Elvira Gámiz, Christine T. H. Davies, G. Peter Lepage, Junko Shigemitsu, Matthew Wingate
备注：
12 pages, 10 postscript figures, version to appear in Phys.Rev.D. Two new figures, Fig.6 and Fig.10, added. Result on branching fraction Br(B_s \rightarrow mu^+, mu^-) added. Other results on decay constants and on ξunchanged
We study $B_d$ and $B_s$ mixing in unquenched lattice QCD employing the MILC collaboration gauge configurations that include u, d, and s sea quarks based on the improved staggered quark (AsqTad) action and a highly improved gluon action. We implement the valence light quarks also with the AsqTad action and use the nonrelativistic NRQCD action for the valence b quark. We calculate hadronic matrix elements necessary for extracting CKM matrix elements from experimental measurements of mass differences $ΔM_d$ and $ΔM_s$. We find $ξ= f_{B_s} \sqrt{\hat{B}_{B_s}} / f_{B_d} \sqrt{\hat{B}_{B_d}} = 1.258(33)$, $f_{B_d} \sqrt{\hat{B}_{B_d}} = 216(15)$ MeV and $f_{B_s} \sqrt{\hat{B}_{B_s}} = 266(18)$ MeV. We also update previous results for decay constants and obtain $f_{B_d} = 190(13)$ MeV, $f_{B_s} = 231(15)$ MeV and $f_{B_s}/f_{B_d} = 1.226(26)$. The new lattice results lead to updated values for the ratio of CKM matrix elements $|V_{td}|/|V_{ts}|$ and for the Standard Model prediction for $Br(B_s \rightarrow μ^+ μ^-)$ with reduced errors. We determine $|V_{td}|/|V_{ts}| = 0.214(1)(5)$ and $Br(B_s \rightarrow μ^+ μ^-) = 3.19(19) \times 10^{-9}$.
We present recent results for the prediction of the Bs lifetime difference from lattice Heavy Quark Effective Theory simulations. In order to get a next-to-leading order result we have calculated the matching between QCD and HQET and the two-loop anomalous dimensions in the HQET for all the ΔB=2 operators, in particular for the operators which enter the width difference. We present results from quenched and, for the first time, from unquenched simulations. We obtain for the Bs lifetime difference, (ΔΓ_Bs/Γ_Bs)^{(que.)}=(5.1+/- 1.9+/- 1.7)10^(-2) and (ΔΓ_Bs/Γ_Bs)^{(unq.)}=(4.3+/- 2.0+/- 1.9)10^…
We present determinations of the B meson decay constant f_B and of the ratio f_{B_s}/f_B using the MILC collaboration unquenched gauge configurations which include three flavors of light sea quarks. The mass of one of the sea quarks is kept around the strange quark mass, and we explore a range in masses for the two lighter sea quarks down to m_s/8. The heavy b quark is simulated using Nonrelativistic QCD, and both the valence and sea light quarks are represented by the highly improved (AsqTad) staggered quark action. The good chiral properties of the latter action allow for a much smoother chi…
We report results for the masses of the flavour non-singlet light 0++, 1--, and 1+- mesons from unquenched lattice QCD at two lattice spacings. The twisted mass formalism was used with two flavours of sea quarks. For the 0++ and 1+- mesons we look for the effect of decays on the mass dependence. For the light vector mesons we study the chiral extrapolations of the mass. We report results for the leptonic and transverse decay constants of the rho meson. We test the mass dependence of the KRSF relations.
We present results for the static-light meson from unquenched lattice QCD. The unquenched gauge configurations were generated using the non-perturbatively improved clover action. At the fixed lattice spacing of 0.1 fm the lightest sea quark mass used is a third of the strange quark mass. A comparison is made between heavy-light chiral perturbation theory and the f_B^(static) decay constant. The mass of the bottom quark is also reported: m_b(m_b) = 4.25(2)(11) GeV, where the first error is statistical and the last error is the systematic uncertainty.
We present results of an exploratory study of singlet scalar states in unquenched QCD using both glueball and meson operators. Results for non-singlet non-strange scalar mesons are also presented. We use Asqtad improved staggered fermions and gauge configurations generated by the MILC collaboration at lattice spacings of .12 and .09 fm. In this formulation, the glueball mass is not significantly different from the quenched value at finite lattice spacing. Significant taste violations are present in the scalar sector. At light quark masses, decay channels complicate the mass determinations. The…
We present our preliminary results for semileptonic form factors of $D$ mesons in unquenched lattice QCD. Simulations are carried out with $n_f=2+1$ dynamical quarks using gauge configurations generated by the MILC collaboration. For the valence quarks, we adopt an improved staggered light quark action and the clover heavy quark action. Our results for $D \to K$ and $D \to π$ form factors at $q^2=0$ are in agreement with the experimental values.
We calculate the neutral kaon mixing parameter B_K in unquenched lattice QCD using asqtad-improved staggered sea quarks and domain-wall valence quarks. We use the "2+1" flavor gauge configurations generated by the MILC Collaboration, and simulate with multiple valence and sea quark masses at two lattice spacings of a ~ 0.12 fm and a ~ 0.09 fm. We match the lattice determination of B_K to the continuum value using the nonperturbative method of Rome-Southampton, and extrapolate B_K to the continuum and physical quark masses using mixed action chiral perturbation theory. The "mixed-action" method…
We review some decays that require knowledge of the decay constants of $0^{+}$ heavy-light mesons. We compute the decay constants of P-wave heavy-light mesons from unquenched lattice QCD, with two degenerate flavours of sea quarks, at a single lattice spacing. The lightest sea quark mass used in the calculation is a third of the strange quark mass. For the charm-strange meson we obtain the decay constant: $f_{D_{s 0^+}} = 340(110)$ MeV using our normalisation conventions. We obtain the $f_{P_s}^{static}$ (static-strange P-wave) decay constant as $302(39)$ MeV.
We present non-perturbative first-principle results for quark-, gluon- and meson $1$PI correlation functions of two-flavour Landau-gauge QCD in the vacuum. These correlation functions carry the full information about the theory. They are obtained by solving their Functional Renormalisation Group equations in a systematic vertex expansion, aiming at apparent convergence. This work represents a crucial prerequisite for quantitative first-principle studies of the QCD phase diagram and the hadron spectrum within this framework. In particular, we have computed the gluon, ghost, quark and scalar-pse…
We discuss the recent progress in computing the D-meson decay constant and D->pi l nu form factors from the lattice QCD simulations with Nf=2 dynamical using Wilson quarks. We report fD=201(20)MeV and F+(1GeV^2)/fD=4.04(78)GeV^-1 at a=0.08fm.
The recent progress on unquenched QCD simulations is critically reviewed. After some discussions on problems and subtleties in unquenched simulations, hadron spectra obtained from both quenched and unquenched simulations are compared among various gauge and quark actions. It is found that the Edinburgh plot does not agree in the continuum limit between Wilson and KS quark actions even in quenched QCD. Dynamical quark effects on hadron spectra, in particular, on meson masses are then presented for Wilson-type quark actions. Finally dynamical quark effects on other quantities such as the topolog…
I review our qualitative understanding of the increase in the value of the B meson decay constant (fB), when dynamical fermions are included in lattice QCD calculations.
We present a precise lattice computation of pseudoscalar and vector heavy-light meson masses for heavy-quark masses ranging from the physical charm mass up to $\simeq 4$ times the physical b-quark mass. We employ the gauge configurations generated by the European Twisted Mass Collaboration (ETMC) with $N_f = 2+1+1$ dynamical quarks at three values of the lattice spacing ($a \simeq 0.062, 0.082, 0.089$ fm) with pion masses in the range $M_π\simeq 210 - 450$ MeV. The heavy-quark mass is simulated directly on the lattice up to $\simeq 3$ times the physical charm mass. The interpolation to the phy…
We present an unquenched lattice calculation for the $B^0-\bar{B}^0$ transition amplitude. The calculation, carried out at an inverse lattice spacing $1/a$ = 2.22(4) GeV, incorporates two flavors of dynamical quarks described by the fully $O(a)$-improved Wilson fermion action and heavy quarks described by NRQCD. A particular attention is paid to the uncertainty that arises from the chiral extrapolation, especially the effect of pion loops, for light quarks, which we find could be sizable for the leptonic decay of the $B_d$ meson, whereas it is small for the $B_s$ meson and the $B$ parameters. …
We calculate the $\bar{s}s$ condensate in the D - and B - mesons using the unquenched hopping parameter expansion at infinite coupling for the Wilson lattice action. We discuss the phenomenological relevance of our result.
By combining the first unquenched lattice computation of the B-meson binding energy with the recently calculated two-loop contribution to the lattice HQET mass, we determine the $\bar{MS}$ b-quark mass, $\bar{m}_{b}(\bar{m}_{b})$ at the NNLO. We find $\bar{m}_{b}(\bar{m}_{b}) = (4.26\pm 0.03 \pm 0.04 \pm 0.05) {\rm GeV}$. The inclusion of the two-loop effects is one of the steps necessary to extract $\bar{m}_{b}(\bar{m}_{b})$ with a precision better than ${\cal O}(Λ_{QCD})$, which is the uncertainty due to the presence of an IR renormalon singularity in the perturbative series of the residual …
We test the one-loop chiral perturbation theory formula on unquenched lattice data of pseudoscalar meson decay constants. The chiral extrapolation including the effect of the chiral logarithm is attempted and its uncertainty is discussed.
We demonstrate a method for calculating the neutral B-meson decay constants and mixing matrix elements in unquenched lattice QCD with domain-wall light quarks and static b-quarks. Our computation is performed on the "2+1" flavor gauge configurations generated by the RBC and UKQCD Collaborations with a lattice spacing of a approx 0.11 fm (a^-1 = 1.729 GeV) and a lattice spatial volume of approximately (1.8 fm)^3. We simulate at three different light sea quark masses with pion masses down to approximately 430 MeV, and extrapolate to the physical quark masses using a phenomenologically-motivated …
We determine hadronic matrix elements relevant for the mass and width differences, $ΔM_s$ & $ΔΓ_s$ in the $B^0_s - \bar{B^0_s}$ meson system using fully unquenched lattice QCD. We employ the MILC collaboration gauge configurations that include $u$, $d$ and $s$ sea quarks using the improved staggered quark (AsqTad) action and a highly improved gluon action. We implement the valence $s$ quark also with the AsqTad action and use Nonrelativistic QCD for the valence $b$ quark. For the nonperturbative QCD input into the Standard Model expression for $ΔM_s$ we find $f_{B_s} \sqrt{\hat{B}_{B_s}} = 0.2…
We present a new lattice determination of some of the parameters appearing both in the Operator Product Expansion (OPE) analysis of the inclusive semileptonic $B$-meson decays and in the Heavy Quark Expansion (HQE) of the pseudoscalar (PS) and vector (V) heavy-light meson masses. We perform a lattice QCD (LQCD) computation of PS and V heavy-light meson masses for heavy-quark masses $m_h$ in the range from $m_c^{\rm phys}$ to $\simeq 4m_b^{\rm phys}$. We employed the $N_f = 2+1+1$ gauge configurations of the European Twisted Mass Collaboration (ETMC) at three values of the lattice spacing $a \s…
The semileptonic process, B --> πl ν, is studied via full QCD Lattice simulations. We use unquenched gauge configurations generated by the MILC collaboration. These include the effect of vacuum polarization from three quark flavors: the $s$ quark and two very light flavors ($u/d$) of variable mass allowing extrapolations to the physical chiral limit. We employ Nonrelativistic QCD to simulate the $b$ quark and a highly improved staggered quark action for the light sea and valence quarks. We calculate the form factors $f_+(q^2)$ and $f_0(q^2)$ in the chiral limit for the range 16 GeV$^2 \leq q^2…
The quark mass dependence of meson masses and decay constants in N_f=2 QCD is studied at a fixed gauge coupling with different dynamical quark masses. Partially Quenched Wilson Chiral Perturbation Theory (PQWchiPT) is applied to obtain the extrapolation to zero quark mass. It is shown, that in our analysis NNLO-terms play a more important role than O(a)-terms, which can be neglected. Also we compare our results with recent CP-PACS results.
We calculate the light meson spectrum and the light quark masses by lattice QCD simulation, treating all light quarks dynamically and employing the Iwasaki gluon action and the nonperturbatively O(a)-improved Wilson quark action. The calculations are made at the squared lattice spacings at an equal distance a^2~0.005, 0.01 and 0.015 fm^2, and the continuum limit is taken assuming an O(a^2) discretization error. The light meson spectrum is consistent with experiment. The up, down and strange quark masses in the \bar{MS} scheme at 2 GeV are \bar{m}=(m_{u}+m_{d})/2=3.55^{+0.65}_{-0.28} MeV and m_…
We perform a quark model calculation of the $b\bar{b}$ and $c\bar{c}$ spectra from a screened funnel potential form suggested by unquenched lattice calculations. A connection between the lattice screening parameter and an effective gluon mass directly derived from QCD is established. Spin-spin energy splittings, leptonic widths and radiative decays are also examined providing a test for the description of the states.
We present a preliminary calculation of B_K using domain-wall valence quarks and 2+1 flavors of improved staggered sea quarks. Both the size of the residual quark mass, which measures the amount of chiral symmetry breaking, and of the mixed meson splitting Delta_mix, a measure of taste-symmetry breaking, show that discretization effects are under control in our mixed action lattice simulations. We show preliminary data for pseudoscalar meson masses, decay constants and B_K. We discuss general issues associated with the chiral extrapolation of lattice data, and, as an example, present a prelimi…
The $B^* Bπ$ coupling is a fundamental parameter of chiral effective Lagrangian with heavy-light mesons and can constrain the chiral behavior of $f_B$, $B_B$ and the $B\to πl ν$ form factor in the soft pion limit. We compute the $B^* B π$ coupling with the static heavy quark and the $O(a)$-improved Wilson light quark. Simulations are carried out with $n_f=2$ unquenched $12^3\times 24$ lattices at $β=1.80$ and $16^3\times 32$ lattices at $β=1.95$ generated by CP-PACS collaboration. To improve the statistical accuracy, we employ the all-to-all propagator technique and the static quark action wit…
By combining the first unquenched lattice computation of the B-meson binding energy and the two-loop contribution to the lattice HQET residual mass, we determine the (\bar{MS}) (b)-quark mass, (\bar{m}_{b}(\bar{m}_{b})). The inclusion of the two-loop corrections is essential to extract (\bar{m}_{b}(\bar{m}_{b})) with a precision of ({\cal O}(Λ^{2}_{QCD}/m_{b})), which is the uncertainty due to the renormalon singularities in the perturbative series of the residual mass. Our best estimate is (\bar{m}_{b}(\bar{m}_{b}) = (4.26 \pm 0.09) {\rm GeV}), where we have combined the different errors in q…
We present our latest results for the excitations of static-light mesons on both quenched and unquenched lattices, where the light quarks are simulated using the chirally improved (CI) lattice Dirac operator.
The B* B pi coupling is a fundamental parameter of chiral effective Lagrangian with heavy-light mesons and can constrain the B->pi l nu form factor in the soft pion limit which will be useful for precise determination of |Vub|. We compute the B* B pi coupling with the static heavy quark and the O(a)-improved Wilson light quark. Simulations are carried out with n_f=2 unquenched 12^3x24 lattices at beta=1.80 generated by CP-PACS collaboration. Following the quenched study by Negishi et al., we employ the all-to-all propagator with 200 low eigenmodes as well as HYP smeared link to improve the sta…
We present recent results in unquenched lattice QCD with two degenerate light sea quarks using the truncated determinant approximation (TDA). In the TDA the infrared modes contributing to the quark determinant are computed exactly up to some cutoff in quark off-shellness (typically 2$Λ_{QCD}$). This approach allows simulations to be performed at much lighter quark masses than possible with conventional hybrid MonteCarlo techniques. Results for the static energy and topological charge distributions are presented using a large ensemble generated on very coarse (6$^4$) but physically large lattic…
String breaking by dynamical quarks in (2+1)-d lattice QCD is demonstrated in this project, by measuring the static potential and the local color-electric field strength between a heavy quark and antiquark pair at large separations. Simulations are done for unquenched SU(2) color with two flavors of staggered quarks. An improved gluon action is used which allows simulations to be done on coarse lattices, providing an extremely efficient means to access the quark separations and propagation times at which string breaking occurs. The static quark potential is extracted using only Wilson loop ope…
We present an update of our calculations of the decay constants of the D, D_s, B, and B_s mesons in unquenched 2+1 flavor QCD. We use the MILC library of improved staggered gauge ensembles at lattice spacings 0.09, 0.12, and 0.15 fm, clover heavy quarks with the Fermilab normalizations, and improved staggered light valence quarks.
String breaking by dynamical quarks in three-dimensional lattice QCD is analyzed through measurements of the potential and the local color-electric field strength generated by a static quark-antiquark pair. Simulations were done for unquenched SU(2) color with two flavors of staggered light quarks. An improved gluon action was used, which allows simulations to be done on coarse lattices, providing an extremely efficient means to access the large quark separations and long propagation times at which string breaking occurs. The static sources were generated using Wilson loop operators, hence no …
We compute the masses of the flavour singlet 0++ mesons using (n_f=2) unquenched lattice QCD with the Iwasaki and Wilson gauge actions. Both fermionic and glueball interpolating operators are used to create the states. The mass of the lightest 0++ meson is suppressed relative to the mass of the 0++ glueball in quenched QCD at an equivalent lattice spacing. We discuss two possible physical reasons for this.
We consider 2+1 flavor Wilson Chiral Perturbation Theory including the lattice spacing contributions of O($a^{2}$). We adopt a power counting appropriate for the unquenched lattice simulations carried out by the CP-PACS/JLQCD collaboration and compute the pseudo scalar meson masses to one loop. These expression are required to perform the chiral extrapolation of the CP-PACS/JLQCD lattice data.
We review various B meson decays that require knowledge of the transverse decay constant of the b1(1235) meson. We report on an exploratory lattice QCD calculation of the transverse decay constant of the b1 meson. The lattice QCD calculations used unquenched gauge configurations, at two lattice spacings, generated with two flavours of sea quarks. The twisted mass formalism is used.
The potential between static-light mesons forming a meson-meson or a meson-antimeson system is calculated in quenched and unquenched SU(3) gauge theory. We use the Sheikholeslami-Wohlert action and statistical estimators of light quark propagators with maximal variance reduction. The dependence of the potentials on the light quark spin and isospin and the effect of meson exchange is investigated. Our main motivation is exploration of bound states of two mesons and string breaking. The latter also involves the two-quark potential and the correlation between two-quark and two-meson states.
We summarise the current status of lattice QCD computations of neutral meson parameters in the $B_d^0$ and the $B_s^0$ systems. We comment on recent results and anticipate further improvements on the uncertainties in the future.
The heavy-quark expansion for inclusive semi-leptonic B decays introduces $\barΛ$ and $λ_1$, which are matrix elements in heavy-quark effective field theory. We review how they can be obtained from an analysis of the heavy quark mass dependence of heavy-light meson masses in lattice QCD. We present preliminary results for the bottom quark mass, $m_b$, using $\barΛ$ and $λ_1$ for the $B_s$ meson from a 2+1 sea-flavor unquenched calculation.
The couplings between the soft pion and the doublet of heavy-light mesons are basic parameters of the ChPT approach to the heavy-light systems. We compute the unquenched (Nf=2) values of two such couplings in the static heavy quark limit: (1) g^, coupling to the lowest doublet of heavy-light mesons, and (2) g~, coupling to the first orbital excitations. A brief description of the calculation together with a short discussion of the results is presented.
We present high-statistics results for neutral $B$-meson mixing and heavy-light-meson leptonic decays in the quenched approximation from tadpole-improved clover actions at $β= 6.0$ and $β= 6.2$. We consider quantities such as $B_{B_{d(s)}}$, $f_{D_{d(s)}}$, $f_{B_{d(s)}}$ and the full $ΔB=2$ matrix elements as well as the corresponding SU(3)-breaking ratios. These quantities are important for determining the CKM matrix element $|V_{td}|$.
We present updates of our results for neutral $B$-meson mixing and leptonic decay constants obtained in the quenched approximation from a mean-field-improved Sheikholeslami-Wohlert action at two values of lattice spacing. We consider quantities such as $B_{B_{d(s)}}$, $f_{D_{(s)}}$, $f_{B_{(s)}}$ and the full $ΔB=2$ matrix-elements, as well as the corresponding SU(3)-breaking ratios.
We discuss the symmetries of quenched QCD with Wilson fermions, starting from its lagrangian formulation, taking into account the constraints needed for convergence of the ghost-quark functional integral. We construct the corresponding chiral effective lagrangian, including terms linear and quadratic in the lattice spacing. This allows us to study the phase structure of the quenched theory, and compare it to that in the unquenched theory. In particular we study whether there may be an Aoki phase (with parity and flavor spontaneously broken) or a first order transition line (with no symmetry br…
We perform a precise calculation of the mass of the B_c meson using unquenched configurations from the MILC collaboration including 2+1 flavours of improved staggered quarks. Lattice NRQCD and the Fermilab formalism are used to describe the b and c quarks respectively. We find the mass of the B_c meson to be 6.304(16) GeV
We evaluate properties of neutral mesons in Nf=2 dynamical simulations of TMQCD at maximal twist. The pion is explored - establishing the size of the isospin splitting (an order a^2 effect). We investigate the eta' (the Nf=2 flavour singlet pseudoscalar meson) and neutral rho and scalar mesons. We show that disconnected diagrams can be evaluated very efficiently in TMQCD using variance reduction methods.
The importance of $S$-matrix unitarity in realistic meson spectroscopy is reviewed, both its historical development and more recent applications. First the effects of imposing $S$-matrix unitarity on meson resonances is demonstrated in both the elastic and the inelastic case. Then, the static quark model is revisited and its theoretical as well as phenomenological shortcomings are highlighted. A detailed account is presented of the mesons in the tables of the Particle Data Group that cannot be explained at all or only poorly in models describing mesons as pure quark-antiquark bound states. Nex…
We report on progress in measuring disconnected correlators associated with pseudoscalar flavor-singlet mesons. This will eventually allow us to compute the masses of the eta and eta' mesons. Flavor-singlet physics also presents an interesting test of the staggered fermion formulation, as disconnected correlators are sensitive to whether the same action governs both sea quarks and valence quarks. It can also help test the validity of the ``fourth-root trick'' used in unquenched lattice calculations where the number of flavors $N_f<4$.
Correlators of vector, axial and pseudoscalar currents have been calculated in external strong magnetic field in SU(2) gluodynamics on the lattice. Neutral $ρ$ and $A$ meson masses with a zero spin projection to the axis parallel to the external magnetic field $B$ are calculated. The mass of the neutral $ρ$ meson with zero spin decreases with increasing of the magnetic field for available values of the magnetic field $eB\lesssim 2-2.5\, \Gev^2$, such behavior is necessary for a condensation of $ρ$ mesons in a strong magnetic field.
Neutral-meson mixing is loop suppressed in the Standard Model, leading to the possibility of enhanced sensitivity to new physics. The uncertainty in Standard Model predictions for $B$-meson oscillation frequencies is dominated by theoretical uncertainties within the short-distance $B$-meson hadronic matrix elements, motivating the need for improved precision. In $D$-meson mixing, the Standard Model short-distance contributions are further suppressed by the GIM mechanism allowing for the possibility of large new physics enhancements. A first-principle determination of the $D$-meson short-distan…
The recent calculation of the complex isospin-two decay amplitude A_2 with physical kinematics is presented together with exploratory calculations of the isospin-zero decay amplitude A_0. Prospects for accurate calculation of A_0 as well as the mass difference between the K_L and K_S mesons are discussed.
The energies of different angular momentum states of a heavy-light meson were measured on a lattice in PRD 58, 34506 (1998) . We have now continued this study using several different lattices, quenched and unquenched, that have different physical lattice sizes, clover coefficients, hopping parameters and quark-gluon couplings. The heavy quark is taken to be infinitely heavy, whereas the light quark mass is approximately that of the strange quark. By interpolating in the heavy and light quark masses we can thus compare the lattice results with the B_s meson. Most interesting is the lowest P-wav…
We present some simple scenarios for string breaking on the lattice based on a crude strong coupling model introduced previously. We review the dependence of the model on lattice spacing and extend it to include degenerate dynamical quarks and also meson exchange diagrams. A comparison is made between quenched and unquenched calculations. We examine string breaking in the presence of a static quark-diquark system, a situation that is specific to SU(3).
The energies of different angular momentum states of a heavy-light meson were measured on a lattice in Michael and Peisa, Phys. Rev. D 58, 34506 (1998). We have now repeated this study using several different lattices, quenched and unquenched, that have different physical lattice sizes, clover coefficients and quark-gluon couplings. The heavy quark is taken to be infinitely heavy, whereas the light quark mass is approximately that of the strange quark. By interpolating and extrapolating in the light quark mass we can thus compare the lattice results with B and B_s meson experiments. Most inter…
