Standard model benchmarks for D0 → K−K+, π−π+, $$ {K}_{\mathrm{S}}^0{K}_{\mathrm{S}}^0 $$ decays

A bstract The non-leptonic D 0 → K − K + and D 0 → 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 $$ {D}^0\to {K}_{\mathrm{S}}^0{K}_{\mathrm{S}}^0 $$ D 0 → K S 0 K 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 → K − K + results using the isospin symmetry, we find a consistent benchmark picture. Specifically, we can accommodate the measured $$ {D}^0\to {K}_{\mathrm{S}}^0{K}_{\mathrm{S}}^0 $$ D 0 → K S 0 K 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 → K − K + , D 0 → π − π + tree contributions. Finally, we explore the resulting range for direct CP violation in $$ {D}^0\to {K}_{\mathrm{S}}^0{K}_{\mathrm{S}}^0 $$ D 0 → K S 0 K S 0 , obtaining upper bounds in our benchmark scenarios of a few per mille, offering an exciting target for future measurements.