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Register a new userExploring $B_s to D_s^{(*)pm} K^mp$ Decays in the Presence of a Sizable Width Difference $DeltaGamma_s$
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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 $phi_s+gamma$.
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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.
Amplitude models are constructed to describe the resonance structure of ${D^{0}to K^{-}pi^{+}pi^{+}pi^{-}}$ and ${D^{0} to K^{+}pi^{-}pi^{-}pi^{+}}$ decays using $pp$ collision data collected at centre-of-mass energies of 7 and 8 TeV with the LHCb experiment, corresponding to an integrated luminosity of $3.0mathrm{fb}^{-1}$. The largest contributions to both decay amplitudes are found to come from axial resonances, with decay modes $D^{0} to a_1(1260)^{+} K^{-}$ and $D^{0} to K_1(1270/1400)^{+} pi^{-}$ being prominent in ${D^{0}to K^{-}pi^{+}pi^{+}pi^{-}}$ and $D^{0}to K^{+}pi^{-}pi^{-}pi^{+}$, respectively. Precise measurements of the lineshape parameters and couplings of the $a_1(1260)^{+}$, $K_1(1270)^{-}$ and $K(1460)^{-}$ resonances are made, and a quasi model-independent study of the $K(1460)^{-}$ resonance is performed. The coherence factor of the decays is calculated from the amplitude models to be $R_{K3pi} = 0.459pm 0.010,(mathrm{stat}) pm 0.012,(mathrm{syst}) pm 0.020,(mathrm{model})$, which is consistent with direct measurements. These models will be useful in future measurements of the unitary-triangle angle $gamma$ and studies of charm mixing and $C!P$ violation.
We consider two-loop QCD corrections to the element $Gamma_{12}^q$ of the decay matrix in $B_q-bar{B}_q$ mixing, $q=d,s$, in the leading power of the Heavy Quark Expansion. The calculated contributions involve one current-current and one penguin operator and constitute the next step towards a theory prediction for the width difference $DeltaGamma_s$ matching the precise experimental data. We present compact analytic results for all matching coefficients in an expansion in $m_c/m_b$ up to second order. Our new corrections are comparable in size to the current experimental error and slightly increase $DeltaGamma_s$.
Recent studies of several multi-body $D^0$ meson decays have revealed that the final states are dominantly $CP$-even. However, the small value of the width difference between the two physical eigenstates of the $D^0$-$overline{D}{}^0$ system indicates that the total widths of decays to $CP$-even and $CP$-odd final states should be the same to within about a percent. The known contributions to the width difference from hadronic $D^0$ decays are discussed, and it is shown that an apparent excess of quasi-$CP$-even modes is balanced, within current uncertainty, by interference effects in quasi-flavour-specific decays. Decay modes which may significantly affect the picture with improved measurements are considered.
The width difference $Delta Gamma$ among the two mass eigenstates of the $B_s$-$bar B_s$ system is measured with a precision of 7%. The theory prediction has a larger uncertainty which mainly stems from unknown perturbative higher-order QCD corrections. I discuss the subset of next-to-next-to-leading order diagrams proportional to $alpha_s^2, N_f$, where $N_f=5$ is the number of quark flavours. The results are published in [1].
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