Radiative corrections of order $O(\alpha E_e/m_N)$ to Sirlin's radiative corrections of order $O(\alpha/\pi)$, induced by the hadronic structure of the neutron

TL;DR

This paper calculates the neutron's hadronic structure contributions to radiative corrections in neutron beta decay, showing they are of the order of 10^{-5} to 10^{-4}, consistent with previous results, using an effective quantum field theory approach.

Contribution

It provides a detailed calculation of the neutron's hadronic structure effects on radiative corrections within a chiral sigma model and Standard Model framework, extending prior work.

Findings

Inner radiative corrections are of order 10^{-5} to 10^{-4}.

Results agree with previous calculations by Ivanov et al.

Renormalization follows Sirlin's prescription.

Abstract

We investigate the contributions of the hadronic structure of the neutron to radiative $O(\alpha E_e/m_N)$ corrections (or the inner $O(\alpha E_e/m_N)$ RC) to the neutron beta decay, where $\alpha$, $E_e$ and $m_N$ are the fine-structure constant, the electron energy and the nucleon mass, respectively. We perform the calculation within the effective quantum field theory of strong low-energy pion-nucleon interactions described by the linear $\sigma$-model with chiral $SU(2) \times SU(2)$ symmetry and electroweak hadron-hadron, hadron-lepton and lepton-lepton interactions for the electron-lepton family with $SU(2)_L \times U(1)_Y$ symmetry of the Standard Electroweak Theory (Ivanov et al., Phys. Rev. D99, 093006 (2019)). We show that after renormalization, carried out in accordance with Sirlin's prescription (Sirlin, Phys. Rev. 164, 1767 (1967)), the inner $O(\alpha E_e/m_N)$ RC are of the order of a few parts of $10^{-5} - 10^{-4}$. This agrees well with the results obtained in (Ivanov et al., Phys. Rev. D99, 093006 (2019)).