A new angle on an old problem: Helicity approach to neutron beta decay in the Standard Model

TL;DR

This paper introduces a helicity-based approach to neutron beta decay, analyzing angular observables and recoil corrections within the Standard Model, revealing certain observables are protected from higher-order recoil effects.

Contribution

It presents a novel helicity approach to neutron beta decay, connecting cascade and three-body decay descriptions, and assesses recoil corrections up to NNLO in the Standard Model.

Findings

Rate and three polarization observables are protected from NLO recoil corrections.

Helicity approach links heavy and light hadron decay descriptions.

Recoil corrections up to NNLO are quantified for neutron beta decay.

Abstract

We elaborate on the dichotomy between the description of the semileptonic decays of heavy hadrons on the one hand and the semileptonic decays of light hadrons such as neutron $\beta$ decays on the other hand. For example, almost without exception the semileptonic decays of heavy baryons are described in cascade fashion as a sequence of two two-body decays $B_1 \to B_2 + W_{\rm off-shell}$ and $W_{\rm off-shell} \to \ell + \nu_\ell$ whereas neutron $\beta$ decays are analyzed as true three-body decays $n \to p + e^- +\bar \nu_e$. Within the cascade approach it is possible to define a set of seven angular observables for polarized neutron $\beta$ decays as well as the longitudinal, transverse and normal polarization of the decay electron. We determine the dependence of the observables on the usual vector and axial vector form factors. In order to be able to assess the importance of recoil corrections we expand the rate and the $q^2$ averages of the observables up to NLO and NNLO in the recoil parameter $\delta=(M_n-M_p)/(M_n+M_p)= 0.689\cdot 10^{-3}$. Remarkably, we find that the rate and three of the four parity conserving polarization observables that we analyze are protected from NLO recoil corrections when the second class current contributions are set to zero.