Nowadays it is generally accepted that the neutron beta decay is a nice laboratory for tests of the Standard Model (SM). Because of Sirlin (1967), Shann (1971), Wilkinson (1982) and Ivanov (2017) the neutron lifetime and correlation coefficients of the electron energy angular distributions of the rate of the neutron beta decay of a polarized neutron with i) unpolarized electron and proton (Sirlin1967, Shann1971, Wilkinson1982) and ii) a polarized electron and unpolarized proton (Ivanov2017) have been described at the level of 10−3 to first order in fine–structure constant and next–to–leading order in the large nucleon mass expansion, caused by the weak magnetism and proton recoil, defining the theoretical background for experimental tests of the SM at the level of 10−4 (Gudkov2006,Ivanov2013). Of course, for predictions at the level of 10−4, it is apparent that the higher order corrections of order 10−5 should be included (Wilkinson1982,Ivanov2017), since ”discovery” experiments with the required 5 sensitivity demand experimental uncertainties of a few parts in 10−5. The aim of this project is the calculation of the parameters of the neutron beta decays at the level of 10−5. The realization of this project goes through i) the consistent analysis of gauge invariance of Feynman diagrams for radiative corrections with two photon exchanges, taking into account the contributions of strong low–energy interaction, described by the linear –model, which is equivalent to the current algebra in the limit of an infinite mass of the scalar –meson, ii) the calculation of corrections to first order in the fine–structure constant and to next–to–leading order in the large nucleon mass expansion for radiative with one–photon exchanges, and iii) the calculation of the next–to–next–to–leading order corrections in the large nucleon mass expansion, caused by the weak magnetism and proton recoil. The use of the renormalizable –model and its equivalence to the current algebra should allow to define radiative corrections at the same confidence level as Sirlin’s result and shed light on gauge invariant properties of strong low–energy interactions for the raditive corrections to second order of the fine–structure constant. These corrections together with those of order 10−5, analysed by Wilkinson (1982) and Ivanov (2017), define a complete set of contributions in the SM at the level of 10−5. All of these corrections should provide a robust theoretical background at the level of 10−5 and a new impetus for the development of experimental technologies and methods for new higher levels of experimental accuracies, which are important for experimental searches of interactions beyond the SM with uncertainties of a few parts in 10−5 in the neutron beta decays.
