Standard Model Benchmarks for $D^0\to K^{-}{K}^{+},{\pi }^{-}{\pi }^{+},K_{\mathrm{S}}^0{K}_{\mathrm{S}}^0$ Decays

Abstract

The non-leptonic $D^0\to K^{-}{K}^{+}$ and $D^0\to {\pi }^{-}{\pi }^{+}$ decays are powerful probes of the Standard Model and are related to each other through the $U$-spin symmetry of the strong interaction. Using lattice QCD inputs we calculate the corresponding colour-allowed tree amplitudes in factorisation and demonstrate that non-factorisable contributions and $U$-spin-breaking effects at the level of 50% allow us to accommodate the measured branching ratios in the Standard Model. An exciting direct probe of such non-factorisable and $U$-spin breaking effects is provided by the $D^0\to K_{\mathrm{S}}^0{K}_{\mathrm{S}}^0$ channel. This decay is governed by non-factorisable exchange topologies and essentially vanishes in the $U$-spin limit, although it is experimentally well established with a prominent branching ratio. Extrapolating our $D^0\to K^{-}{K}^{+}$ results using the isospin symmetry, we find a consistent benchmark picture. Specifically, we can accommodate the measured $D^0\to K_{\mathrm{S}}^0{K}_{\mathrm{S}}^0$ branching ratio with $U$-spin-breaking effects at the 50% level and exchange amplitudes at the level of 50% of the colour-allowed $D^0\to K^{-}{K}^{+}$, $D^0\to {\pi }^{-}{\pi }^{+}$ tree contributions. Finally, we explore the resulting range for direct CP violation in $D^0\to K_{\mathrm{S}}^0{K}_{\mathrm{S}}^0$, obtaining upper bounds in our benchmark scenarios of a few per mille, offering an exciting target for future measurements.

Comments: 33 pages, 13 figures