Heavy-light Decay Constants Research Articles

Mini-review on QCD spectral sum rules

Taking the example of the most popular and well-established Borel / Laplace / Exponential sum rule (LSR), I shortly review some of its recent applications in hadron physics namely the estimates of non-perturbative condensates, the determination of the light and heavy quark masses, the extraction of the heavy-light decay constants, the estimates of charmonium and bottomium molecule masses and the properties of scalar gluonium. In addition to the standard τ (sum rule variable) and tc (QCD continuum threshold) stablity criteria, I introduce a new stability criterion versus the arbitrary QCD subtraction point μ for extracting the optimal results when radiative QCD corrections are included. Future improvements on further uses of QCD spectral sum rules (QSSR) are commented.

HEAVY AND LIGHT QUARKS WITH LATTICE CHIRAL FERMIONS

The feasibility of using lattice chiral fermions which are free of O(a) errors for both the heavy and light quarks is examined. The fact that the effective quark propagators in these fermions have the same form as that in the continuum with the quark mass being only an additive parameter to a chirally symmetric anti-Hermitian Dirac operator is highlighted. This implies that there is no distinction between the heavy and light quarks and no mass dependent tuning of the action or operators as long as the discretization error O(m2a2) is negligible. Using the overlap fermion, we find that the O(m2a2) (and O(ma2)) errors in the dispersion relations of the pseudoscalar and vector mesons and the renormalization of the axial-vector current and scalar density are small. This suggests that the applicable range of ma may be extended to ~0.56 with only 5% error, which is a factor of ~2.4 larger than the corresponding range of the improved Wilson action. We show that the generalized Gell–Mann–Oakes–Renner relation with unequal masses can be utilized to determine the finite ma corrections in the renormalization of the matrix elements for the heavy-light decay constants and semileptonic decay constants of the B/D meson.

Lattice calculation of SU(3) flavor breaking ratios inB0−B¯0mixing

We present an unquenched lattice calculation for the SU(3) flavor breaking ratios of the heavy-light decay constants and the {delta}B=2 matrix elements. The calculation was performed on 16{sup 3}x32 lattices with two dynamical flavors of domain-wall quarks and inverse lattice spacing 1/a=1.69(5) GeV. Heavy quarks were implemented using an improved lattice formulation of the static approximation. In the infinite heavy-quark mass limit we obtain f{sub B{sub s}}/f{sub B{sub d}}=1.29(4)(6), B{sub B{sub s}}/B{sub B{sub d}}=1.06(6)(4), {xi}=1.33(8)(8) where the first error is statistical and the second systematic.

Erratum: Application of heavy-quark effective theory to lattice QCD. II. Radiative corrections to heavy-light currents [Phys. Rev. D65, 094513 (2002)

We apply heavy-quark effective theory to separate long- and short-distance effects of heavy quarks in lattice gauge theory. In this approach, the inverse heavy-quark mass and the lattice spacing are treated as short distances, and their effects are lumped into short-distance coefficients. We show how to use this formalism to match lattice gauge theory to continuum QCD, order by order in the heavy-quark expansion. In this paper, we focus on heavy-light currents. In particular, we obtain one-loop results for the matching factors of lattice currents, needed for heavy-quark phenomenology, such as the calculation of heavy-light decay constants, and heavy-to-light transition form factors. Results for the Brodsky-Lepage-Mackenzie scale $q^*$ are also given.

Heavy-light decay constants using clover valence quarks and three flavors of dynamical improved staggered quarks

Starting in 2001, the MILC Collaboration began a large scale calculation of heavy-light meson decay constants using clover valence quarks on esembles of three flavor configurations. For the coarse configurations, with a = 0.12 fm , eight combinations of dynamical light and strange quarks have been analyzed. For the fine configurations, with a = 0.09 fm , three combinations of quark masses are studied. Since we last reported on this calculation, statistics have been increased on the fine ensembles, and, more importantly, a preliminary value fir the perturbative renormalization of the axial-vector current has become available. Thus, results for f B , f B s , f D and f D s can, in principle, be calculated in MeV, in addition to decay-constant ratios that were calculated previously.

Heavy meson chiral perturbation theory in finite volume

We study finite volume effects in heavy quark systems in the framework of heavy meson chiral perturbation theory for full, quenched, and partially quenched QCD. A novel feature of this investigation is the role played by the scales ${\ensuremath{\Delta}}_{*}$ and ${\ensuremath{\delta}}_{s},$ where ${\ensuremath{\Delta}}_{*}$ is the mass difference between the heavy-light vector and pseudoscalar mesons of the same quark content, and ${\ensuremath{\delta}}_{s}$ is the mass difference due to light flavor $\mathrm{SU}(3)$ breaking. The primary conclusion of this work is that finite volume effects arising from the propagation of Goldstone particles in the effective theory can be altered by the presence of these scales. Since ${\ensuremath{\Delta}}_{*}$ varies significantly with the heavy quark mass, these volume effects can be amplified in both heavy and light quark mass extrapolations (interpolations). As an explicit example, we present results for B parameters of neutral B meson mixing matrix elements and heavy-light decay constants to one-loop order in finite volume heavy meson chiral perturbation theory for full, quenched, and ${N}_{f}=2+1$ partially quenched QCD. Our calculation shows that for high-precision determinations of the phenomenologically interesting $\mathrm{SU}(3)$ breaking ratios, finite volume effects are significant in quenched and not negligible in partially quenched QCD, although they are generally small in full QCD.

Heavy-light decay constants from the step scaling method

We discuss results for the heavy-light decay constants in the continuum limit of quenched lattice QCD from finite size scaling techniques. We disentangle the simultaneous presence of the different energy scales characterizing heavy-light physics by first performing simulations at the unphysical volume L_0=0.4 fm, and then evolving the results towards the infinite volume. We find f_{Bs}= 192(6)(4) MeV and f_{Ds}=240(5)(5) MeV. The approach has been developed by the APE group at the University of Rome ``Tor Vergata''.

Heavy-light decay constants for B and D mesons in nf = 2 unquenched QCD in Fermilab formalism

Abstract We report our calculation of the heavy-light decay constants f B and f D on a 20 3 × 48 lattice at β = 5.2 with n f = 2 sea quarks by the fully 0(a)-improved Wilson fermion and heavy quarks in Fermilab formalism. We find that the B meson decay constants are consistent with those obtained with the NRQCD formalism. It is shown that the quark mass dependence almost cancels in the B/D ratio of the decay constant so that the systematic errors in the chiral extrapolation can be reduced. Taking the Grinstein ratio, remaining uncertainties from the perturbation and discretization also cancel to give a precise prediction of ( f B s f B d ) ( f D s f D d ) of 1% accuracy.

Heavy–light decay constants in the continuum limit of quenched lattice QCD

We compute the decay constants for the heavy–light pseudoscalar mesons in the quenched approximation and continuum limit of lattice QCD. Within the Schrödinger functional framework, we make use of the step scaling method, which has been previously introduced in order to deal with the two scale problem represented by the coexistence of a light and a heavy quark. The continuum extrapolation gives us a value f B s =192(6)(4) MeV for the B s meson decay constant and f D s =240(5)(5) MeV for the D s meson.

Heavy quark systems in anisotropic lattice QCD

We examine whether the O( a) improved quark action on anisotropic lattices can be used as a framework for the heavy quark, which enables precision computation of matrix elements of heavy-light mesons. To this end, it is crucial to verify that a mass independent and nonperturbative tuning of the parameters is possible. As a first step, we observe the dispersion relation of heavy-light mesons on a quenched lattice using the action which is nonperturbatively tuned only for the leading terms. We also apply the action to a calculation of heavy-light decay constants in the charm quark mass region.

Chiral extrapolation of light-light and heavy-light decay constants in unquenched QCD

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.

Precise determination of the Grinstein ratio of heavy-light decay constant in unquenched QCD

We study the chiral behavior of the ratio of heavy-light decay constants on unquenched lattices with two flavor dynamical quarks using the plaquette gauge action and the nonperturbatively O(a)-improved Wilson fermion action at β = 5.2. The heavy quarks are described by the clover action and the NRQCD action. We find that the sea quark mass dependence of the decay constants largely cancels in the double ratio R 1 =f B s /f B d /f D s /f D d and the systematic error in the chiral limit can be drastically reduced. Our preliminary result with heavy clover is R 1 = 1.018 ± 0.006 ± 0.010, where the first and the second errors are the statistical and the systematics errors.

Heavy-light meson in anisotropic lattice QCD

We examine whether the O(a) improved quark action on anisotropic lattices can be used as a framework for the heavy quark, which enables precision computation of matrix elements of heavy-light mesons. To this end, it is crucial to verify that a mass independent and nonperturbative tuning of the parameters is possible. As a first step, we observe the dispersion relation of heavy-light mesons on a quenched lattice using the action which is non-perturbatively tuned only for the leading terms. On a lattice with the spatial cutoff a σ −1 ≅ 1.6 GeV and the anisotropy ξ = 4, the relativity relation holds within 2% accuracy in the quark mass region a σm Q ≤ 1.2 with the bare anisotropy parameter tuned for the massless quark. We also apply the action to a calculation of heavy-light decay constants in the charm quark mass region.

Lattice calculation of heavy-light decay constants with two flavors of dynamical quarks

We present results for ${f}_{B},$ ${f}_{{B}_{s}},$ ${f}_{D},$ ${f}_{{D}_{s}}$ and their ratios in the presence of two flavors of light sea quarks ${(N}_{f}=2).$ We use Wilson light valence quarks and Wilson and static heavy valence quarks; the sea quarks are simulated with staggered fermions. Additional quenched simulations with nonperturbatively improved clover fermions allow us to improve our control of the continuum extrapolation. For our central values the masses of the sea quarks are not extrapolated to the physical u, d masses; that is, the central values are ``partially quenched.'' A calculation using ``fat-link clover'' valence fermions is also discussed but is not included in our final results. We find, for example, ${f}_{B}{=190(7)(}_{\ensuremath{-}17}^{+24}{)(}_{\ensuremath{-}2}^{+11}{)(}_{\ensuremath{-}0}^{+8})\mathrm{MeV},$ ${f}_{{B}_{s}}{/f}_{B}{=1.16(1)(2)(2)(}_{\ensuremath{-}0}^{+4}),$ ${f}_{{D}_{s}}{=241(5)(}_{\ensuremath{-}26}^{+27}{)(}_{\ensuremath{-}4}^{+9}{)(}_{\ensuremath{-}0}^{+5})\mathrm{MeV},$ and ${f}_{B}{/f}_{{D}_{s}}{=0.79(2)(}_{\ensuremath{-}4}^{+5}{)(3)(}_{\ensuremath{-}0}^{+5}),$ where in each case the first error is statistical and the remaining three are systematic: the error within the partially quenched ${N}_{f}=2$ approximation, the error due to the missing strange sea quark and to partial quenching, and an estimate of the effects of chiral logarithms at small quark mass. The last error, though quite significant in decay constant ratios, appears to be smaller than has been recently suggested by Kronfeld and Ryan, and Yamada. We emphasize, however, that as in other lattice computations to date, the lattice $u,d$ quark masses are not very light and chiral log effects may not be fully under control.

Application of heavy-quark effective theory to lattice QCD. II. Radiative corrections to heavy-light currents

We apply heavy-quark effective theory to separate long- and short-distance effects of heavy quarks in lattice gauge theory. In this approach, the inverse heavy-quark mass and the lattice spacing are treated as short distances, and their effects are lumped into short-distance coefficients. We show how to use this formalism to match lattice gauge theory to continuum QCD, order by order in the heavy-quark expansion. In this paper, we focus on heavy-light currents. In particular, we obtain one-loop results for the matching factors of lattice currents, needed for heavy-quark phenomenology, such as the calculation of heavy-light decay constants, and heavy-to-light transition form factors. Results for the Brodsky-Lepage-Mackenzie scale ${q}^{*}$ are also given.

Heavy-light decay constants with three dynamical flavors

We present preliminary results for the heavy-light leptonic decay constants in the presence of three light dynamical flavors. We generate dynamical configurations with improved staggered and gauge actions and analyze them for heavy-light physics with tadpole improved clover valence quarks. When the scale is set by m ρ, we find an increase of ≈23% in f B with three dynamical flavors over the quenched case. Discretization errors appear to be small (≲3%) in the quenched case but have not yet been measured in the dynamical case.

Heavy-light decay constants on the lattice

We present results for the leptonic decays of heavy-light mesons in the quenched approximation and a preliminary result for f D s with dynamical fermions for N f = 2. We examine the systematic effects of extrapolating the decay constants from the charm to the bottom quark mass, and find this extrapolation to be under control. We present a preliminary result for f N f=2 D s and compare to f N f=0 D s matched to have the same lattice spacing set by the Sommer scale, r 0. We find no significant difference.

B meson B-parameters and the decay constant in two-flavor dynamical QCD

We present a two-flavor dynamical QCD calculation of the B meson B parameters and decay constant. We use NRQCD for heavy quark and the nonperturbatively O( a)-improved Wilson action for light quark at β = 5.2 on a 20 3 × 48 lattice. We confirm that the sea quark effect increases the heavy-light decay constant, while estimate of its magnitude depends significantly on the fitting form in the chiral extrapolation. For the B parameters, on the other hand, we do not find a significant sea quark effect. The chiral extrapolation with logarithmic term is examined for both quantities and compared with the prediction of ChPT.

Scale determination using the static potential with two dynamical quark flavors

We study the static potential using gauge configurations that include the effects of two flavors of dynamical Kogut-Susskind quarks. The configurations, generated by the MILC collaboration, and used to study the spectrum and heavy-light decay constants, cover a range 5.3 ⪯ 6 g 2 ⪯ 5.6 . There are at least four quark masses for each coupling studied. Determination of r 0 from the potential can be used to set a scale. This alternative scale is useful to study systematic errors on the spectrum and decay constants.

Heavy-light decay constants with dynamical gauge configurations and wilson or improved valence quark actions

We describe a calculation of heavy-light decay constants including virtual quark loop effects. We have generated dynamical gauge configurations at three β values using two flavors of Kogut-Susskind quarks with a range of masses. These are analyzed with a Wilson valence quark action. Preliminary results based on a “fat-link” clover valence quark action are also reported. Results from the two methods differ by 30 to 50 MeV, which is presumably due to significant — but as yet unobserved — lattice spacing dependence in one or both of the approaches.