Five-particle contributions to the inclusive rare $\bar B \to X_{s(d)} \, \ell^+\ell^-$ decays

TL;DR

This paper calculates five-particle tree-level contributions to inclusive rare B meson decays involving leptons, providing analytical results and assessing their phenomenological significance at the percent level or below.

Contribution

It introduces the first complete calculation of five-particle contributions to these decays, including analytical expressions and partial higher-order effects.

Findings

Contributions are at the percent level or below.

Analytical formulas for differential branching ratios are provided.

CKM suppression affects $b o s$ transitions.

Abstract

We calculate tree-level contributions to the inclusive rare $\bar B \to X_{s(d)} \, \ell^+\ell^-$ decays. At the partonic level they stem from the five-particle process $b \to s(d) \, q \bar q \, \ell^+\ell^-$, with $q \in \{u,d,s\}$. While for $b \to d$ transitions such five-body final states contribute at the same order in the Wolfenstein expansion compared to the three-body partonic decay, they are CKM suppressed in $b \to s$ decays. In the perturbative expansion, we include all leading-order contributions, as well as partial next-to-leading order QCD and QED effects. In the case of the differential branching ratio, we present all results completely analytically in terms of polylogarithmic functions of at most weight three. We also consider the differential forward-backward asymmetry, where all except one interference could be obtained analytically. From a phenomenological point of view the newly calculated contributions are at the percent level or below.