss in detail is the Fermi function additivity. The model dependence in the radiative corrections yields important effects which must be incorporated. We show that this is the only source of uncertainty that is out of control still at the mentioned order. As an application, we compare the values of the CKM matrix element |Vud | from this decay with the values both from the superallowed Fermi transition beta decays and the unitarity of the CKM matrix. We discuss the relevance of the observed discrepancies.