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Reconciling anomalous measurements in $B_s-\bar{B}_s$ mixing: the role of CPT-conserving and CPT-violating new physics

Recently observed anomalies in the $B_s \to J/ψϕ$ 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 $Γ_{12}$ of the NP contribution to the effective Hamiltonian. We constrain these parameters using the four observables $ΔM_s$, $ΔΓ_s$, the mixing phase $β_s^{J/ψϕ}$, 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 $B_s \to τ^+ τ^-$.