A model-independent measurement of the CKM angle ${\hat{I}}^3$ in the decays $B^{\pm }\to [K^{+}{K}^{-}\ddot{I}{€}^{+}\ddot{I}{€}^{-}{]}_D{h}^{\pm }$ and $B^{\pm }\to [\ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^{+}\ddot{I}{€}^{-}{]}_D{h}^{\pm }$ ($h=K,\ddot{I}€$)

Abstract

A model-independent determination of the CKM angle ${\hat{I}}^3$ is presented, using the $B^{\pm }\to [K^{+}{K}^{-}\ddot{I}{€}^{+}\ddot{I}{€}^{-}{]}_D{h}^{\pm }$ and $B^{\pm }\to [\ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^{+}\ddot{I}{€}^{-}{]}_D{h}^{\pm }$ decays, with $h=K,\ddot{I}€$. This measurement is the first phase-space-binned study of these decay modes, and uses a sample of proton-proton collision data collected by the LHCb experiment, corresponding to an integrated luminosity of $9$fb${}^{-1}$. The phase-space bins are optimised for sensitivity to ${\hat{I}}^3$, and in each bin external inputs from the BESIII experiment are used to constrain the charm strong-phase parameters. The result of this binned analysis is ${\hat{I}}^3=(53.9_{-8.9}^{+9.5}{)}^{\circ }$, where the uncertainty includes both statistical and systematic contributions. Furthermore, when combining with existing phase-space-integrated measurements of the same decay modes, a value of ${\hat{I}}^3=(52.6_{-6.4}^{+8.5}{)}^{\circ }$ is obtained, which is one of the most precise determinations of ${\hat{I}}^3$ to date.

All figures and tables, along with machine-readable versions and any supplementary material and additional information, are available at https://lbfence.cern.ch/alcm/public/analysis/full-details/3993/ (LHCb public pages)