Gauge and infrared properties of hadronic structure of nucleon in neutron beta decay to order O(α/π) in standard V − A effective theory with QED and linear sigma model of strong low-energy interactions

Abstract

Within the standard [Formula: see text] theory of weak interactions, Quantum Electrodynamics (QED) and the linear [Formula: see text]-model [Formula: see text] of strong low-energy hadronic interactions we analyze gauge and infrared properties of hadronic structure of the neutron and proton in the neutron [Formula: see text]-decay to leading order in the large nucleon mass expansion. We show that the complete set of Feynman diagrams describing radiative corrections of order [Formula: see text], induced by hadronic structure of the nucleon, to the rate of the neutron [Formula: see text]-decay is gauge noninvariant and unrenormalizable. We show that a gauge noninvariant contribution does not depend on the electron energy in agreement with Sirlin’s analysis of contributions of strong low-energy interactions (Phys. Rev. 164, 1767 (1967)). We show that infrared divergent and dependent on the electron energy contributions from the neutron radiative [Formula: see text]-decay and neutron [Formula: see text]-decay, caused by hadronic structure of the nucleon, are canceled in the neutron lifetime. Nevertheless, we find that divergent contributions of virtual photon exchanges to the neutron lifetime, induced by hadronic structure of the nucleon, are unrenormalizable even formally. Such an unrenormalizability can be explained by the fact that the effective [Formula: see text] vertex of hadron–lepton current–current interactions is not a vertex of the combined quantum field theory including QED and [Formula: see text], which are renormalizable theories. We assert that for a consistent gauge invariant and renormalizable analysis of contributions of hadronic structure of the nucleon to the radiative corrections of any order to the neutron decays one has to use a gauge invariant and fully renormalizable quantum field theory including the Standard Electroweak Model (SEM) and the [Formula: see text], where the effective [Formula: see text] vertex of hadron–lepton current–current interactions is caused by the [Formula: see text]-electroweak-boson exchange.