  Recently observed anomalies in the $B_s \to J/\psi \phi$ decay and the
like-sign dimuon asymmetry $A^b_{sl}$ hint at possible new physics (NP) in the
$\bsbsbar$ mixing. We parameterize the NP with four model-independent
quantities: the magnitudes and phases of the dispersive part $M_{12}$ and the
absorptive part $\Gamma_{12}$ of the NP contribution to the effective
Hamiltonian. We constrain these parameters using the four observables $\Delta
M_s$, $\Delta\Gamma_s$, the mixing phase $\beta_s^{J/\psi\phi}$, and
$A^b_{sl}$. Our quantitative fit indicates that the NP should contribute a
significant dispersive as well as absorptive part. In fact, models that do not
contribute a new absorptive part are disfavored at more than 99% confidence
level. We extend this formalism to include CPT violation, and show that CPT
violation by itself, or even in presence of CPT-conserving new physics without
an absorptive part, helps only marginally in the simultaneous resolution of
these anomalies. The NP absorptive contribution to $\bsbsbar$ mixing therefore
seems to be essential, and would imply a large branching fraction for channels
like $B_s \to \tau^+ \tau^-$.
