A model-independent measurement of the CKM angle ${\hat{I}}^3$ in partially reconstructed $B^{\pm }\to D^{\ast }{h}^{\pm }$ decays with $D\to K_S^0{h}^{+}{h}^{-}$ $(h=\ddot{I}€,K)$

Abstract

A measurement of $CP$-violating observables in $B^{\pm }\to D^{\ast }{K}^{\pm }$ and $B^{\pm }\to D^{\ast }\ddot{I}{€}^{\pm }$ decays is made where the photon or neutral pion from the $D^{\ast }\to D{\hat{I}}^3$ or $D^{\ast }\to D\ddot{I}{€}^0$ decay is not reconstructed. The $D$ meson is reconstructed in the self-conjugate decay modes, $D\to K_S^0\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ or $D\to K_S^0{K}^{+}{K}^{-}$. The distribution of signal yields in the $D$ decay phase space is analysed in a model-independent way. The measurement uses a data sample collected in proton-proton collisions at centre-of-mass energies of 7, 8, and 13 TeV, corresponding to a total integrated luminosity of approximately 9 fb${}^{-1}$. The $B^{\pm }\to D^{\ast }{K}^{\pm }$ and $B^{\pm }\to D^{\ast }\ddot{I}{€}^{\pm }$ $CP$-violating observables are interpreted in terms of hadronic parameters and the CKM angle ${\hat{I}}^3$, resulting in a measurement of ${\hat{I}}^3=(92_{-17}^{+21}{)}^{\circ }$. The total uncertainty includes the statistical and systematic uncertainties, and the uncertainty due to external strong-phase inputs.

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