General Analysis of New Physics in $B\to J/\psi K$

We present a model-independent parametrization of the $B^\pm\to J/\psi K^\pm$, $B_d\to J/\psi K_S$ decay amplitudes by taking into account the constraints that are implied by the isospin symmetry of strong interactions. Employing estimates borrowed from effective field theory, we explore the impact of physics beyond the Standard Model and introduce -- in addition to the usual mixing-induced CP asymmetry $A_{CP}^{mix}$ in $B_d\to J/\psi K_S$ -- a set of three observables, allowing a general analysis of possible new-physics effects in the $B\to J/\psi K$ system. Imposing a dynamical hierarchy of amplitudes, we argue that one of these observables may already be accessible at the first-generation $B$-factories, whereas the remaining ones will probably be left for second-generation $B$ experiments. However, in the presence of large rescattering effects, all three new-physics observables may be sizeable. We also emphasize that a small value of $A_{CP}^{mix}$ could be due to new-physics effects arising at the $B\to J/\psi K$ decay-amplitude level. In order to establish such a scenario, the observables introduced in this paper play a key role.