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Yuehong Xie
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This is a comment on the recent paper by Soumitra Nandi1 and Ulrich Nierste ``Resolving the sign ambiguity in $Delta Gamma_s$ with $B_s to D_s K$, arXiv:0801.0143 [hep-ph].
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The analysis of tagged B_s -> J/psi phi decays determines the CP phase phi_s in B_s-anti-B_s mixing with a two-fold ambiguity. The solutions differ in the sign of cos(phi_s) which equals the sign of the width difference Delta Gamma_s among the two B_s mass eigenstates. We point out that this ambiguity can be removed with the help of B_s -> D_s K decays. We compare untagged and tagged strategies and find the tagged analysis more promising. The removal of the sign ambiguity in Delta Gamma_s can be done with relatively low statistics and could therefore be a target for the early stage of B_s -> D_s K studies.
Semi-leptonic $B_s to K ell u$ and $B_s to D_s ell u$ decays provide an alternative $b$-decay channel to determine the CKM matrix elements $|V_{ub}|$ and $|V_{cb}|$ or to obtain $R$-ratios to investigate lepton flavor universality violations. In addition, these decays may shed further light on the discrepancies seen in the analysis of inclusive vs. exclusive decays. Using the nonperturbative methods of lattice QCD, theoretical results are obtained with good precision and full control over systematic uncertainties. This talk will highlight ongoing efforts of the $B$-physics program by the RBC-UKQCD collaboration.
We report the measurements of the $CP$-violating parameters in $B_s^0 to D_s^{mp} K^{pm}$ decays observed in $pp$ collisions, using a data set corresponding to an integrated luminosity of $3.0,text{fb}^{-1}$ recorded with the LHCb detector. We measure $C_f = 0.73 pm 0.14 pm 0.05$, $A^{Delta Gamma}_f = 0.39 pm 0.28 pm 0.15$, $A^{Delta Gamma}_{overline{f}} = 0.31 pm 0.28 pm 0.15$, $S_f = -0.52 pm 0.20 pm 0.07$, $S_{overline{f}} = -0.49 pm 0.20 pm 0.07$, where the uncertainties are statistical and systematic, respectively. These parameters are used together with the world-average value of the $B_s^0$ mixing phase, $-2beta_s$, to obtain a measurement of the CKM angle $gamma$ from $B_s^0 to D_s^{mp} K^{pm}$ decays, yielding $gamma = (128,_{-22}^{+17})^circ$ modulo $180^circ$, where the uncertainty contains both statistical and systematic contributions. This corresponds to $3.8,sigma$ evidence for $CP$ violation in the interference between decay and decay after mixing.
The $B_s to D_s^{(*)pm} K^mp$ decays allow a theoretically clean determination of $phi_s+gamma$, where $phi_s$ is the $B^0_s$-$bar B^0_s$ mixing phase and $gamma$ the usual angle of the unitarity triangle. A sizable $B_s$ decay width difference $DeltaGamma_s$ was recently established, which leads to subtleties in analyses of the $B_s to D_s^{(*)pm} K^mp$ branching ratios but also offers new untagged observables, which do not require a distinction between initially present $B^0_s$ or $bar B^0_s$ mesons. We clarify these effects and address recent measurements of the ratio of the $B_sto D_s^pm K^mp$, $B_sto D_s^pmpi^mp$ branching ratios. In anticipation of future LHCb analyses, we apply the SU(3) flavour symmetry of strong interactions to convert the $B$-factory data for $B_dto D^{(*)pm}pi^mp$, $B_dto D_s^{pm}pi^mp$ decays into predictions of the $B_s to D_s^{(*)pm} K^mp$ observables, and discuss strategies for the extraction of $phi_s+gamma$, with a special focus on untagged observables and the resolution of discrete ambiguities. Using our theoretical predictions as a guideline, we make simulations to estimate experimental sensitivities, and extrapolate to the end of the planned LHCb upgrade. We find that the interplay between the untagged observables, which are accessible thanks to the sizable $DeltaGamma_s$, and the mixing-induced CP asymmetries, which require tagging, will play the key role for the experimental determination of $phi_s+gamma$.
We have studied Bs0 -> Ds- pi+ and Bs0 -> Ds^(-/+) K^(+/-) decays using 23.6 /fb of data collected at the Upsilon(5S) resonance with the Belle detector at the KEKB e+e- collider. This highly pure Bs0 -> Ds- pi+ sample is used to measure the branching fraction, BR(Bs0 -> Ds- pi+)=[3.67 +0.35,-0.33}(stat.) +0.43,-0.42(syst.) +-0.49(f_s)] x 10^{-3} (f_s=N(Bs(*) Bs(*)bar)/N(bbar b)) and the fractions of Bs0 event types at the Upsilon(5S) energy, {in particular N(Bs* Bs*bar}/N(N(Bs(*) Bs(*)bar)=(90.1 +3.8,-4.0 +-0.2)%. We also determine the masses M(Bs0)=(5364.4 +-1.3 +-0.7) MeV/c^2 and M(Bs*)=(5416.4 +-0.4 +-0.5) MeV/c^2. In addition, we observe Bs0 -> Ds^(-/+) K^(+/-) decays with a significance of 3.5sigma and measure BR(Bs0 -> Ds^(-/+) K^(+/-))=[2.4 +1.2,-1.0(stat.) +-0.3(syst.) +-0.3(f_s)] x 10^{-4}.
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