Remarks on the $A_{SL}^s$ and $\Delta\Gamma_s$ Studies at the Tevatron and Beyond

Abstract

We give an assessment of the three approaches, undertaken by the D$\emptyset$ experiment, to probe CP violation in $B_s$ mixing without measurement of $B_s$-$\bar B_s$ oscillations or tagging: dimuon charge asymmetry $A_{SL}$, untagged single muon charge asymmetry $A_{SL}^s$, and lifetime difference in untagged $B_s \to J/\psi\phi$ decay. The latter two approaches provide an alternative avenue, if not crosscheck, to the usual mixing-decay interference study in modes such as $B_s \to J/\psi\phi$. Prospects at the Tevatron, LHC and (Super) B factories are discussed.