Decay Constants Of Vector Mesons Research Articles

Coupling of the light vector meson to the vector and to the tensor current

We present results for the coupling of the light vector mesons to the tensor current, relative to the standard vector meson decay constants. From an (a)-improved lattice study, performed at three values of the lattice spacing in the quenched approximation, our final values (in the continuum limit), in the MS-bar scheme at μ = 2 GeV, are: fρT/fρ = 0.72(2)(+2−0), fK*T/fK* = 0.74(2), fϕT/fϕ = 0.76(1).

FLAVOR-SPIN SYMMETRY AND THE TENSOR CHARGE

Exploiting an approximate phenomenological symmetry of the JPC = 1+- light axial vector mesons and using pole dominance, we calculate the flavor contributions to the nucleon tensor charge. The result depends on the decay constants of the axial vector mesons and their couplings to the nucleons.

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.

Flavor-spin symmetry estimate of the nucleon tensor charge.

The axial vector and tensor charge, defined as the first moments of the forward nucleon matrix elements of corresponding quark currents, are essential for characterizing the spin structure of the nucleon. There are no definitive theoretical predictions for the tensor charge, aside from several model-dependent calculations. We present a new approach that exploits the approximate mass degeneracy of the light axial vector mesons [ a1(1260), b1(1235), and h1(1170)] and uses pole dominance to calculate the tensor charge. The result is simple in form. It depends on the decay constants of the axial vector mesons and their couplings to the nucleons.

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.

Bethe-Salpeter study of vector meson masses and decay constants

The masses and decay constants of the light vector mesons $\ensuremath{\rho}/\ensuremath{\omega},$ $\ensuremath{\varphi},$ and ${K}^{\ensuremath{\star}}$ are studied within a ladder-rainbow truncation of the coupled Dyson-Schwinger and Bethe-Salpeter equations of QCD with a model two-point gluon function. The approach is consistent with quark and gluon confinement, reproduces the correct one-loop renormalization group behavior of QCD, generates dynamical chiral symmetry breaking, and preserves the relevant Ward identities. The one phenomenological parameter and two current quark masses are fixed by requiring that the calculated ${f}_{\ensuremath{\pi}},$ ${m}_{\ensuremath{\pi}},$ and ${m}_{K}$ are correct. The resulting ${f}_{K}$ is within 3% of the experimental value. For the vector mesons, all eight transverse covariants are included and the dominant ones are identified; the complete angle dependence of the amplitudes is also retained. The calculated values for the masses ${m}_{\ensuremath{\rho}},$ ${m}_{\ensuremath{\varphi}},$ and ${m}_{{K}^{\ensuremath{\star}}}$ are within 5%, while the decay constants ${f}_{\ensuremath{\rho}},$ ${f}_{\ensuremath{\varphi}},$ and ${f}_{{K}^{\ensuremath{\star}}}$ for electromagnetic and leptonic decays are within 10% of the experimental values.

Isospin-breaking vector meson decay constants from continuous families of finite energy sum rules

The isospin-breaking vector meson decay constants are determined from a QCD sum rule analysis of the vector current correlator $<O| T(V^3_\mu V^8_\nu)| O>$, using a recently proposed implementation of the finite energy sum rule approach. The analysis employs the three-loop version of the OPE, and two different families of weight functions. It is shown that the requirement of consistency between results obtained using these two different weight families leads to a rather good determination of the parameter describing the deviation of the D=6 condensate term in the OPE from its vacuum saturation value, and that the ability to determine this value has non-trivial numerical consequences to the analysis. The phenomenological relevance of the results to the extraction of the strange quark mass and the determination of the $6^{th}$ order chiral low energy constant, $Q$, is also briefly discussed.

Scaling tests in O( a)—improved quenched lattice QCD

We present a scaling investigation of renormalized correlation functions in O( a)—improved quenched lattice QCD. As one observable the renormalized PCAC quark mass is considered, others are constructed such that they become the vector meson mass, and the pseudoscalar and vector meson decay constants in large volume. Presently, we remain in intermediate volume, (0.75 3 × 1.5) fm 4, and study the approach to the continuum limit.

Boundqq¯systems in the framework of the different versions of the three-dimensional reductions of the Bethe-Salpeter equation

Bound $q\overline{q}$ systems are studied in the framework of different three-dimensional relativistic equations derived from the Bethe-Salpeter equation with the instantaneous kernel in the momentum space. Except the Salpeter equation, all these equations have a correct one-body limit when one of the constituent quark masses tends to infinity. The spin structure of the confining $\mathrm{qq}$ interaction potential is taken in the form $x{\ensuremath{\gamma}}_{1}^{0}{\ensuremath{\gamma}}_{2}^{0}+(1\ensuremath{-}{x)I}_{1}{I}_{2},$ with $0&lt;~x&lt;~1.$ At first stage, the one-gluon-exchange potential is neglected and the confining potential is taken in the oscillator form. For the systems $(u\overline{s}),(c\ifmmode \bar{u}\else \={u}\fi{}),(c\overline{s})$ and $(u\ifmmode \bar{u}\else \={u}\fi{}),(s\overline{s})$ a comparative qualitative analysis of these equations is carried out for different values of the mixing parameter x and the confining potential strength parameter. We investigate (1) the existence/nonexistence of stable solutions of these equations, (2) the parameter dependence of the general structure of the meson mass spectum and leptonic decay constants of pseudoscalar and vector mesons. It is demonstrated that none of the three-dimensional equations considered in the present paper simultaneously describes even general qualitative features of the whole mass spectrum of $q\overline{q}$ systems. At the same time, these versions give an acceptable description of the meson leptonic decay characteristics.

Lattice investigation of the Das-Mathur-Okubo sum rule

An evaluation of charged pion polarizability using correlation functions measured on a 16^{3}\times 24 lattice in the context of the Das, Mathur, Okubo (DMO) sum rule is carried out. The calculation is limited to the so-called intrinsic part of the polarizability. This contribution, equivalent to a Euclidean time integral over vector and axial vector momentum-differentiated propagators, is evaluated in both a continuous and discrete sense. In the continuous case, the time behavior of the correlation functions is fit to the continuum quark model; the discrete case is handled by a straightforward application of Simpson's rule for integration after subtracting the pion contributions. A comparison of the implied vector meson and pion decay constants with phenomenological values is carried out. Results for the intrinsic polarizability are extrapolated across four quark mass values to the chiral limit. An extensive discussion of the lattice systematics in this calculation is given.

Chiral corrections to vector meson decay constants

We calculate the leading quark mass corrections of order $m_q\log(m_q)$, $m_q$ and $m_q^{3/2}$ to the vector meson decay constants within Heavy Vector Meson Chiral Perturbation Theory. We discuss the issue of electromagnetic gauge invariance and the heavy mass expansion. Reasonably good fits to the observed decay constants are obtained.

Light vector meson decay constants and the renormalization factor from a tadpole-improved action

The $\ensuremath{\rho}$, ${K}^{*}$, and $\ensuremath{\varphi}$ decay constants and the vector current renormalization factor are studied by using an ${O(a}^{2})$ classically improved, tadpole-improved action. Tree-level calculations are used to show how the classical improvement of the action, involving next-nearest-neighbor time steps, is transferred to the matrix elements. Simulations are performed on coarse lattices and compared to Wilson results from both coarse and fine lattices. The improved action data are found to resemble Wilson data obtained at 1/3 of the lattice spacing, which is the same degree of improvement that is seen by comparing the mass spectra.

Hadron masses and decay constants with Wilson quarks at beta =5.85 and 6.0.

We present results of a high statistics calculation of hadron masses and meson decay constants in the quenched approximation to lattice QCD with Wilson quarks at $\beta=$ 5.85 and 6.0 on $24^3 \times 54$ lattices. We analyze the data paying attention in particular to the systematic errors due to the choice of fitting range and due to the contamination from excited states. We find that the systematic errors for the hadron masses with quarks lighter than the strange quark amount to 1 --- 2 times the statistical errors. When the lattice scale is fixed from the $\rho$ meson mass, the masses of the $\Omega^{-}$ baryon and the $\phi$ meson at two $\beta$'s agree with experiment within about one standard deviation. On the other hand, the central value of the nucleon mass at $\beta=6.0$ (5.85) is larger than its experimental value by about 15\% (20\%) and that of the $\Delta$ mass by about 15\% (4\%): Even when the systematic errors are included, the baryon masses at $\beta=6.0$ do not agree with experiment. Vector meson decay constants at two values of $\beta$ agree well with each other and are consistent with experiment for a wide range of the quark mass, when we use current renormalization constants determined nonperturbatively by numerical simulations. The pion decay constant agrees with experiment albeit with large errors. Results for the masses of excited states of the $\rho$ meson and the nucleon are also presented.

Hadron spectrum and matrix elements in QCD with dynamical Wilson fermions at 6/g2=5.3.

We present results of a lattice simulation of quantum chromodynamics with two degenerate flavors of dynamic Wilson fermions at $6/g^2=5.3$ at each of two dynamical fermion hopping parameters, $\kappa=0.1670$ and 0.1675, corresponding to pion masses in lattice units of about 0.45 and 0.31. The simulations include three other values of valence quark mass, in addition to the dynamical quarks. We present calculations of masses and of the decay constants of vector mesons and of pseudoscalars, including the D-meson decay constant. The effects of sea quarks on matrix elements and spectroscopy are small.

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.

Vector meson and axial-vector diquark decay constants

We propose a natural generalization to the case of unequal constituent masses of the formula which gives the correct decay constants for vector mesons of the quarkonium type. Within the philosophy where diquarks are used as baryonic constituents, this allows us to evaluate the decay widths for all vector particles both mesons and diquarks to be used later in the calculation of baryon lifetimes.