Euan McLean, Christine T. H. Davies, Brian Colquhoun, Andrew Lytle
We report on progress of a lattice QCD calculation of the $B\to Dlν$ and $B_s\to D_s lν$ semileptonic form factors. We use a relativistic staggered action (HISQ) for light and charm quarks, and an improved non-relativistic (NRQCD) action for bottom, on the second generation MILC ensembles.
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One leading source of uncertainty in the lattice computation of semi-leptonic form factors in B decay, and to a lesser extent B meson decay constants, comes from the extrapolation of the light quark mass to the physical up/down mass. This talk presents first explorations of simulating the light quark with staggered fermion actions, which are free of the spurious zero modes that effect Wilson-like Dirac operators and are less costly. Methods for fitting to Euclidean-time NRQCD-staggered meson propagators are discussed, and some preliminary spectrum results are presented.
We calculate form factors relevant for rare B decays using moving-NRQCD for the b quark and the AsqTad action for the light quarks. Moving NRQCD allows us to work directly with the physical b quark mass and go to higher recoil momentum compared to standard NRQCD. Here, we show first results for the matrix elements and the operator matching coefficients. Some difficulties and possible ways of improvement are discussed.
We report on exploratory studies of heavy-light meson semileptonic decays using Asqtad light quarks, NRQCD heavy quarks and Symanzik improved glue on coarse quenched lattices. Oscillatory contributions to three-point correlators coming from the staggered light quarks are found to be handled well by Bayesian fitting methods. B meson decays to both the Goldstone pion and to one of the point-split non-Goldstone pions are investigated. One-loop perturbative matching of NRQCD/Asqtad heavy-light currents is incorporated.
We calculate semileptonic form factors for the decays $B_c \to η_c \, l ν$ and $B_c \to J/ψ\, l ν$ over the entire $q^2$ range, using a highly improved lattice quark action for charm at several lattice spacings down to $a=0.045$ fm. We have two ways of treating the $b$ quark: either with an $O(α_s)$ improved NRQCD formalism or by extrapolating a heavy mass $m_h$ to $m_b$ in the relativistic formalism. Comparison of the two approaches provides an important cross-check of methodologies in lattice QCD. Nonperturbative renormalisation of the currents in the relativistic theory also allows us then …
We present further results for one-loop matching of heavy-light axial and vector currents between continuum QCD and a lattice theory with NRQCD heavy quarks and massless clover quarks.
We present {\it preliminary} results for the spectrum and decay constants of B mesons using NRQCD heavy and Wilson light quarks on configurations at $β=5.6$ with two dynamical flavours of staggered fermions. All terms to order $1/M_Q$ are included in the NRQCD action; matrix elements are corrected to this order by calculating the small components of the heavy quark propagator.
We calculate the one loop renormalisation parameters for the heavy-light axial-vector and vector currents using lattice perturbation theory. We use NonRelativistic QCD (NRQCD) heavy quarks and the Highly Improved Staggered Quark (HISQ) action for the light quarks. We present results for heavy-light currents with massless HISQ quarks and briefly discuss the extension to heavy-heavy currents with massive HISQ quarks.
One-loop matching of heavy-light currents is carried out for a highly improved lattice action, including the effects of dimension 4 O(1/M) and O(a) operators. We use the NRQCD action for heavy quarks, the Asqtad improved naive action for light quarks, and the Symanzik improved glue action. As part of the matching procedure we also present results for the NRQCD self energy and for massless Asqtad quark wavefunction renormalization with improved glue.
We present preliminary results using NRQCD to describe heavy quarks on the MILC 2+1 flavour dynamical extra coarse ensemble. We calculate the spectra of low lying states in bottomonium to complement earlier results on the finer MILC ensembles. We then exploit the coarseness of the lattices to calculate charm propagators using NRQCD. These are used to examine the charmonium spectrum and to calclate the mass of the $B_c$ using NRQCD. Finally we look breifly at the $B_d$ and $B_s$ systems using the imporoved staggered formalism to describe the light valence quarks.
We present one-loop matching coefficients between continuum and lattice QCD for the heavy-light four-fermion operators relevant for neutral B meson mixing both within and beyond the Standard Model. For the lattice theory we use nonrelativistic QCD (NRQCD) to describe b quarks and improved staggered fermions (AsqTad) for light quarks. The gauge action is the tree-level Symanzik improved gauge action. Matching to full QCD is carried out through order alpha_s, Lambda_{QCD}/M_b, and alpha_s/(aM_b).
Preliminary results from an extensive lattice calculation of the B, B_c, and Υspectrum at quenched β= 6.0 are presented. The study includes radially and orbitally excited mesons, and baryons containing b quarks. The b quarks are formulated using NRQCD; for light and c quarks, a tadpole-improved clover action is used.
We determine the mass spectra of heavy baryons containing one or more bottom quarks along with their hyperfine splittings and various mass differences on MILC 2+1 Asqtad lattices at three different lattice spacings. NRQCD action is used for bottom quarks whereas relativistic HISQ action for the lighter up/down, strange and charm quarks. We consider all possible combinations of bottom and lighter quarks to construct the bottom baryon operators for the states $J^P=1/2^+$ and $3/2^+$.
I review recent results for heavy-heavy spectroscopy using Lattice NRQCD. The NRQCD collaboration reports that spin-independent splittings for the $Υ$ are scaling for a sensible range of $β$ values in the quenched approximation. Spin-dependent splittings are not, if the scale is set by spin-independent splittings. Results which include higher order spin-dependent relativistic and discretisation corrections show differences from previous (NRQCD collaboration) results without these. As expected, the differences are small for $Υ$ but rather large for charmonium. New results from the SESAM collabo…
We present a calculation of the heavy quark's self energy in moving NRQCD to one-loop in perturbation theory. Results for the energy shift and external momentum renormalisation are discussed and compared with non-perturbative results. We show that the momentum renormalisation is small, which is the result of a remnant of re-parameterisation invariance on the lattice.
One-loop matching of heavy-light currents is carried out for a highly improved lattice action, including the effects of mixings with dimension 4 O(1/M) and O(a) operators. We use the NRQCD action for heavy quarks, the Asqtad improved naive action for light quarks, and the Symanzik improved glue action. These results are being used in recent heavy meson decay constant and semileptonic form factor calculations on the MILC dynamical configurations.
We match the continuum and lattice axial vector and vector currents at one loop in perturbation theory. For the heavy quarks we use the nonrelativistic QCD (NRQCD) action and for the light quarks the Highly Improved Staggered Quark (HISQ) action. We present results for both massless and massive HISQ quarks and as part of the matching procedure we include a discussion of the one loop HISQ renormalisation parameters.
We give a progress report on studies of B_s and B_d mixing with valence NRQCD b quarks and asqtad light quarks on the MILC configurations including the effect of 2+1 flavours of sea quarks. We explore methods for reducing statistical and systematic errors in the ratio ξ= f_{B_s}\sqrt{B_{B_s}}/f_{B_d}\sqrt{B_{B_d}}.
We present a perturbative calculation of the renormalization constants for the $ΔB=2$ four-quark operators, which is needed to evaluate the bag parameters $B_B$ and $B_S$ in lattice QCD. The one-loop coefficients are calculated for the $O(1/M)$ NRQCD heavy quark action and the $O(a)$-improved Wilson action for light quark. Using these coefficients, which remove $O(α_s/aM)$ error, we reanalyze our previous calculation of the bag parameters.
Using the lattice NRQCD action for heavy quark, we calculate the heavy quark expansion parameters $μ_π^2$ and $μ_G^2$ for heavy-light mesons and heavy-light-light baryons. The results are compared with the mass differences among heavy hadrons to test the validity of HQET relations on the lattice.
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 HPQCD collaboration has used radiatively-improved NonRelativistic QCD (NRQCD) for $b$ quarks in bottomonium to determine the decay rate of $Υ$ and $Υ^\prime$ mesons to leptons in lattice QCD. Using time-moments of vector bottomonium current-current correlators, we are also able to determine the $b$ quark mass in the $\overline{\mathrm{MS}}$ scheme. We use the same NRQCD $b$ quarks and Highly Improved Staggered Quark (HISQ) light quarks -- with masses down to their physical values -- to give a complete picture of heavy-light meson decay constants including those for vector mesons. We also s…
We present a quenched lattice calculation of heavy-light meson decay constants, using non-relativistic (NRQCD) heavy quarks in the mass region of the $b$ quark and heavier, and clover-improved light quarks. The NRQCD Hamiltonian and the heavy-light current include the corrections at first order in the expansion in the inverse heavy quark mass. We study the dependence of the decay constants on the heavy meson mass $M$, for light quarks with the tree level ($c_{SW}$ = 1), as well as the tadpole improved clover coefficient. We compare decay constants from NRQCD with results from clover ($c_{SW}=1…
We present new values for the $\bar{MS}$ masses of $b$ and $c$ quarks based on lattice NRQCD simulations of the $Υ(b\bar{b})$ and $ψ(c\bar{c})$ systems. These include three measurements of the $b$ mass based on quenched simulations with lattice spacings ranging from 0.05fm to 0.15fm, which we find to be largely independent of lattice spacing. In addition, we find a consistent value from an unquenched simulation at 0.08fm.
We construct $bb\bar{u}\bar{d}$ states on lattice using NRQCD action for bottom and HISQ action for the light up/down quarks. The NRQCD-HISQ tetraquark operators are constructed for "bound" $[bb][\bar{u}\bar{d}]$ and "molecular" $[b\bar{u}] [b\bar{d}]$ states. Corresponding to these different operators, two different appropriately tuned light quark masses are needed to obtain the desired spectra. We explain this requirement of different $m_{u/d}$ in the light of relativised quark model involving Hartree-Fock calculation. The mass spectra of double bottom tetraquark states are obtained on MILC …
Lattice NRQCD has proven successful in describing the physics of the upsilon system and B-mesons, though some concerns arise when it is used in simulations of charm quarks. It is certainly possible that the NRQCD expansion is not converging fast enough at this scale. We present some preliminary results on the low-mass breakdown of NRQCD, in particular the behaviour of heavy quarkonium and heavy-light meson spectra as the bare heavy quark mass is decreased well below 1, with the aim of understanding more about the manifestation of this breakdown.
We present the first application of the background field method to Non-Relativistic QCD (NRQCD) on the lattice in order to determine the one-loop radiative corrections to the coefficients of the NRQCD action in a manifestly gauge-covariant manner. The coefficient of the $σ\cdot B$ term in the NRQCD action is computed at the one-loop level; the resulting shift of the hyperfine splitting of bottomonium is found to bring the lattice predictions in line with experiment.
We report results on semileptonic $B\toπl\barν$ decay form factors near $q^2_{\rm max}$ using NRQCD heavy quark and clover light quark actions and currents improved through $O(αa)$. An inconsistency with the soft pion relation $f^0(q^2_{\rm max})= f_B/f_π$ found in a previous work is confirmed, and a possible solution with nonperturbative renormalization is discussed. We find that $f^+(q^2)$ is well described by the $B^*$ pole near $q^2_{\rm max}$, and its $1/M_B$ scaling is also consistent with the prediction of the pole dominance model.
We present preliminary results from our study of the heavy-light spectrum and decay constants. For the heavy quark, we use NRQCD at various masses around and above the $b$ quark mass. For the first time, the heavy quark action and the heavy-light current consistently include corrections at second order in the non-relativistic expansion, as well as the leading finite $a$ corrections. The light quarks are simulated using a tadpole-improved Clover action at various masses in the strange and $c$ quark region.
We calculate perturbative renormalization constants for the ΔB=2 four-quark operators in lattice NRQCD. Continuum operators \bar{b}γ_μ(1-γ_5)q~ \bar{b}γ_μ(1-γ_5)q and \bar{b}(1-γ_5)q~\bar{b}(1-γ_5)q, which are necessary in evaluating the mass and width differences in $B^0_{d(s)}-\bar{B}^0_{d(s)}$ systems, are matched at one-loop with corresponding lattice operators constructed from the NRQCD heavy quarks and the ${\cal O}(a)$-improved light quarks. Using these perturbative coefficients, we also reanalyse our previous simulation results for the matrix elements of the above operators. Our new re…
We report on a study of B mesons on N_f = 2 full QCD configurations using an RG-improved gauge action, NRQCD heavy quark action and tadpole-improved clover light quark action. Results on the heavy-light spectrum and the decay constants from 16^3x32 lattices at a^{-1} ~ 1.5 GeV are presented, and compared with quenched results obtained with the same action combination at matching lattice spacings.
Results for the spectrum of S and P-wave charmed mesons are obtained in the quenched approximation from a tadpole-improved anisotropic gauge field action and a D234 quark action. This is compared to the spectrum obtained from an NRQCD charm quark and a D234 light antiquark. NRQCD results for bottom mesons are also discussed.
To study the in-medium modification of quarkonium properties, charmonium correlators at $140.4 (β=6.664) \le T \le 221 (β= 7.280)$ (MeV) are calculated using the NRQCD formalism on $48^3 \times 12$ gauge configurations with dynamical $N_f = 2 + 1$ flavors of Highly Improved Staggered Quarks (HISQ). To determine the "zero energy shift" for these lattices, we perform a fine zero temperature scan ($β=6.664, 6.740, 6.800, 6.880, 6.950, 7.030, 7.150$ and $7.280$). We find that the temperature dependence of charmonium correlators is stronger than the temperature dependence of bottomonium correlators…
We construct the S-wave part of the electromagnetic vector annihilation current to $O(α_s v^2)$, where $v$ is the non-relativistic quark velocity, for heavy quarks whose dynamics are described by the NRQCD action on the lattice. The NRQCD vector current for $Q\bar{Q}$ annihilation is expressed as a linear combination of lattice operators with quantum numbers L=0, $J^P=1^-$, and the coefficients are determined by matching to the corresponding continuum current in QCD to$O(v^2)$ at one-loop. The annihilation channel gives a complex amplitude with Coulomb-exchange and infrared singularities, maki…
We present a lattice QCD calculation of the heavy quark expansion parameters $μ_π^2$ and $μ_G^2$ for heavy-light mesons and heavy-light-light baryons. The calculation is carried out on a 20$^3\times$48 lattice at $β$ = 6.0 in the quenched approximation, using the lattice NRQCD action for heavy quarks. We obtain the parameters $μ_π^2$ and $μ_G^2$ in two different methods: a direct calculation of the matrix elements and an indirect calculation through the mass spectrum, and confirm that the both methods give consistent results. We also discuss an application to the lifetime ratios.
We give results for B, Bs, Bc and bottomonium spectroscopy using NRQCD heavy quarks and HISQ valence and sea quarks. Five MILC ensembles of gluon configurations with three values of the lattice spacing and m(light)/m(strange) values down to 0.1 are used that include 2+1+1 flavours of sea quark. Systematic errors in the NRQCD action are improved through the radiative correction of the coefficients of terms at v^4. Improved results for S-wave and P-wave bottomonium states are discussed as well as a prediction for the full D-wave spectrum. Preliminary results for the ground state B meson masses a…
Semileptonic, B --> pi, l nubar, decays are studied on quenched anisotropic lattices using tree-level tadpole improved Symanzik glue, NRQCD heavy quark and D234 light quark actions. Constrained fitting methods are applied to extract groundstate contributions to two-point and three-point correlators. We agree with previous lattice determinations of the form factors. The major source of systematic error here, as in previous work, comes from the chiral extrapolation to the physical pion mass. Future calculations must work at lighter quark masses to resolve this.
We discuss preliminaries of a calculation of the form factors for the semileptonic decays B -> pi lv, B_s -> K lv, and B -> K ll. We simulate with NRQCD heavy and HISQ light valence quarks on the MILC 2+1 dynamical asqtad configurations. The form factors are calculated over a range of momentum transfer to allow determination of their shape and the extraction of |V_ub|. Additionally, we are calculating ratios of these form factors to those for the unphysical decay B_s -> eta_s. We are studying the possibility of combining these precisely determined ratios with future calculations of B_s ->eta_s…
We present the status of our ongoing calculation of the zero-recoil form factor for the semileptonic decay $\bar{B}^0\rightarrow D^{*+}l^-\barν$ using lattice QCD with 2+1+1 flavours of highly improved staggered quarks in the sea (the MILC HISQ configurations) and using non-relativistic QCD for the bottom quark. We combine our result for $ F(1)$ with the latest HFAG average of $η_{EW} F(1)|V_{cb}|$ to get a preliminary value for $|V_{cb}|$.
Using NRQCD b quarks and HISQ light, strange and charm quarks we have calculated B meson masses and B^*-B splittings. We quote results for a range of lattice spacings and sea quark masses, enabling controlled extrapolation to the physical point. Since the $b$ quark masses and lattice spacing are fixed from the Υand other meson masses, this allows accurate, parameter-free tests of B, B_s, and B_c masses against experiment. We can also predict the mass of the B^*_c meson.
The temporal and spatial components of the heavy-light vector current and the spatial components of the axial current are expressed in terms of lattice-regulated operators suitable for simulations of B and D mesons. The currents are constructed by matching the appropriate scattering amplitudes in continuum QCD and a lattice model to one-loop order in perturbation theory. In the lattice theory, the heavy quarks are treated using the nonrelativistic (NRQCD) formulation and the light quarks are described by the tadpole-improved clover action. The light quarks are treated as massless. Our currents…
We compare mean-link and average plaquette tadpole renormalization schemes in the context of the quarkonium hyperfine splittings in lattice NRQCD. Simulations are done for the three quarkonium systems $c\bar c$, $b\bar c$, and $b\bar b$. The hyperfine splittings are computed both at leading and at next-to-leading order in the relativistic expansion. Results are obtained at a large number of lattice spacings. A number of features emerge, all of which favor tadpole renormalization using mean links. This includes much better scaling of the hyperfine splittings in the three quarkonium systems. We …
We calculate the heavy-light meson decay constant using lattice NRQCD action for the heavy quark and Wilson quark action for the light quark over a wide range in the heavy quark mass. Simulations are carried out on a 16^3 x 32 lattice with 120 quenched gauge configurations generated with the plaquette action at beta=5.8. For the heavy quark part of the calculation, two sets of lattice NRQCD action and current operator are employed. The first set includes terms up to O(1/m_Q) both in the action and the current operator, and the second set up to O(1/m_Q^2), where m_Q is the bare mass of the heav…
Preliminary results on spectrum and decay constant of $B$ mesons from a quenched simulation at $β= 6.0$ on an $16^3\times48$ lattice are discussed. The heavy quark has been implemented using both an NRQCD and the static formulation, the light one with a clover improved Wilson formulation. Both the NRQCD Hamiltonian and the heavy-light current consistently include terms of $O(1/M_{Q})$, the inverse heavy quark mass.
We present a lattice investigation, partially including the effects of dynamical quarks, of the heavy-light mesons using NRQCD for the heavy quark and the Wilson action for the light quark. We performed an extensive calculation of the spectrum employing a multi-state, multi-exponential fitting analysis which enabled us to extract the $2S{-}1S$ splitting as well as the $^1P_1{-}\bar{S}$ and hyperfine splittings. The Wilson action introduces a large systematic error into the calculation, and within this uncertainty we obtain agreement with experiment. We performed a comprehensive calculation of …
We apply the background field (BF) method to Non-Relativistic QCD (NRQCD) on the lattice in order to determine the one-loop radiative corrections to the coefficients of the NRQCD action in a manifestly gauge-covariant manner by matching the NRQCD prediction for particular on-shell processes with those of relativistic continuum QCD. We explain how the BF method is implemented in automated perturbation theory and discuss the technique for matching the relativistic and non-relativistic theories. We compute the one-loop radiative corrections to the sigma.B and Darwin terms for the NRQCD action cur…
Semileptonic B decays are studied on quenched anisotropic lattices using Symanzik improved glue, NRQCD heavy quark and D234 light quark actions. We employ constrained fits to extract ground state contributions to two- and three-point correlators. Results for the B --> pi, l nubar decay form factors are compared with previous lattice results. We find that our systematic errors (excluding quenching errors) are dominated by chiral extrapolation uncertainties.
We present results for the mass of the $b$ quark in the $\bar{MS}$ scheme obtained by calculating the binding energy of the $B$ meson in the static limit. The self energy of a static quark, $E_0^\infty$ needed for this purpose, is now known to $O(α^3)$ in the quenched approximation. We find a {\it preliminary} value of $\bar{m_b}(\bar{m_b})=4.34(7)$ GeV at $n_f=0$. The error is dominated by the remaining uncertainty in $E_0^\infty$. In addition, using $E_0^\infty$ at $O(α^2)$, we estimate that the quark mass is reduced by approximately 70 MeV when two flavours of dynamical quarks are introduce…
We present {\it preliminary} results for the decay constants of heavy-light mesons using NRQCD heavy and tadpole improved Clover light quarks. A comparison is made with data obtained using Wilson light quarks. We present an analysis of the 1/M corrections to the decay constants in the static limit and compare with the predictions of HQET.
We construct the S-wave part of the electromagnetic vector annihilation current to O(alpha_s v^2)$ on the lattice for heavy quarks whose dynamics are described by the NRQCD action, where v is the non-relativistic quark velocity. The lattice vector current for QQbar annihilation is expressed as a linear combination of lattice operators with quantum numbers L=0, J^P=1^-, and the coefficients are determined by matching this lattice current to the corresponding continuum current in QCD to O(v^2) to one-loop. The annihilation channel gives a complex amplitude and a proper choice for the contours of…
Heavy-light mesons can be studied using the 1/M expansion of NRQCD, provided the heavy quark mass is sufficiently large. Calculations of the S-wave charmed meson masses from a classically and tadpole-improved action are presented. A comparison of O(1/M), O(1/M^2) and O(1/M^3) results allows convergence of the expansion to be discussed. It is shown that the form of discretized heavy quark propagation must be chosen carefully.
The behavior of bottomonium state correlators at non-zero temperature, $140.4 (β= 6.664) \le T \le 221 (β= 7.280)$ (MeV), where the transition temperature is $154(9)$ (MeV), is studied, using lattice NRQCD on $48^3 \times 12$ HotQCD HiSQ action configurations with light dynamical $N_f = 2 + 1$ ($m_{u,s}/m_s = 0.05$) staggered quarks. In order to understand finite temperature effects on quarkonium states, zero temperature behavior of bottomonium correlators is compared based on $32^4$ ($β= 6.664, 6.800$ and $6.950$) and $48^3 \times 64$ ($β= 7.280)$ lattices. We find that temperature effects on…
We present a quenched calculation of the form factors of the semileptonic weak decay $B \to πl \barν$ with $O(1/m_Q)$ NRQCD heavy quark and Wilson light quark on a $16^3 \times 32$ lattice at $β=5.8$. The form factors are evaluated at six heavy quark masses, in the range of $m_Q \sim 1.5-8$ GeV. $1/m_Q$ dependence of matrix elements are investigated and compared with HQET predictions. We observe clear signal for the form factors near $q^2_{max}$, even at the $b$-quark mass range. $f^0(q^2_{max})$ is compared with $f_B/f_π$ based on the soft pion theorem and significant difference is observed.
The temporal component of the heavy-light axial vector current is constructed to one-loop order in perturbation theory and to order 1/M, where M is the heavy quark mass, in terms of operators suitable for use in lattice simulations of B and D mesons. The O(a)-improved clover action is used for the massless light quark, where a is the lattice spacing, and propagation of the heavy quark is described by a nonrelativistic lattice action.
This talk summarizes the quenched calculation of $f_B$ and $f_{B_s}$ presented in hep-lat/9801038. The heavy quark is simulated using an $O(1/M^2)$ improved NRQCD action, and the tadpole improved clover action is used for the light quarks. The axial current includes the $O(1/M)$ corrections in one-loop perturbation theory and the $O(1/M^2)$ ones at tree-level. We discuss the various systematic effects and consistency checks made in the calculation.
Recent results for B meson decay constants with NRQCD b-quarks and clover light quarks are discussed. Perturbative matching factors through O($α/M$) are now available and incorporated into the analyses. An O($αa$) improvement term to the heavy-light axial current is identified and included. The slope of $f_{PS}\sqrt{M_{PS}}$ versus $1/M_{PS}$ is significantly reduced by these corrections.
The spectrum of heavy-quark hybrids is studied in the leading Born-Oppenheimer (LBO) approximation and using leading-order NRQCD simulations with an improved gluon action on anisotropic lattices. The masses of four hybrid states are obtained from our simulations for lattice spacings 0.1 fm and 0.2 fm and are compared to the LBO predictions obtained using previously-determined glue-excited static potentials. The consistency of results from the two approaches reveals a compelling physical picture for heavy-quark hybrid states.
The present status of lattice calculations of the B spectrum and f_B, using NRQCD for the b quark, is discussed.
Following the Non-Relativistic QCD approach we use a gauge invariant smearing method with factorization to measure the excitation energies for a heavy $Q\bar{Q}$ system on a $24^3\times 48$ lattice at $β=6.2$. The results come from averaging over an ensemble of 60 QCD configurations. In order to enhance the signal from each configuration we use wall sources for quark propagators. The quark Hamiltonian contains only the simplest non-relativistic kinetic energy term. The results are listed for a range of bare quark masses. The mass splittings are insensitive to this variable though there are a s…
We present a progress report on new calculations of B and B_s meson decay constants employing NRQCD heavy and HISQ light valence quarks and using MILC N_f = 2+1 AsqTad lattices. Bare quark masses have been retuned in accord with HPQCD's new r_1 scale. We find significant reductions in discretization effects compared to previous calculations with AsqTad light valence quarks. Matching of the NRQCD/HISQ heavy-light axial vector current is carried out at one-loop order including all relevant dimension 4 current corrections.
We present a determination of the b-quark mass accurate through O(α_s^2) in perturbation theory and including partial contributions at O(α_s^3). Nonperturbative input comes from the calculation of the Upsilon and B_s energies in lattice QCD including the effect of u, d and s sea quarks. We use an improved NRQCD action for the b-quark. This is combined with the heavy quark energy shift in NRQCD determined using a mixed approach of high-beta simulation and automated lattice perturbation theory. Comparison with experiment enables the quark mass to be extracted: in the MS bar scheme we find m_b(m_…
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