Measurement of the CKM angle $\gamma$ and $B^0_s$-$\bar{B}^0_s$ mixing frequency with $B^0_s \rightarrow D_s^\mp h^\pm \pi^\pm \pi^\mp$ decays

TL;DR

This paper reports the first measurement of the CKM angle gamma using $B_s$ decays, along with a precise determination of the $B_s$-$ar{B}_s$ mixing frequency, utilizing data from the LHCb detector.

Contribution

It introduces a novel time-dependent amplitude analysis to measure gamma and provides the most precise $B_s$ mixing frequency to date.

Findings

Measured gamma as (44 ± 12)° with combined uncertainties.

Alternative model-independent gamma measurement: (44^{+20}_{-13})°.

Determined $B_s$-$ar{B}_s$ oscillation frequency as 17.757 ± 0.007 (stat) ± 0.008 (syst) ps^{-1}.

Abstract

The CKM angle $\gamma$ is measured for the first time from mixing-induced $CP$ violation between $B^0_s \rightarrow D_s^\mp K^\pm \pi^\pm \pi^\mp$ and $\bar{B}^0_s \rightarrow D_s^\pm K^\mp \pi^\mp \pi^\pm$ decays reconstructed in proton-proton collision data corresponding to an integrated luminosity of 9 ${\rm fb}^{-1}$ recorded with the LHCb detector. A time-dependent amplitude analysis is performed to extract the $CP$-violating weak phase $\gamma-2\beta_s$ and, subsequently, $\gamma$ by taking the $B^0_s$-$\bar{B}^0_s$ mixing phase $\beta_{s}$ as an external input. The measurement yields $\gamma = (44 \pm 12)^\circ$ modulo $180^\circ$, where statistical and systematic uncertainties are combined. An alternative model-independent measurement, integrating over the five-dimensional phase space of the decay, yields $\gamma = (44^{\,+\,20}_{\,-\,13})^\circ$ modulo $180^\circ$. Moreover, the $B^0_s$-$\bar{B}^0_s$ oscillation frequency is measured from the flavour-specific control channel $B^0_s \rightarrow D_s^- \pi^+ \pi^+ \pi^-$ to be $\Delta m_s = (17.757 \pm 0.007 \,({\rm stat.}) \pm 0.008 \,({\rm syst.})) \text{ps}^{-1}$, consistent with and more precise than the current world-average value.