Radiative corrections of order O(αEe/mN) to Sirlin's radiative corrections of order O(α/π) to the neutron lifetime

We calculate the radiative corrections of order O(alpha E-e/m(N)) as next-to-leading order corrections in the large nucleon mass expansion to Sirlin's radiative corrections of order O(alpha/pi) to the neutron lifetime. The calculation is carried out within a quantum field theoretic model of strong low-energy pion-nucleon interactions described by the linear sigma model (L sigma M) with chiral SU(2) x SU(2) symmetry and electroweak hadron-hadron, hadron-lepton and lepton-lepton interactions for the electron-lepton family with SU(2)(L) x U(1)(Y) symmetry of the standard electroweak model (SEM). Such a quantum field theoretic model is some kind a hadronized version of the Standard Model. From a gauge invariant set of the Feynman diagrams with one-photon exchanges we reproduce Sirlin's radiative corrections of order O(alpha/pi), calculated to leading order in the large nucleon mass expansion, and calculate next-to-leading corrections of order O(alpha E-e/m(N)). This confirms Sirlin's confidence level of the radiative corrections O(alpha E-e/m(N)). The contributions of the L sigma M are taken in the limit of the infinite mass of the scalar isoscalar sigma meson. In such a limit the L sigma M reproduces the results of the current algebra [S. Weinberg, Phys. Rev. Lett. 18, 188 (1967)] in the form of effective chiral Lagrangians of pion-nucleon interactions with nonlinear realization of chiral SU(2) x SU(2) symmetry. In such a limit the L sigma M is also equivalent to Gasser-Leutwyler's chiral quantum field theory or chiral perturbation theory with chiral SU(2) x SU(2) symmetry and the exponential parametrization of a pion-field [(G. Ecker, Prog. Part. Nucl. Phys. 35, 1 (1995)].