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We present results for the $SU(3)$ breaking ratios of decay constants $f_{D_s}/f_D$ and $f_{B_s}/f_B$ and - for the first time with physical pion masses - the ratio of bag parameters $B_{B_s}/B_{B_d}$, as well as the ratio $xi$, forming the ratio of the nonpeturbative contributions to neutral $B_{(s)}$ meson mixing. Our results are based on Lattice QCD simulations with chirally symmetric 2+1 dynamical flavors of domain wall fermions. Eight ensembles at three different lattice spacing in the range $a = 0.11 - 0.07,mathrm{fm}$ enter the analysis two of which feature physical light quark masses. Multiple heavy quark masses are simulated ranging from below the charm quark mass to half the bottom quark mass. The $SU(3)$ breaking ratios display a very benign heavy mass behaviour allowing for extrapolation to the physical bottom quark mass. The results in the continuum limit including all sources of systematic errors are $f_{D_s}/f_D = 1.1740(51)_mathrm{stat}(^{+68}_{-68})_mathrm{sys}$, $f_{B_s}/f_B = 1.1949(60)_mathrm{stat}(^{+hphantom{0}95}_{-175})_mathrm{sys}$, $B_{B_s}/B_{B_d} = 0.9984(45)_mathrm{stat}(^{+80}_{-63})_mathrm{sys}$ and $xi = 1.1939(67)_mathrm{stat}(^{+hphantom{0}95}_{-177})_mathrm{sys}$. Combining these with experimentally measured values we extract the ratios of CKM matrix elements $|V_{cd}/V_{cs}| = 0.2164(57)_mathrm{exp}(^{+12}_{-12})_mathrm{lat}$ and $|V_{td}/V_{ts}| = 0.20329(41)_mathrm{exp}(^{+162}_{-301})_mathrm{lat}$.
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We determine the spectrum of $B_s$ 1P states using lattice QCD. For the $B_{s1}(5830)$ and $B_{s2}^*(5840)$ mesons, the results are in good agreement with the experimental values. Two further mesons are expected in the quantum channels $J^P=0^+$ and $1^+$ near the $BK$ and $B^{*}K$ thresholds. A combination of quark-antiquark and $B^{(*)}$ meson-Kaon interpolating fields are used to determine the mass of two QCD bound states below the $B^{(*)}K$ threshold, with the assumption that mixing with $B_s^{(*)}eta$ and isospin-violating decays to $B_s^{(*)}pi$ are negligible. We predict a $J^P=0^+$ bound state $B_{s0}$ with mass $m_{B_{s0}}=5.711(13)(19)$ GeV. With further assumptions motivated theoretically by the heavy quark limit, a bound state with $m_{B_{s1}}= 5.750(17)(19)$ GeV is predicted in the $J^P=1^+$ channel. The results from our first principles calculation are compared to previous model-based estimates.
We present recent progress in the lattice calculation of leptonic decay constants for $B_{(s)}$ and $D_{(s)}$ mesons using the Oktay-Kronfeld (OK) action for charm and bottom valence quarks, whose masses are tuned non-perturbatively. The calculations are done on 6 HISQ ensembles generated by the MILC collaboration with $N_f=2+1+1$ flavors. We also use the HISQ action for the light spectator quarks. Results are presented for the ratios $f_{B_s}/f_B$ and $f_{D_s}/f_D$, which reflect $SU(3)$ flavor symmetry breaking, and are independent of the renormalization constants of the axial currents.
$D_s$ mesons are studied in three quantum channels ($J^P=0^+$, $1^+$ and $2^+$), where experiments have identified the very narrow $D_{s0}^*(2317)$, $D_{s1}(2460)$ and narrow $D_{s1}(2536)$, $D_{s2}^*(2573)$. We explore the effect of nearby $DK$ and $D^*K$ thresholds on the subthreshold states using lattice QCD. Our simulation is done on two very different ensembles of gauge configurations (2 or 2+1 dynamical quarks, Pion mass of 266 or 156 MeV, lattice size $16^3times 32$ or $32^3times 64$). In addition to $bar{q}q$ operators we also include meson-meson interpolators in the correlation functions. This clarifies the identification of the states above and below the scattering thresholds. The ensemble with $m_pi simeq 156~$MeV renders the $D_{s1}(2460)$ as a strong interaction bound state 44(10)MeV below $D^*K$ threshold, which is in agreement with the experiment. The $D_{s0}^*(2317)$ is found 37(17)MeV below $DK$ threshold, close to experiment value of 45MeV. The narrow resonances $D_{s1}(2536)$ and $D_{s2}^*(2573)$ are also found close to the experimental masses.
We present a calculation of the form factors, $f_0$ and $f_+$, for the $B_{(s)} to D_{(s)}$ semileptonic decays. Our work uses the MILC $n_f=2+1$ AsqTad configurations with NRQCD and HISQ valence quarks at four values of the momentum transfer $q^2$. We provide results for the chiral-continuum extrapolations of the scalar and vector form factors.
The branching fraction of the decay $B_{s}^{0} rightarrow D_{s}^{(*)+}D_{s}^{(*)-}$ is measured using $pp$ collision data corresponding to an integrated luminosity of $1.0fb^{-1}$, collected using the LHCb detector at a centre-of-mass energy of $7$TeV. It is found to be begin{align*} {mathcal{B}}(B_{s}^{0}rightarrow~D_{s}^{(*)+}D_{s}^{(*)-}) = (3.05 pm 0.10 pm 0.20 pm 0.34)%, end{align*} where the uncertainties are statistical, systematic, and due to the normalisation channel, respectively. The branching fractions of the individual decays corresponding to the presence of one or two $D^{*pm}_{s}$ are also measured. The individual branching fractions are found to be begin{align*} {mathcal{B}}(B_{s}^{0}rightarrow~D_{s}^{*pm}D_{s}^{mp}) = (1.35 pm 0.06 pm 0.09 pm 0.15)%, ewline{mathcal{B}}(B_{s}^{0}rightarrow~D_{s}^{*+}D_{s}^{*-}) = (1.27 pm 0.08 pm 0.10 pm 0.14)%. end{align*} All three results are the most precise determinations to date.
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