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Within the standard V - A theory of weak interactions, QuantumElectrodynamics (QED) and the linear sigma-model (LsM) of strong low-energyhadronic interactions we analyse gauge properties of hadronic structure of theneutron and proton in the neutron radiative beta-decay. We show that theFeynman diagrams, describing contributions of hadronic structure to theamplitude of the neutron radiative beta-decay in the tree-approximation forstrong low-energy interactions in the LsM, are gauge invariant. In turn, thecomplete set of Feynman diagrams, describing the contributions of hadron-photoninteractions in the one-hadron-loop approximation, is not gauge invariant. Inthe infinite limit of the scalar sigma-meson, reproducing the current algebraresults (Weinberg, Phys. Rev. Lett. 18, 188 (1967)), and to leading order inthe large nucleon mass expansion the Feynman diagrams, violating gaugeinvariance, do not contribute to the amplitude of the neutron radiativebeta-decay in agreement with Sirlin's analysis of strong low-energyinteractions in neutron beta decays. We assert that the problem of appearanceof gauge non-invariant Feynman diagrams of hadronic structure of the neutronand proton is related to the following. The vertex of the effective V-A weakinteractions does not belong to the combined quantum field theory including theLsM and QED. We argue that gauge invariant set of Feynman diagrams of hadrons,coupled to real and virtual photons in neutron beta decays, can be obtainedwithin the combined quantum field theory including the Standard ElectroweakModel (SEM) and the LsM, where the effective V-A vertex of weak interactions isa result of the W^- - electroweak boson exchange.

international journal of modern physics a

Gauge Properties of Hadronic Structure of Nucleon in Neutron Radiative  Beta Decay to Order O(alpha/pi) in Standard V - A Effective Theory with QED  and Linear Sigma Model of Strong Low--Energy Interactions