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

Optimal binning schemes in the phase space of $D\rightarrow K_{\mathrm S}^0\pi^+\pi^-$ and $D\rightarrow K_{\mathrm S}^0K^+K^-$ decays for experimental measurements. These are parametrised as a 500x500 grid of sub-bins on a Dalitz plot and stored as TH2 histograms in the .root files. See below for a description of the schemes contained in each file: "newgamma.root" - The NEWGAMMA scheme with $\mathcal{N}=10$ bins optimised for sensitivity to CKM angle $\gamma$ with $D\rightarrow K_{\mathrm S}^0\pi^+\pi^-$ decays. "newcharm.root" - The NEWCHARM scheme with $\mathcal{N}=10$ bins optimised for sensitivity to the charm mixing parameters, $x_{CP}$ and $\Delta x$, with $D\rightarrow K_{\mathrm S}^0\pi^+\pi^-$ decays. "optimal_kskk_2.root" - Scheme with $\mathcal{N}=2$ bins optimised for sensitivity to CKM angle $\gamma$ with $D\rightarrow K_{\mathrm S}^0K^+K^-$ decays. "optimal_kskk_3.root" - Scheme with $\mathcal{N}=3$ bins optimised for sensitivity to CKM angle $\gamma$ with $D\rightarrow K_{\mathrm S}^0K^+K^-$ decays. "optimal_kskk_4.root" - Scheme with $\mathcal{N}=4$ bins optimised for sensitivity to CKM angle $\gamma$ with $D\rightarrow K_{\mathrm S}^0K^+K^-$ decays. For more details on the methods used and choices made in producing these schemes, along with discussing of the expected sensitivities, see the accompanying preprint on ArXiv.