Phase space analysis for three and four massive particles in final states

TL;DR

This paper develops analytical formulae for phase space integrals involving three and four massive particles, applying them to phenomenological cases and complex B_s meson decay calculations at NNLO.

Contribution

It introduces new formulae for phase space integrals with massive particles and applies them to complex B_s decay processes at NNLO.

Findings

Derived fully integrated analytic phase space formulas.

Analyzed mass effects in phenomenological cases.

Calculated a complex master integral for B_s decay at NNLO.

Abstract

We propose formulae for computing the phase space integrals of $1\to 3$ and $1\to 4$ processes with massive particles in final states. As an application of these formulae we study the final state mass effects in some interesting phenomenological cases, giving fully integrated analytic results for the corresponding phase spaces. We consider also the $B_s-\bar{B}_s$ process at NNLO and calculate one of the most complicated master integrals, which contributes to the $\Delta\Gamma_{B_s}$ at $O(\alpha_s^2)$.