CP violation in $B_{(s)}\to \phi K$ decays: Standard Model and isospin-dependent New Physics

The penguin-dominated $B\to \phi K$ decays provide sensitive probes of physics beyond the Standard Model. Interpreting them at increasing experimental precision requires control of doubly Cabibbo-suppressed hadronic contributions. Using a factorization approach, we obtain Standard Model benchmarks for the branching ratios and CP-violating observables, including the hadronic phase shift in $B_d^0\to \phi K_{\mathrm{S}}$. The $B_s^0\to \phi K_{\mathrm{S}}$ channel, in which the corresponding penguin effects are not Cabibbo-suppressed, offers additional insight into these contributions. Comparing the neutral and charged $B\to \phi K$ modes further allows the construction of isospin observables. We discuss their Standard-Model expectations and sensitivity to New Physics in the $I=0$ and $I=1$ sectors. The available data are consistent with the Standard Model, while leaving substantial room for New Physics contributions.