The non-leptonic D0 → K−K+ and D0 → π−π+ 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 D0 → 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 D0 → K−K+, D0 → π−π+ 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.
