Recoil contributions in neutron beta decay and their corrections to the correlation coefficients

TL;DR

This paper calculates recoil corrections to neutron beta decay correlation coefficients with polarized particles, emphasizing a comprehensive approach that improves precision to 10^-5 by including general couplings and full differential cross section expansion.

Contribution

It introduces a direct expansion of the full differential cross section and incorporates general coupling forms, enhancing the accuracy of recoil correction calculations in neutron beta decay.

Findings

Recoil corrections are significant at the 10^-5 precision level.

Full differential cross section expansion yields more accurate correlation coefficients.

General coupling forms impact the decay correlation calculations.

Abstract

In this work, the recoil corrections to the correlation coefficients in the neutron beta decay with polarized neutron and electron are evaluated to order O(m_n^-2) in the Born approximation. Different from the usual calculations applied in the literatures where the phase space factor and the amplitude are expanded independently, we directly expand the full differential scattering cross section and then integrate the solid angles of the neutrino. Furthermore, the most general coupling forms in Wpn are kept in the calculation and the analytic expressions for the angular correlation coefficients are given. The numerical comparisons between the results by the different treatments of the phase space factor and the different choices of the coupling parameters are also presented. The results show that the careful treatment of the expansion on m_n^-1 and the inclusion of the general coupling forms are necessary when aiming to reach the precision 10^-5