Multipole decomposition of tensor interactions of fermionic probes with composite particles and BSM signatures in nuclear reactions

Abstract

A multipole decomposition of a cross section is a useful tool to simplify the analysis of reactions due to their symmetry properties. By using a new approach to decompose antisymmetric tensor-type interactions within the multipole analysis, we introduce a general mathematical formalism for working with tensor couplings. This allows us to present a general tensor nuclear response, which is particularly useful for ongoing $\ensuremath{\beta}$-decay experiments looking for physics beyond the Standard Model (BSM), as well as other exotic particle scatterings off nuclei, e.g., in dark matter direct detection experiments. Using this method, BSM operators identify with the known Standard Model operators, eliminating the need for calculations of additional matrix elements. We present in detail BSM expressions useful for $\ensuremath{\beta}$-decay experiments and give an exemplary application for $^{6}\mathrm{He}$ $\ensuremath{\beta}$-decay, although the formalism is easily generalizable for calculating other exotic scattering reactions.