Leptonic Decay Constants Research Articles

A numerical study of partially twisted boundary conditions

We investigate the use of partially twisted boundary conditions in a lattice simulation with two degenerate flavours of improved Wilson sea quarks. The use of twisted boundary conditions on a cubic volume (L3) gives access to components of hadronic momenta other than integer multiples of 2π/L. Partial twisting avoids the need for new gluon configurations for every choice of momentum, while, as recently demonstrated, keeping the finite-volume errors exponentially small for the physical quantities investigated in this letter. In this study we focus on the spectrum of pseudo scalar and vector mesons, on their leptonic decay constants and on ZP, the matrix element of the pseudo scalar density between the pseudo scalar meson and the vacuum. The results confirm the momentum shift imposed by these boundary conditions and in addition demonstrate that they do not introduce any appreciable noise. We therefore advocate the use of partially twisted boundary conditions in applications where good momentum resolution is necessary.

LEPTONIC DECAYS OF VECTOR MESONS

In this paper, the general structure of leptonic decay constants of vector mesons is evaluated in the framework of the Bethe–Salpeter equation under the Covariant Instantaneous Ansatz (CIA), which is a Lorentz-invariant generalization of Instantaneous Approximation (IA). The numerical values of fV in this CIA framework are on the low side in comparison to recent calculations of these quantities. However, the overall asymptotic behavior of fV is in conformity with QCD predictions.

ON THE COMPLEXION OF PSEUDOSCALAR MESONS

A strongly momentum-dependent dressed-quark mass function is basic to QCD. It is central to the appearance of a constituent-quark mass-scale and an existential prerequisite for Goldstone modes. Dyson-Schwinger equation (DSEs) studies have long emphasised this importance, and have proved that QCD's Goldstone modes are the only pseudoscalar mesons to possess a nonzero leptonic decay constant in the chiral limit when chiral symmetry is dynamically broken, while the decay constants of their radial excitations vanish. Such features are readily illustrated using a rainbow-ladder truncation of the DSEs. In this connection we find (in GeV): fηc(1S)=0.233, mηc(2S)=3.42; and support for interpreting η(1295), η(1470) as the first radial excitations of η(548), η′(958), respectively, and K(1460) as the first radial excitation of the kaon. Moreover, such radial excitations have electromagnetic diameters greater than 2 fm. This exceeds the spatial length of lattices used typically in contemporary lattice-QCD.

Leptonic decay constants [formula omitted] and [formula omitted] in three flavor lattice QCD

We determine the leptonic decay constants f D s and f D in three flavor unquenched lattice QCD. We use O ( a 2 ) -improved sraggered light quarks and O ( a ) -improved charm quarks in the Fermilab heavy quark formalism. Our preliminary results, based upon an analysis at a single lattice spacing, are f D s = 263 −9 +5 ± 24 MeV and f D = 225 −13 +11 ± 21 MeV . In each case, the first reported error is statistical while the second is the combined systematic uncertainty.

Pseudoscalar and vector mesons as qq̄ bound states

Two-body bound states such as mesons are described by solutions of the Bethe-Salpeter equation. We discuss recent results for the pseudoscalar and vector meson masses and leptonic decay constants, ranging from pions up to cc̄ bound states. Our results are in good agreement with data. Essential in these calculation is a momentum-dependent quark mass function, which evolves from a constituent-quark mass in the infrared region to a currentquark mass in the perturbative region. In addition to the mass spectrum, we review the electromagnetic form factors of the light mesons. Electromagnetic current conservation is manifest and the influence of intermediate vector mesons is incorporated self-consistently. The results for the pion form factor are in excellent agreement with experiment.

Pseudoscalar meson radial excitations

Goldstone modes are the only pseudoscalar mesons to possess a nonzero leptonic decay constant in the chiral limit when chiral symmetry is dynamically broken. The decay constants of their radial excitations vanish. These features and aspects of their impact on the meson spectrum are illustrated using a manifestly covariant and symmetry preserving model of the kernels in the gap and Bethe-Salpeter equations.

Correspondence between QCD sum rules and constituent quark models

We compare two widely used approaches to the description of hadron properties: QCD sum rules and constituent quark models. Making use of the dispersion formulation of the quark model, we show that both approaches lead to similar spectral representations for hadron observables with an important difference that quark model is based on Feynman diagrams with massive quarks, whereas QCD sum rules are based on the same Feynman diagrams for current quarks with the additional condensate contributions for light quarks and gluons. We give arguments for a similarity of the smearing function in sum rules and the hadron wave function of the quark model. Analyzing the sum rule for the leptonic decay constant of the heavy pseudoscalar meson containing a light $u$ or $s$ quark, we find that the quark condensates at the chiral symmetry-breaking scale $\mu_\chi\simeq 1$ GeV, $<\bar u u > = - (230 \pm 15 {\rm MeV})^3$ and $<\bar s s > = - (220 \pm 15 {\rm MeV})^3$ correspond to constituent quark masses $m_u\simeq 220$ MeV and $m_s \simeq 350$ MeV, respectively. We also obtain the running of the quark model parameters above the chiral scale $\mu_\chi$. The observed correspondence between constituent quark models and QCD sum rules allows a deeper understanding of both methods and their parameters. It also provides a QCD basis for constituent quark models, extending their applicability above the scale of chiral symmetry breaking.

Bs and Ds decay constants in three-flavor lattice QCD.

Capitalizing on recent advances in lattice QCD, we present a calculation of the leptonic decay constants f(B(s)) and f(D(s)) that includes effects of one strange sea quark and two light sea quarks via an improved staggered action. By shedding the quenched approximation and the associated lattice scale uncertainty, lattice QCD greatly increases its predictive power. Nonrelativistic QCD is used to simulate heavy quarks with masses between 1.5m(c) and m(b). We arrive at the following results: f(B(s))=260+/-7+/-26+/-8+/-5 and f(D(s))=290+/-20+/-29+/-29+/-6 MeV. The first quoted error is the statistical uncertainty, and the rest estimate the sizes of higher order terms neglected in this calculation. All of these uncertainties are systematically improvable by including another order in the weak coupling expansion, the nonrelativistic expansion, or the Symanzik improvement program.

B(0)-B(0) mixing in unquenched lattice QCD.

We present an unquenched lattice calculation for the B(0)-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 O(a)-improved Wilson fermion action and heavy quarks described by nonrelativistic QCD. 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 constant, whereas it is small for the B parameters. We obtain f(B(d))=191(10)(+12-22) MeV, f(B(s))/f(B(d))=1.13(3)(+13-2), B(B(d))(m(b))=0.836(27)(+56-62), B(B(s))/B(B(d))=1.017(16)(+56-17), and xi=1.14(3)(+13-2), where the first error is statistical, and the second is systematic, including uncertainties due to chiral extrapolation, finite lattice spacing, heavy quark expansion, and perturbative operator matching.

Pseudoscalar decay constants in staggered chiral perturbation theory

In a continuation of an ongoing program, we use staggered chiral perturbation theory to calculate the one-loop chiral logarithms and analytic terms in the pseudoscalar meson leptonic decay constants, $f_{\pi^+_5}$ and $f_{K^+_5}$. We consider the partially quenched, ``full QCD'' (with three dynamical flavors), and quenched cases.

A precise determination of the decay constant of the Ds-meson in quenched QCD

We present a lattice determination of the leptonic decay constant FDs of the Ds-meson using its mass and FK as experimental input. Setting the scale with FK=160 MeV, our final result is FDs=252(9) MeV. The error contains all uncertainties apart from the quenched approximation. Setting the scale with the nucleon mass instead leads to an decrease of 20(1) MeV of the leptonic decay constant.

B0−B0mixing in quenched lattice QCD

We present our results of lattice calculations of $B$ parameters, which parameterize $\Delta B$=2 transition amplitudes together with the leptonic decay constant. Calculations are made in the quenched approximation at $\beta$=5.7, 5.9, 6.0 and 6.1, using NRQCD action for heavy quark and the $O(a)$-improved Wilson action for light quark. The operators are perturbatively renormalized including the correction of $O(\alpha_s/(aM)^m)$ ($m\ge$0). We examine the scaling behavior of $B$ parameters, and discuss the systematic uncertainties based on the results with several different truncations of higher order terms in 1/M and $\alpha_s$ expansions. We find $B_{B_d}(m_b)=0.84(3)(5)$, $B_{B_s}/B_{B_d}=1.020(21)(^{+15}_{-16})(^{+5}_{-0})$ and $B_{S_s}(m_b)=0.85(1)(5)(^{+1}_{-0})$ in the quenched approximation. The errors represent statistical and systematic as well as the uncertainty in the determination of strange quark mass.

PHENOMENOLOGY FROM LATTICE QCD

I review two subject in which lattice simulations are making, or can make in the future, a significant contribution to particle physics phenomenology. The first subject is the evaluation of quantities which enter into the determination of the vertex A of the unitarity triangle from experimental measurements of decay rates and mixing amplitudes. These quantities include the form-factors for semileptonic B-decays, the leptonic decay constants of the B and Bs mesons and the B-parameters for [Formula: see text] and [Formula: see text] mixing and the corresponding parameter for [Formula: see text] mixing, BK. In the second part of this talk I will review the status and prospects for the evaluation of K → π π amplitudes and for the subsequent study of the Δ I = 1/2 rule and the evalution of ε′/ε.

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.

Lattice results for the decay constant of heavy-light vector mesons

We compute the leptonic decay constants of heavy-light vector mesons in the quenched approximation. The reliability of lattice computations for heavy quarks is checked by comparing the ratio of vector to pseudoscalar decay constant with the prediction of Heavy Quark Effective Theory in the limit of infinitely heavy quark mass. Good agreement is found. We then calculate the decay constant ratio for B mesons: $f_{B^*}/f_B= 1.01(0.01)(^{+0.04}_{-0.01})$. We also quote quenched $f_{B^*}=177(6)(17)$ MeV.

Study of heavy-light mesons on the transverse lattice

We present results from a study of meson spectra and structure in the limit where one quark is infinitely heavy. The calculations, based on the framework of light-front QCD formulated on a transverse lattice, are the first non-perturbative studies of B mesons in light-front QCD. We calculate the Isgur-Wise form factor, light-cone distribution amplitude, the heavy-quark parton distribution function and the leptonic decay constant of B mesons.

Weak annihilation in the rare radiativeB→ργdecay

The ampitude of the $B\to\rho\gamma$ decay induced by the flavour-changing neutral currents contains the penguin contribution and the weak-annihilation contribution generated by the 4-quark operators in the effective Hamiltonian. The penguin contribution is known quite well. We analyse the weak-annihilation which is suppressed by the heavy-quark mass compared to the penguin contribution. In the factorization approximation, the weak annihilation amplitude is represented in terms of the leptonic decay constants and the meson-photon matrix elements of the weak currents. The latter contain the $B\gamma$, $\rho\gamma$ transition form factors and contact terms determined by the equations of motion. We calculate the $B\gamma$ and $\rho\gamma$ form factors within the relativistic dispersion approach and obtain numerical estimates for the weak annihilation amplitude.

Standard model matrix elements for neutralB-meson mixing and associated decay constants

We present results of quenched lattice calculations of the matrix elements relevant for ${B}_{d}\ensuremath{-}{B}_{d}$ and ${B}_{s}\ensuremath{-}{B}_{s}$ mixing in the standard model. Results for the corresponding $\mathrm{SU}(3)$-breaking ratios, which can be used to constrain or determine $|{V}_{\mathrm{td}}|,$ are also given. The calculations are performed at two values of the lattice spacing, corresponding to $\ensuremath{\beta}=6.0$ and $\ensuremath{\beta}=6.2,$ with quarks described by a mean-field-improved Sheikholeslami-Wohlert action. As a by-product, we obtain the leptonic decay constants of B and D mesons. We also present matrix elements relevant for ${D}^{0}\ensuremath{-}{D}^{0}$ mixing. Our results are summarized in the Introduction.

Heavy quark physics on the lattice

I review the current status of lattice calculations of the properties of bound states containing one or more heavy quarks. Many of my remarks focus on the heavy-light leptonic decay constants, such as f B , for which the systematic errors have by now been quite well studied. I also discuss B-parameters, semileptonic form factors, and the heavy-light and heavy-heavy spectra. Some of my “world averages” are: f B = 200(30) MeV, ▪, f B s / f B = 1.16(4) and ▪.

MESON DECAY IN AN INDEPENDENT QUARK MODEL

Leptonic decay widths and leptonic decay constants of light vector mesons and weak leptonic decay widths and weak decay constants of light and heavy pseudoscalar mesons have been studied in a field-theoretic framework based on the independent quark model with a scalar-vector power-law potential. The results are in very good agreement with the experimental data.