# Radiative corrections of order O(alpha E_e/m_N) to Sirlin's radiative corrections of order O(alpha/pi) to neutron lifetime

## TL;DR

This paper calculates higher-order radiative corrections to neutron decay within a quantum field theoretic model, confirming the validity of previous leading-order results and extending precision in theoretical predictions.

## Contribution

It provides the first calculation of next-to-leading order radiative corrections of order O(alpha E_e/m_N) within a hadronized Standard Model framework.

## Key findings

- Confirmed the accuracy of Sirlin's leading-order radiative corrections.
- Calculated next-to-leading corrections of order O(alpha E_e/m_N).
- Reproduced results consistent with chiral perturbation theory in the infinite sigma-meson mass limit.

## Abstract

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 L$\sigma$M 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)).

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Source: https://tomesphere.com/paper/1905.01178