A simple relation for B_s-mixing

TL;DR

This paper revisits a commonly used relation in B_s-mixing studies, clarifying its limitations and utility in estimating penguin contributions rather than eliminating theoretical uncertainties.

Contribution

It demonstrates that the relation cannot eliminate the theory prediction for 2 but can help estimate penguin effects in B_s  decays.

Findings

The relation is not suitable for removing 2 theory uncertainties.

It can be used to estimate penguin contributions.

Current theory predictions for 2 have limited precision.

Abstract

We reinvestigate a simple relation between the semileptonic CP asymmetry a_{sl}^s, the decay rate difference \Delta \Gamma_s, the mass difference \Delta M_s and S_{\psi \phi} extracted from the angular analysis of the decay B_s \to \psi \phi, which is regularly used in the literature. We find that this relation is not suited to eliminate the theory prediction for \Gamma_{12}, it can, however be used to determine the size of the penguin contributions to the decay B_s \to \psi \phi. Moreover we comment on the current precision of the theory prediction for \Gamma_{12}.