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.

Within the standard V − A theory of weak interactions, Quantum Electrodynamics (QED) and the linear σ -model (L σ M) of strong low-energy hadronic interactions we analyze gauge and infrared properties of hadronic structure of the neutron and proton in the neutron β − -decay to leading order in the large nucleon mass expansion. We show that the complete set of Feynman diagrams describing radiative corrections of order O (α / π) , induced by hadronic structure of the nucleon, to the rate of the neutron β − -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 β − -decay and neutron β − -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 V − A vertex of hadron–lepton current–current interactions is not a vertex of the combined quantum field theory including QED and L σ M , 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 L σ M , where the effective V − A vertex of hadron–lepton current–current interactions is caused by the W − -electroweak-boson exchange. [ABSTRACT FROM AUTHOR]