Optimal binning of $D\to K_{\mathrm{S}}^0{\pi }^{+}{\pi }^{-}$ and $D\to K_{\mathrm{S}}^0{K}^{+}{K}^{-}$ phase space for experimental measurements

Abstract

New binning schemes for the Dalitz plots of $D\to K_{\mathrm{S}}^0{\pi }^{+}{\pi }^{-}$ and $D\to K_{\mathrm{S}}^0{K}^{+}{K}^{-}$ decays are presented. These are determined using a new figure of merit for optimisation that better represents the sensitivity to $\gamma$ than previous metrics. Further augmentation comes from including consideration of degeneracy with other physics parameters determined simultaneously and a more accurate treatment of relevant backgrounds. The overall expected improvement in the precision of $\gamma$ measurements using $B^{\pm }\to D{K}^{\pm }$ decays, followed by $D\to K_{\mathrm{S}}^0{\pi }^{+}{\pi }^{-}$, is estimated at around 5$\%$. In addition, the first dedicated optimisation is performed for the observables relevant to charm mixing, $x_{CP}$ and $\Delta x$, in $D\to K_{\mathrm{S}}^0{\pi }^{+}{\pi }^{-}$ decays. This procedure accounts for both statistical sensitivity and the migration of events between bins due to detector resolution. The resulting binning scheme leads to an estimated gain of approximately 20$\%$ in statistical sensitivity, while maintaining the bias due to bin migration at a level comparable to the currently used scheme.

Prepared for submission to JHEP