Bs-B¯s mixing, CP violation, and extraction of CKM phases from untagged Bs data samples

Abstract

A width difference of the order of 20% has previously been predicted for the two mass eigenstates of the ${\mathit{B}}_{\mathit{s}}$ meson. The dominant contributor to the width difference is b→cc¯s transition, with final states common to both ${\mathit{B}}_{\mathit{s}}$ and B${\mathrm{¯}}_{\mathit{s}}$. All current experimental analyses fit the time dependences of flavor-specific ${\mathit{B}}_{\mathit{s}}$ modes to a single exponential, which essentially determines the average ${\mathit{B}}_{\mathit{s}}$ lifetime. We stress that the same data sample allows even the measurement of the width difference. To see that, this article reviews the time-dependent formulas for tagged ${\mathit{B}}_{\mathit{s}}$ decays, which involve rapid oscillatory terms depending on Δ mt. In untagged data samples the rapid oscillatory terms cancel. Their time evolutions depend only on the much more slowly varying exponential falloffs. We discuss in detail the extraction of the two widths, and identify the large (small) CP-even (-odd) rate with that of the light (heavy) ${\mathit{B}}_{\mathit{s}}$ mass eigenstate. It is demonstrated that decay length distributions of some untagged ${\mathit{B}}_{\mathit{s}}$ modes, such as ${\mathrm{\rho }}^0$ ${\mathit{K}}_{\mathit{S}}$,ω${\mathit{K}}_{\mathit{S}}$,${\mathit{D}}_{\mathit{s}}^{\left(\mathrm{*}\right)\pm }$ ${\mathit{K}}^{\left(\mathrm{*}\right)\mp }$, can be used to extract the notoriously difficult CKM unitarity triangle γ. Sizable CP-violating effects may be seen with such untagged ${\mathit{B}}_{\mathit{s}}$ data samples. Listing ΔΓ as an observable allows for additional important standard model constraints. Within the CKM model, the ratio ΔΓ/Δm involves no CKM parameters, only a hadronic uncertainty. Thus a measurement of ΔΓ(Δm) would predict Δm(ΔΓ), up to the uncertainty. A large width difference would automatically solve the puzzle of the number of charmed hadrons per B decay in favor of theory. We also derive an upper limit of (‖ΔΓ‖/Γ${)}_{\mathit{B}\mathit{s}}$≲0.3. Further, we must abandon the notion of branching fractions of ${\mathit{B}}_{\mathit{s}}$→f, and instead consider B(${\mathit{B}}_{\mathit{L}\left(\mathit{H}\right)}^0$→f), in analogy with the neutral kaons.