Radiative corrections of order O(αEe/mN) to Sirlin’s radiative corrections of order O(α/π) , induced by the hadronic structure of the neutron

Ya. A. Berdnikov,A. N. Ivanov,R. Höllwieser,N. I. Troitskaya,M. Wellenzohn

doi:10.1103/physrevd.103.113007

Ya. A. Berdnikov, A. N. Ivanov + Show 3 more

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https://doi.org/10.1103/physrevd.103.113007

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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)).

Highlights

According to Sirlin [1,2], the contribution of the hadronic structure of the neutron to the radiative Oðα=πÞ corrections [or the inner Oðα=πÞ radiative corrections (RC) [3] ] to the neutron lifetime is a constant, calculated to leading order (LO) in the large nucleon mass mN expansion, where α is the fine-structure constant [4]
We investigate the contributions of the hadronic structure of the neutron to radiative OðαEe=mNÞ corrections [or the inner OðαEe=mNÞ RC] to the neutron beta decay, where α, Ee, and mN are the finestructure constant, the electron energy, and the nucleon mass, respectively
[10], we have calculated the OðαEe=mNÞ RC as next-to-leading order (NLO) corrections in the large nucleon mass mN expansion to Sirlin’s Oðα=πÞ RC [1], where Ee is an electron energy, We have carried out the calculation within the effective quantum field theory of strong and electroweak low-energy interactions linear σ model (LσM) & standard electroweak theory (SET)

Summary

INTRODUCTION

According to Sirlin [1,2], the contribution of the hadronic structure of the neutron to the radiative Oðα=πÞ corrections [or the inner Oðα=πÞ radiative corrections (RC) [3] ] to the neutron lifetime is a constant, calculated to leading order (LO) in the large nucleon mass mN expansion, where α is the fine-structure constant [4]. [10], we have calculated the OðαEe=mNÞ RC as next-to-leading order (NLO) corrections in the large nucleon mass mN expansion to Sirlin’s Oðα=πÞ RC [1] (or to the outer model-independent RC [3]), where Ee is an electron energy, We have carried out the calculation within the effective quantum field theory of strong and electroweak low-energy interactions LσM & SET. In this theory, strong low-energy pion-nucleon interactions are described by the linear σ model (LσM) with chiral SUð2Þ × SUð2Þ symmetry [11,12,13].

Published by the American Physical Society

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DISCUSSION

We would like to emphasize that the problem of the