Measurement of the CKM angle ${\hat{I}}^3$ and $B_s^0$-${\bar{B}}_s^0$ mixing frequency with $B_s^0\to D_s^{\mp }{h}^{\pm }\ddot{I}{€}^{\pm }\ddot{I}{€}^{\mp }$ decays

Abstract

The CKM angle ${\hat{I}}^3$ is measured for the first time from mixing-induced $CP$ violation between $B_s^0\to D_s^{\mp }{K}^{\pm }\ddot{I}{€}^{\pm }\ddot{I}{€}^{\mp }$ and ${\bar{B}}_s^0\to D_s^{\pm }{K}^{\mp }\ddot{I}{€}^{\mp }\ddot{I}{€}^{\pm }$ decays reconstructed in proton-proton collision data corresponding to an integrated luminosity of 9 ${\mathrm{fb}}^{-1}$ recorded with the LHCb detector. A time-dependent amplitude analysis is performed to extract the $CP$-violating weak phase ${\hat{I}}^3-2{\hat{I}}_s^2$ and, subsequently, ${\hat{I}}^3$ by taking the $B_s^0$-${\bar{B}}_s^0$ mixing phase ${\hat{I}}_s^2$ as an external input. The measurement yields ${\hat{I}}^3=(44\pm 12{)}^{\circ }$ 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 ${\hat{I}}^3=(44_{-13}^{+20}{)}^{\circ }$ modulo $180^{\circ }$. Moreover, the $B_s^0$-${\bar{B}}_s^0$ oscillation frequency is measured from the flavour-specific control channel $B_s^0\to D_s^{-}\ddot{I}{€}^{+}\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ to be $\hat{I}”m_s=(17.757\pm 0.007(stat.)\pm 0.008(syst.)){\text{ps}}^{-1}$, consistent with and more precise than the current world-average value.

All figures and tables, along with any supplementary material and additional information, are available at https://cern.ch/lhcbproject/Publications/p/LHCb-PAPER-2020-030.html (LHCb public pages)