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 (LsM)
with chiral SU(2)xSU(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 (SM).
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 LsM are taken in the limit of the infinite mass of the
scalar isoscalar sigma-meson. In such a limit the LsM reproduces the results of
the current algebra (Weinberg, Phys. Rev. Lett. {\bf 18}, 188 (1967)) in the
form of effective chiral Lagrangians of pion-nucleon interactions with
non--linear realization of chiral SU(2)xSU(2) symmetry. In such a limit the
LσM is also equivalent to Gasser-Leutwyler's chiral quantum field theory
or chiral perturbation theory (ChPT) with chiral SU(2)xSU(2)symmetry and the
exponential parametrization of a pion-field (Ecker, Prog. Part. Nucl. Phys.
{\bf 35}, 1 (1995)).Comment: 50 pages, 7 figures. arXiv admin note: text overlap with
arXiv:1805.0970
