Exploring $B_s \to D_s^{(*)\pm} K^\mp$ Decays in the Presence of a Sizable Width Difference $\Delta\Gamma_s$

TL;DR

This paper investigates $B_s o D_s^{(*) ext{ extpm}} K^ ext{ extminus}$ decays considering the sizable width difference $ riangle ext{ extGamma}_s$, proposing new untagged observables and strategies for measuring the phase $ ext{ extphi}_s + ext{ extgamma}$ at LHCb.

Contribution

It introduces untagged observables enabled by the large $ riangle ext{ extGamma}_s$, and applies SU(3) symmetry to predict $B_s$ decay observables from $B_d$ data for future experimental analysis.

Findings

Untagged observables become accessible due to sizable $ riangle ext{ extGamma}_s$.

Predictions for $B_s$ decay observables derived from $B_d$ data using SU(3) symmetry.

Strategies outlined for extracting $ ext{ extphi}_s + ext{ extgamma}$ at LHCb.

Abstract

The $B_s \to D_s^{(*)\pm} K^\mp$ decays allow a theoretically clean determination of $\phi_s+\gamma$, where $\phi_s$ is the $B^0_s$-$\bar B^0_s$ mixing phase and $\gamma$ the usual angle of the unitarity triangle. A sizable $B_s$ decay width difference $\Delta\Gamma_s$ was recently established, which leads to subtleties in analyses of the $B_s \to D_s^{(*)\pm} K^\mp$ branching ratios but also offers new "untagged" observables, which do not require a distinction between initially present $B^0_s$ or $\bar B^0_s$ mesons. We clarify these effects and address recent measurements of the ratio of the $B_s\to D_s^\pm K^\mp$, $B_s\to D_s^\pm\pi^\mp$ branching ratios. In anticipation of future LHCb analyses, we apply the SU(3) flavour symmetry of strong interactions to convert the $B$-factory data for $B_d\to D^{(*)\pm}\pi^\mp$, $B_d\to D_s^{\pm}\pi^\mp$ decays into predictions of the $B_s \to D_s^{(*)\pm} K^\mp$ observables, and discuss strategies for the extraction of $\phi_s+\gamma$, with a special focus on untagged observables and the resolution of discrete ambiguities. Using our theoretical predictions as a guideline, we make simulations to estimate experimental sensitivities, and extrapolate to the end of the planned LHCb upgrade. We find that the interplay between the untagged observables, which are accessible thanks to the sizable $\Delta\Gamma_s$, and the mixing-induced CP asymmetries, which require tagging, will play the key role for the experimental determination of $\phi_s+\gamma$.