Infrared Properties of Hadronic Structure of Nucleon in Neutron Beta Decays 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 sigma-model (LsM) of strong low-energy hadronic interactions we analyse infrared properties of hadronic structure of the neutron and proton in the neutron beta decays to leading order in the large nucleon mass expansion. We confirm validity and high confidence level of contributions of hadronic structure of the nucleon to the radiative corrections, calculated by Sirlin (Phys. Rev. 164, 1767 (1967)) to leading order in the large nucleon mass expansion. At the level of order 10^{-5} relative to Sirlin's infrared divergent contribution to the neutron radiative beta decay (inner bremsstrahlung) we find an infrared divergent contribution, induced by hadronic structure of the nucleon through the one-pion-pole exchange, to the rate of the neutron lifetime from the neutron radiative beta decay, which should be cancelled by contributions of virtual photon exchanges to the neutron beta decay. Following Ivanov et al. 1805.09702 [hep-ph] we argue that a consistent analysis of such a cancellation may be carried out well in the combined quantum field theory including the Standard Electroweak Model (SEM) and the LsM of strong low-energy interactions, where the effective V - A hadron-lepton current-current vertex is caused by the W^- - electroweak-boson exchange.