Vector Decay Constants Research Articles

Di-electron and two-photon widths in charmonium

The vector and pseudoscalar decay constants are calculated in the framework of the Field Correlator Method. Di-electron widths: Γ ee (J/ψ) = 5.41 keV, Γ ee (ψ′(3686)) = 2.47 keV, Γ ee (ψ″(3770)) = 0.248 keV, in good agreement with experiment, are obtained with the same coupling, α s = 0.165, in the QCD radiative corrections. We show that the larger α s = 0.191 ± 0.004 is needed to reach agreement with experiment for Γ γγ (χ c ) = 7.22 keV, Γ γγ (χ c (3 P0)) = 3.3 keV, Γ γγ χ c (3 P 2)) = 0.54 keV, and also for Γ(J/ψ → 3g) = 59.5 keV, Γ(J/ψ → γ2g) = 5.7 keV. Meanwhile, even larger α s = 0.238 gives rise to good description of Γ(ψ′ → 3g) = 52.7 keV, Γ(ψ′ → γ2g) = 3.5 keV, and provides correct ratio of the branching fractions: \( \frac{{\mathcal{B}({J \mathord{\left/ {\vphantom {J \psi }} \right. \kern-\nulldelimiterspace} \psi } \to light hadrons)}} {{\mathcal{B}(\psi ' \to light hadrons)}} = 0.24 \).

MASS SPECTRA OF HEAVY QUARKONIA AND Bc DECAY CONSTANT FOR STATIC SCALAR-VECTOR INTERACTIONS WITH RELATIVISTIC KINEMATICS

We reproduce masses of the self-conjugate and non-self-conjugate mesons in the context of the spinless Salpeter equation taking into account the relativistic kinematics and the quark spins. The hyperfine splittings for the 2S charmonium and 1S bottomonium are also calculated. Further, the pseudoscalar and vector decay constants of the Bc meson and the unperturbed radial wave function at the origin are also calculated. We have obtained a local equation with a complete relativistic corrections to a class of three attractive static interaction potentials of the general form V(r) = -Ar-β + κrβ + V0, with β = 1, 1/2, 3/4 decomposed into scalar and vector parts in the form VV(r) = -Ar-β + (1-∊)κrβ and VS(r) = ∊κrβ + V0; where 0≤∊≤1. We have used the shifted large-N-expansion technique (SLNET) to solve the reduced equation for the scalar (∊ = 1), equal mixture of scalar-vector (∊ = 1/2), and vector (∊ = 0) confinement interaction kernels. The energy eigenvalues are carried out up to the third order approximation.

Bc AND HEAVY MESON SPECTROSCOPY IN THE LOCAL APPROXIMATION OF THE SCHRÖDINGER EQUATION WITH RELATIVISTIC KINEMATICS

We present bound state masses of the self-conjugate and non-self-conjugate mesons in the context of the Schrödinger equation taking into account the relativistic kinematics and the quark spins. We apply the usual interaction by adding the spin dependent correction. The hyperfine splittings for the 2S charmonium and 1S bottomonium are calculated. The pseudoscalar and vector decay constants of the Bc meson and the unperturbed radial wave function at the origin are also calculated. We have obtained a local equation with a complete relativistic corrections to a class of three attractive static interaction potentials of the general form V(r) = -Ar-β+κrβ+V0, with β = 1, 1/2, 3/4 which can also be decomposed into scalar and vector parts in the form VV(r) = -Ar-β+(1-∊)κrβ and VS(r) = ∊κrβ+V0; where 0≤∊≤1. The energy eigenvalues are carried out up to the third order approximation using the shifted large-N-expansion technique.

Decay constants of B and D mesons from non-perturbatively improved lattice QCD

The decay constants of B, D and K mesons are computed in quenched lattice QCD at two different values of the coupling. The action and operators are O(a) improved with non-perturbative coefficients. The results are f B=195(6) +24 −23 MeV, f D=206(4) +17 −10 MeV, f B s =220(6) +23 −28 MeV, f D s =229(3) +23 −12 MeV and f K =150(3) +12 − 8 MeV. Systematic errors are discussed in detail. Results for vector decay constants, flavour symmetry breaking ratios of decay constants, the pseudoscalar-vector mass splitting and D meson masses are also presented.

Leptonic and semi-leptonic B decays

We present results for the semi-leptonic and leptonic decays of B mesons. These non-perturbative matrix elements are important for constraining the CKM matrix. Results are presented for the pseudoscalar and vector decay constants, as well as flavour breaking ratios and heavy quark symmetry relations. We consider the chiral and momentum dependence of the semi-leptonic form factors of the decay B → πιν and the soft pion relation (SPR) on the lattice. These calculations were performed in the quenched approximation at two values of the coupling with non-perturbatively O ( a) improved action and currents.

Simple observables from fat link fermion actions

A comparison is made of the (quenched) light hadron spectrum and of simple matrix elements for a hypercubic fermion action (based on a fixed point action) and the clover action, both using fat links, at a lattice spacing a= 0.18 fm. Renormalization constants for the naive and improved vector current and the naive axial current are computed using Ward identities. The renormalization factors are very close to unity, and the spectroscopy of light hadrons and the pseudoscalar and vector decay constants agree well with simulations at smaller lattice spacings (and with experiment).

Vector decay constants in quarkonia

Lattice NRQCD with leading finite lattice spacing errors removed is used to simulate heavy-heavy vector decay constants. Quenched simulations are performed at three values of the coupling and fifteen values of the quark mass. The improved gauge action with plaquettes and rectangles is used. Landau link improvement is used throughout. “Perturbative” and nonperturbative meson masses are compared. One-loop perturbative matching between lattice and continuum heavy-heavy vector currents is performed. The data is consistent with af V ∝ ▪.

Quenched hadron spectrum and decay constants on the lattice

Abstract In this talk we present the results obtained from a study of O(2000) (quenched) lattice configuration from the APE collaboration, at 6.0 ⩽ Q ⩽ 6.4, using both the Wilson and the SW-Clover fermion action. We determine the light hadronic spectrum and the meson decay constants. For the light-light systems we find an agreement with the experimental data of ∼ 5∼ for mesonic masses and ∼ 10∼-15∼ for baryonic masses and pseudoscalar decay constants; a larger deviation is present for the vector decay constants. For the heavy-light decay constants we find fD1 = 237 ±16MeV, fD = 221 ±17MeV (fD1/fD = 1.07(4)), fB1 = 205±35 MeV, fB = 180±32 McV (fB1/fB = 1.14(8)), in good agreement with previous estimates.

Non-perturbative renormalization of quark bilinears

We compute non-perturbatively the renormalization constants of quark bilinears on the lattice in the quenched approximation at three values of the coupling β = 6/ g 0 2 = 6.0, 6.2, 6.4 using both the Wilson and the tree-level improved SW-Clover fermion action. We perform a Renormalization Group analysis at the next-to-next-to-leading order and compute Renormalization Group invariant values for the constants. The results are applied to obtain a fully non-perturbative estimate of the vector and pseudoscalar decay constants.

Bdecay constants from NRQCD with dynamical fermions

We present a lattice investigation of the heavy-light meson decay constants using Wilson light quarks and NRQCD heavy quarks, partially including the effects of dynamical sea quarks. We calculate the pseudoscalar and vector decay constants over a wide range in heavy quark mass and are able to perform a detailed analysis of heavy quark symmetry. We find consistency between the extrapolation of the NRQCD results and the static case, as expected. We find the slope of the decay constants with $1/M$ is significantly larger than naive expectations and the results of previous lattice calculations. For the first time we extract the non-perturbative coefficients of the slope arising from the $O(1/M)$ heavy quark interactions separately and show the kinetic energy of the heavy quark is dominant and responsible for the large slope. In addition, we find that significant systematic errors remain in the decay constant extracted around the $B$ meson mass due to truncating the NRQCD series at $O(1/M)$. We estimate the higher order contributions to $f_B$ are approximately $20\%$; roughly the same size as the systematic errors introduced by using the Wilson action for light quarks.

Light quenched hadron spectrum and decay constants on different lattices

We present a study of O(2000) (quenched) lattice configurations from the APE collaboration, for 6.0 ≤ β ≤ 6.4 using both the Wilson and the SW-Clover fermion action. We determine the light hadronic spectrum and meson decay constants. We extract the inverse lattice spacing using data at the simulated values of the quark mass. We find an agreemen with the experimental data of ∼5% for mesonic masses and ∼10%–15% for baryonic masses and pseudoscalar decay constants. A larger deviation is present for the vector decay constants.

Decay constants of P- and D-wave heavy-light mesons.

We investigate decay constants of P and D-wave heavy-light mesons within the mock-meson approach. Numerical estimates are obtained using the relativistic quark model. We also comment on recent calculations of heavy-light pseudo-scalar and vector decay constants.

Quark structure of the pion and pion form factor.

We consider the pion structure in the region of low and moderately high momentum transfers: at low $Q^2$, the pion is treated as a composite system of constituent quarks; at moderately high momentum transfers, $Q^2=10\div25\;GeV^2$, the pion \ff is calculated within perturbative QCD taking into account one--gluon hard exchange. Using the data on pion \ff at $Q^2<3\;GeV^2$ and pion axial--vector decay constant, we reconstruct the pion \wf in the soft and intermediate regions. This very wave function combined with one--gluon hard scattering amplitude allows a calculation of the pion \ff in the hard region $Q^2=10\div25\;GeV^2$. A specific feature of the reconstructed pion \wf is a quasi--zone character of the $q\bar q$--excitations. On the basis of the obtained pion \wf and the data on deep inelastic scattering off the pion, the valence quark distribution in a constituent quark is determined.

A comparison of an O( α)-improved and the Wilson fermion actions at β = 6.0 for heavy-quark systems

We calculate the pseudoscalar decay constant for heavy-light mesons, the vector decay constant and the vector pseudoscalar hyperfine mass splitting for heavy-heavy mesons. These calculations are done using the same set of gauge configurations for both an O( α)-improved and the standard Wilson fermion action thus allowing a direct comparison of the two actions. Further comparisons are made with the UKQCD β = 6.2 charm results.

Meson spectroscopy and decay constants with Wilson fermions at β = 6.4

We present an extensive lattice study of the physical properties of mesons, composed of a heavy, H, and a light, q, quark, at β = 6.4 on a 24 3 × 60 lattice, using the Wilson action in the quenched approximation. We have studied the mass spectrum and the decay constants of vector and pseudoscalar mesons. We find significant violations of the mass scaling law ƒ P √M P = const. . (∼ 50% for D-mesons and ∼ 20% for B-mesons). The results using quenched but propagating quarks are remarkably consistent with the static results when the scale is taken from the pion decay constant. Combining the results obtained by several calculations of the pseudoscalar decay constants as a function of the meson mass, at different values of the lattice spacing, we obtain by extrapolation ƒ B √B B = (220 ± 40) MeV (ƒ B = (205 ± 40) MeV and B B = 1.16 ± 0.07) , where B B is the renormalization group invariant B-parameter relevant for B d − B d mixing. We also find ƒ B s 2B B s /ƒ B d 2B B d = 1.19 ± 0.10 . This last result is relevant in experimental studies of B s − B s mixing. The vector-pseudoscalar mass splittings do not follow the predicted behaviour, M V 2 − M P 2 const., which is expected (and found experimentally) in the limit of large heavy quark masses (i.e. when m H ⪢ Λ QCD).

Heavy flavor meson decay constants with Wilson fermions at β = 6.4

We present an extensive lattice study of the physical properties of mesons, composed of a heavy, H , and a light, q , quark, at β = 6.4 on a 24 3 × 60 lattice, using the Wilson action in the quenched approximation. We have studied the mass spectrum and the decay constants of vector and pseudoscalar mesons. We find significant violations of the mass scaling law f P √ M P = const. ( ∼ 50% for D-mesons and ∼ 20% for B-mesons). The results using quenched but propagating quarks are remarkably consistent with the static results when the scale is taken from the pion decay constant. Combining the results obtained by several calculations of the pseudoscalar decay constants as a function of the meson mass, at different values of the lattice spacing, we obtain by extrapolation f B √ B B = (220 ± 40) MeV ( f B = (205 ± 40) MeV and B B = 1.16 ± 0.07), where B B is the renormalization group invariant B-parameter relevant for B d - B d mixing. We also find f B s 2 B B , f B d 2 B B d = 1.19 ± 0.10 . This last result is relevant in experimental studies of B 3 - B 3 mixing. The vector-pseudoscalar mass splittings do not follow the predicted behaviour, M V 2 - M P 2 ∼ const., which is expected (and found experimentally) in the limit of large heavy quark masses (i.e. when m Q ⪢ Λ QCD ).

Lattice heavy-meson decay constants and fermion universality.

The mass dependence of decay constants for vector and pseudoscalar mesons is calculated using both Wilson and staggered-fermion formulations in quenched lattice QCD. For low meson masses, the agreement of the two methods is good and the determination of the vector decay constant agrees with experiment. For pseudoscalar heavy-quark--light-quark systems, we find reasonable agreement between the two fermion formulations as long as Ma\ensuremath{\lesssim}1, where M is the meson mass.