On the correlation coefficient T(E_e) of the neutron beta decay, caused by the correlation structure invariant under discrete P, C and T symmetries

TL;DR

This paper analyzes the correlation coefficient T(E_e) in neutron beta decay, showing it is invariant under discrete symmetries and calculating its value within the Standard Model and beyond, including radiative and recoil corrections.

Contribution

It provides a detailed calculation of T(E_e) including radiative corrections and explores potential contributions from physics beyond the Standard Model.

Findings

T(E_e) is approximately - B_0, of order 1.

Radiative corrections of order 10^{-3} are included.

Beyond Standard Model effects, including second class currents, are considered.

Abstract

We analyze the correlation coefficient T(E_e), which was introduced by Ebel and Feldman (Nucl. Phys. 4, 213 (1957)). The correlation coefficient T(E_e) is induced by the correlations of the neutron spin with the antineutrino 3-momentum and the electron spin with the electron 3-momentum. Such a correlation structure is invariant under discrete P, C and T symmetries. The correlation coefficient T(E_e), calculated to leading order in the large nucleon mass m_N expansion, is equal to T(E_e) = - 2 g_A(1 + g_A)/(1 + 3 g^2_A) = - B_0, i.e. of order |T(E_e)| ~ 1, where $g_A$ is the axial coupling constant. Within the Standard Model (SM) we describe the correlation coefficient $T(E_e)$ at the level of 10^{-3} by taking into the radiative corrections of order O(\alpha/\pi) or the outer model-independent radiative corrections, where \alpha is the fine-structure constant, and the corrections of order O(E_e/m_N), caused by weak magnetism and proton recoil. We calculate also the contributions of interactions beyond the SM, including the contributions of the second class currents.