Gauge and Infrared Properties of Hadronic Structure of Nucleon in Neutron Beta Decay to Order O(α/π) in Standard V - A Effective Theory with QED and Linear Sigma Model of Strong Low--Energy Interactions

Abstract

Within the standard V - A theory of weak interactions, Quantum Electrodynamics (QED) and the linear sigma-model (LsM) of strong low-energy hadronic interactions we analyse gauge and infrared properties of hadronic structure of the neutron and proton in the neutron beta decay to leading order in the large nucleon mass expansion. We show that the complete set of Feynman diagrams describing radiative corrections of order O(α/π), induced by hadronic structure of the nucleon, to the rate of the neutron beta decay is gauge non-invariant and unrenormalisable. We show that a gauge non-invariant contribution does not depend on the electron energy in agreement with Sirlin's analysis of contributions of strong low-energy interactions (Phys. Rev. 164, 1767 (1967)). We show that infrared divergent and dependent on the electron energy contributions from the neutron radiative beta decay and neutron beta decay, caused by hadronic structure of the nucleon, are cancelled in the neutron lifetime. Nevertheless, we find that divergent contributions of virtual photon exchanges to the neutron lifetime, induced by hadronic structure of the nucleon, are unrenormalisable even formally. Such an unrenormalizability can be explained by the fact that the effective V - A vertex of hadron-lepton current-current interactions is not a vertex of the combined quantum field theory including QED and LsM, which are renormalizable theories.

arXiv comment9 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:1806.04630 and arXiv:1805.09702

References in corpus (9)

• Charged Current Neutrino Nucleus Interactions at Intermediate Energies
• Neutron Beta-Decay as Laboratory for Test of Standard Model
• Sharpening Low-Energy, Standard-Model Tests via Correlation Coefficients in Neutron Beta-Decay
• Framework for maximum likelihood analysis of neutron beta decay observables to resolve the limits of the V-A law
• Tests of the Standard Model in Neutron Beta Decay with Polarized Neutron and Electron and Unpolarized Proton
• Precision Theoretical Analysis of Neutron Radiative Beta Decay to Order "O(α^2/π^2)"
• Lorentz Structure of Vector Part of Matrix Elements of Transitions n <-> p, Caused by Strong Low-Energy Interactions and Hypothesis of Conservation of Charged Vector Current
• Gauge Properties of Hadronic Structure of Nucleon in Neutron Radiative Beta Decay to Order O(alpha/pi) in Standard V - A Effective Theory with QED and Linear Sigma Model of Strong Low--Energy Interactions
• Infrared Properties of Hadronic Structure of Nucleon in Neutron Beta Decays to Order O(α/π) in Standard V - A Effective Theory with QED and Linear Sigma Model of Strong Low--Energy Interactions

Cited by in corpus (3)

• Radiative corrections of order O(alpha E_e/m_N) to Sirlin's radiative corrections of order O(alpha/pi) to neutron lifetime
• 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
• Neutron beta decay and exact conservation of charged weak hadronic vector current in the Standard Model