Benchmarks for the new-physics search throughCPviolation inB0→π0KS

Using isospin relations, we predict the standard model correlation between $S_{{\pi }^0{K}_{\mathrm{S}}}\equiv (\sin 2\beta {)}_{{\pi }^0{K}_{\mathrm{S}}}$ and $A_{{\pi }^0{K}_{\mathrm{S}}}$, the mixing-induced and direct $CP$ asymmetries of $B^0\to {\pi }^0{K}_{\mathrm{S}}$. The calculation uses flavor $SU(3)$ only to fix the isospin-$3/2$ amplitude through the $B^{\pm }\to {\pi }^{\pm }{\pi }^0$ branching ratio, and thus has a small irreducible theoretical error. It can reach percent level precision thanks to expected future lattice-QCD progress for the calculation of the relevant $SU(3)$-breaking form-factor ratio, and serves as a benchmark for new-physics searches. We obtain an interesting picture in the $A_{{\pi }^0{K}_{\mathrm{S}}}–S_{{\pi }^0{K}_{\mathrm{S}}}$ plane, where the current experimental data show a discrepancy with the standard model, and comment on the direct $CP$ asymmetries of $B^0\to {\pi }^{-}{K}^{+}$ and $B^{+}\to {\pi }^0{K}^{+}$. A modified electroweak penguin with a large new $CP$-violating phase can explain the discrepancy and allows us to accommodate also the corresponding data for other $b\to s$ penguin-dominated decays.