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Register a new userLattice QCD matrix elements for the ${B_s^0-bar{B}_s^0}$ width difference beyond leading order
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Predicting the $B_s^0-bar{B}_s^0$ width difference $DeltaGamma_s$ relies on the heavy quark expansion and on hadronic matrix elements of $Delta B=2$ operators. We present the first lattice QCD results for matrix elements of the dimension-7 operators $R_{2,3}$ and linear combinations $tilde{R}_{2,3}$ using nonrelativistic QCD for the bottom quark and a highly improved staggered quark (HISQ) action for the strange quark. Computations use MILC ensembles of gauge field configuations with $2+1+1$ flavors of sea quarks with the HISQ discretization, including lattices with physically light up/down quark masses. We discuss features unique to calculating matrix elements of these operators and analyze uncertainties from series truncation, discretization, and quark mass dependence. Finally we report the first Standard Model determination of $DeltaGamma_s$ using lattice QCD results for all hadronic matrix elements through $mathcal{O}(1/m_b)$. The main result of our calculations yields the $1/m_b$ contribution $Delta Gamma_{1/m_b} = -0.022(10)~mathrm{ps}^{-1}$. Adding this to the leading order contribution, the Standard Model prediction is $Delta Gamma_s = 0.092(14)~mathrm{ps}^{-1}$.
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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 $DeltaGamma_s$.
We perform a quantitative analysis of the $bbbar{b}bar{b}$ tetraquark decays into hidden- and open-bottom mesons and calculate, for the first time, the $bbbar{b}bar{b}$ tetraquark total decay width. On the basis of our results, we propose the $bbbar{b}bar{b} to B^{+} B^{-} (B^0 bar{B}^0) (B_s^0 bar{B}_s^0) to l^{+} l^{-}+text{X}$ decays as the most suitable channels to observe the $bbbar{b}bar{b}$ tetraquark states, since the calculated two-lepton cross section upper limit, $simeq 39 $ fb, is so large as to be potentially detectable with the 2018 LHCb sensitivity, paving the way to the observation of the $bbbar{b}bar{b}$ tetraquark in the future LHCb upgrade. The $4mu$ signal for the ground state, $J^{PC}=0^{++}$, is likely to be too small even for the upgraded LHCb, but it may not be hopeless for the $J^{PC}=2^{++}$ fully-bottom state.
We calculate BSM hadronic matrix elements for $K^0-bar K^0$ mixing in the Dual QCD approach (DQCD). The ETM, SWME and RBC-UKQCD lattice collaborations find the matrix elements of the BSM density-density operators $mathcal{O}_i$ with $i=2-5$ to be rather different from their vacuum insertion values (VIA) with $B_2approx 0.5$, $B_3approx B_5approx 0.7$ and $B_4approx 0.9$ at $mu=3~GeV$ to be compared with $B_i=1$ in the VIA. We demonstrate that this pattern can be reconstructed within the DQCD through the non-perturbative meson evolution from very low scales, where factorization of matrix elements is valid, to scales of order $(1~GeV)$ with subsequent perturbative quark-gluon evolution to $mu=3~GeV$. This turns out to be possible in spite of a very different pattern displayed at low scales with $B_2=1.2$, $B_3=3.0$, $B_4=1.0$ and $B_5approx 0.2$ in the large $N$ limit, $N$ being the number of colours. Our results imply that the inclusion of meson evolution in the phenomenology of any non-leptonic transition like $K^0-bar K^0$ mixing and $Ktopipi$ decays is mandatory. While meson evolution, as demonstrated in our paper, is hidden in LQCD results, to our knowledge DQCD is the only analytic approach for non-leptonic transitions and decays which takes this important QCD dynamics into account.
We calculate---for the first time in three-flavor lattice QCD---the hadronic matrix elements of all five local operators that contribute to neutral $B^0$- and $B_s$-meson mixing in and beyond the Standard Model. We present a complete error budget for each matrix element and also provide the full set of correlations among the matrix elements. We also present the corresponding bag parameters and their correlations, as well as specific combinations of the mixing matrix elements that enter the expression for the neutral $B$-meson width difference. We obtain the most precise determination to date of the SU(3)-breaking ratio $xi = 1.206(18)(6)$, where the second error stems from the omission of charm sea quarks, while the first encompasses all other uncertainties. The threefold reduction in total uncertainty, relative to the 2013 Flavor Lattice Averaging Group results, tightens the constraint from $B$ mixing on the Cabibbo-Kobayashi-Maskawa (CKM) unitarity triangle. Our calculation employs gauge-field ensembles generated by the MILC Collaboration with four lattice spacings and pion masses close to the physical value. We use the asqtad-improved staggered action for the light valence quarks, and the Fermilab method for the bottom quark. We use heavy-light meson chiral perturbation theory modified to include lattice-spacing effects to extrapolate the five matrix elements to the physical point. We combine our results with experimental measurements of the neutral $B$-meson oscillation frequencies to determine the CKM matrix elements $|V_{td}| = 8.00(34)(8) times 10^{-3}$, $|V_{ts}| = 39.0(1.2)(0.4) times 10^{-3}$, and $|V_{td}/V_{ts}| = 0.2052(31)(10)$, which differ from CKM-unitarity expectations by about 2$sigma$. These results and others from flavor-changing-neutral currents point towards an emerging tension between weak processes that are mediated at the loop and tree levels.
We calculate in three-flavor lattice QCD the short-distance hadronic matrix elements of all five $Delta C=2$ four-fermion operators that contribute to neutral $D$-meson mixing both in and beyond the Standard Model. We use the MILC Collaborations $N_f = 2+1$ lattice gauge-field configurations generated with asqtad-improved staggered sea quarks. We also employ the asqtad action for the valence light quarks and use the clover action with the Fermilab interpretation for the charm quark. We analyze a large set of ensembles with pions as light as $M_pi approx 180$ MeV and lattice spacings as fine as $aapprox 0.045$ fm, thereby enabling good control over the extrapolation to the physical pion mass and continuum limit. We obtain for the matrix elements in the $overline{text{MS}}$-NDR scheme using the choice of evanescent operators proposed by Beneke emph{et al.}, evaluated at 3 GeV, $langle D^0|mathcal{O}_i|bar{D}^0 rangle = {0.0805(55)(16), -0.1561(70)(31), 0.0464(31)(9), 0.2747(129)(55), 0.1035(71)(21)}~text{GeV}^4$ ($i=1$--5). The errors shown are from statistics and lattice systematics, and the omission of charmed sea quarks, respectively. To illustrate the utility of our matrix-element results, we place bounds on the scale of CP-violating new physics in $D^0$~mixing, finding lower limits of about 10--50$times 10^3$ TeV for couplings of $mathrm{O}(1)$. To enable our results to be employed in more sophisticated or model-specific phenomenological studies, we provide the correlations among our matrix-element results. For convenience, we also present numerical results in the other commonly-used scheme of Buras, Misiak, and Urban.
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