Employing the SU(2) isospin symmetry of strong interactions and
estimates borrowed from effective field theory, we explore the impact
of new physics on the decays $B^\pm\to \phi K^\pm$ and $B_d\to \phi
K_S$ in a model-independent manner. To this end, we introduce
- in addition to the usual mixing-induced CP asymmetry in $B_d\to
\phi K_S$ - a set of three observables, which may not only provide
smoking-gun signals for new-physics contributions to different
isospin channels, but also valuable insights into hadron dynamics.
Imposing dynamical hierarchies of amplitudes, we discuss various
patterns of these observables, including also scenarios with small and
large rescattering processes. Whereas the $B\to\phi K$ system
provides, in general, a powerful tool to search for indications of new
physics, there is also an unfortunate case, where such effects cannot
be distinguished from those of the Standard Model.