Decay Constants Of Pseudoscalar Mesons Research Articles

Quark mass dependence of masses and decay constants of the pseudo-Goldstone bosons in QCD

The dependence of the pseudoscalar meson masses and decay constants on sea and valence quark masses is compared to next-to-leading order (NLO) Chiral Perturbation Theory (ChPT). The numerical simulations with two light dynamical quark flavors are performed with the Wilson-quark lattice action at gauge coupling beta=5.1 and hopping parameters kappa=0.176, 0.1765, 0.177 on a 16^4 lattice. O(a) lattice artifacts are taken into account by applying chiral perturbation theory for the Wilson lattice action. The values of the relevant combinations of Gasser-Leutwyler constants L_4, L_5, L_6 and L_8 are estimated.

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.

Partially quenched chiral perturbation theory and numerical simulations

The dependence of the pseudoscalar meson mass and decay constant is compared to one-loop partially quenched chiral perturbation theory (PQChPT) in a numerical simulation with two light dynamical quarks. The characteristic behaviour with chiral logarithms is observed. The values of the fitted PQChPT-parameters are in a range close to the expectation in continuum in spite of the fact that the lattice spacing is still large, namely a≃0.28 fm.

Light hadron spectrum and quark masses from quenched lattice QCD

We present details of simulations for the light hadron spectrum in quenched QCD carried out on the CP-PACS parallel computer. Simulations are made with the Wilson quark action and the plaquette gauge action on 32^3x56 - 64^3x112 lattices at four lattice spacings (a \approx 0.1-0.05 fm) and the spatial extent of 3 fm. Hadronic observables are calculated at five quark masses (m_{PS}/m_V \approx 0.75 - 0.4), assuming the u and d quarks being degenerate but treating the s quark separately. We find that the presence of quenched chiral singularities is supported from an analysis of the pseudoscalar meson data. We take m_\pi, m_\rho and m_K (or m_\phi) as input. After chiral and continuum extrapolations, the agreement of the calculated mass spectrum with experiment is at a 10% level. In comparison with the statistical accuracy of 1-3% and systematic errors of at most 1.7% we have achieved, this demonstrates a failure of the quenched approximation for the hadron spectrum: the meson hyperfine splitting is too small, and the octet masses and the decuplet mass splittings are both smaller than experiment. Light quark masses are calculated using two definitions: the conventional one and the one based on the axial-vector Ward identity. The two results converge toward the continuum limit, yielding m_{ud}=4.29(14)^{+0.51}_{-0.79} MeV. The s quark mass depends on the strange hadron mass chosen for input: m_s = 113.8(2.3)^{+5.8}_{-2.9} MeV from m_K and m_s = 142.3(5.8)^{+22.0}_{-0} MeV from m_\phi, indicating again a failure of the quenched approximation. We obtain \Lambda_{\bar{MS}}^{(0)}= 219.5(5.4) MeV. An O(10%) deviation from experiment is observed in the pseudoscalar meson decay constants.

Decay constants, light quark masses, and quark mass bounds from light quark pseudoscalar sum rules

The flavor $\mathrm{ud}$ and $\mathrm{us}$ pseudoscalar correlators are investigated using families of finite energy sum rules (FESR's) known to be very accurately satisfied in the isovector vector channel. It is shown that the combination of constraints provided by the full set of these sum rules is sufficiently strong to allow determination of both the light quark mass combinations ${m}_{u}{+m}_{d},$ ${m}_{s}{+m}_{u}$ and the decay constants of the first excited pseudoscalar mesons in these channels. The resulting masses and decay constants are also shown to produce well-satisfied Borel transformed sum rules, thus providing nontrivial constraints on the treatment of direct instanton effects in the FESR analysis. The values of ${m}_{u}{+m}_{d}$ and ${m}_{s}{+m}_{u}$ obtained are in good agreement with the values implied by recent hadronic $\ensuremath{\tau}$ decay analyses and the ratios obtained from ChPT. New light quark mass bounds based on FESR's involving weight functions which strongly suppress spectral contributions from the excited resonance region are also presented.

Hadron spectrum for quenched domain-wall fermions with DBW2 gauge action

We investigate basic physical quantities for quenched simulation with domain-wall fermions and the DBW2 gauge action. Masses and decay constant of pseudoscalar mesons are measured. Scaling properties are tested.

Exploration of sea quark effects in two-flavor QCD with the O( a)-improved Wilson quark action

We explore sea quark effects in the light hadron mass spectrum in a simulation of two-flavor QCD using the nonperturbatively O( a)-improved Wilson fermion action. In order to identify finite-size effects, light meson masses are measured on 12 3 × 48, 16 3 × 48 and 20 3 × 48 lattices with a ∼ 0.1 fm. On the largest lattice, where the finite-size effect is negligible, we find a significant increase of the strange vector meson mass compared to the quenched approximation. We also investigate the quark mass dependence of pseudoscalar meson masses and decay constants and test the consistency with (partially quenched) chiral perturbation theory.

FBandfBsfrom QCD sum rules

The decay constants of the pseudoscalar mesons B and B_s are evaluated from QCD sum rules for the pseudoscalar two-point function. Recently calculated perturbative three-loop QCD corrections are incorporated into the sum rule. An analysis in terms of the bottom quark pole mass turns out to be unreliable due to large higher order radiative corrections. On the contrary, in the MS_bar scheme the higher order corrections are under good theoretical control and a reliable determination of f_B and f_{B_s} becomes feasible. Including variations of all input parameters within reasonable ranges, our final results for the pseudoscalar meson decay constants are f_B = 210 +- 19 MeV and f_B_s = 244 +- 21 MeV. Employing additional information on the product sqrt(B_B) f_B from global fits to the unitarity triangle, we are in a position to also extract the B-meson B-parameter B_B = 1.26 +- 0.45. Our results are well compatible with analogous determinations of the above quantities in lattice QCD.

QCD sum rules for the pseudoscalar decay constants: To constrain the strange quark mass

We study the higher order corrections of quark masses to the Gell-Mann--Oakes--Renner (GOR) relation by constructing QCD sum rules exclusively for pseudoscalar mesons from the axial-vector correlation function, $i\ensuremath{\int}{d}^{4}{\mathrm{xe}}^{\mathrm{ip}\ensuremath{\cdot}x}〈0|T[{A}_{\ensuremath{\mu}}{(x)A}_{\ensuremath{\nu}}(0)]|0〉.$ To project out the pseudoscalar meson contributions, we apply $\ensuremath{-}{p}^{\ensuremath{\mu}}{p}^{\ensuremath{\nu}}{/p}^{2}$ to this correlation function and construct sum rules for the decay constants of pseudoscalar mesons, ${f}_{\ensuremath{\pi}}{,f}_{k},$ and ${f}_{{\ensuremath{\eta}}_{8}}.$ The operator product expansion (OPE) is proportional to quark masses due to PCAC (partial conservation of axial-vector current). To leading order in quark mass, each sum rule reproduces the corresponding GOR relation. For kaon and ${\ensuremath{\eta}}_{8},$ the deviation from the GOR relation due to higher orders in quark mass is found to be substantial. But the deviation gives better agreement with phenomenology. Our sum rule provides a sensitive relation between ${f}_{K}$ and ${m}_{s},$ which stringently constrains the value for ${m}_{s}.$ To reproduce the experimental value for ${f}_{K},$ ${m}_{s}$ is found to be 186 MeV at 1 GeV scale. The ${f}_{{\ensuremath{\eta}}_{8}}$ sum rule also supports this finding.

Dyson-Schwinger calculations of meson form factors

The ladder-rainbow truncation of the set of Dyson-Schwinger equations is used to study the pion and kaon electromagnetic form factors and the γ 7 π 0 γ transition form factor in impulse approximation. With model parameters previously fixed by the pseudoscalar meson masses and decay constants, the obtained form factors are in good agreement with the data.

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.

Scaling investigation of renormalized correlation functions in O( a) improved quenched lattice QCD

We present a scaling investigation of some correlation functions in O( a) improved quenched lattice QCD. In particular, as one observable the renormalized PCAC quark mass is considered. Others are constructed such that they become the vector meson mass and the pseudoscalar meson decay constant when the volume is large. For the present discussion we remain in intermediate volume, (0.75 3 × 1.5) fm 4 with Schrödinger functional boundary conditions. By fixing the ‘pion mass’ and the spatial lattice size in units of the hadronic scale r 0, we simulated four lattices with resolutions ranging from 0.1 to 0.05 fm and performed the extrapolation to the continuum limit. The maximal scaling violation found in the improved theory is a ∼ 6% effect at a ≅ 0.1 fm.

Mixing and decay constants of pseudoscalar mesons: Octet-singlet vs. quark flavor basis

Although η−η′ mixing is qualitatively well understood as a consequence of the U(1) A anomaly in QCD together with a broken SU(3) F flavor symmetry, until recently the values of decay and mixing parameters of the η and η′ were only approximately known, e.g. values for the octet-singlet mixing angle between −20° and −10° could be found in the literature. New experimental data, especially for the reactions γγ ∗ → η,η′ and B → η′ K, together with new theoretical results from higher order corrections in chiral perturbation theory stimulated a phenomenological re-analysis of this subject, which led to a coherent qualitative and quantitative picture of η−η′ mixing and even of η−η′−η c mixing.

Mixing and decay constants of pseudoscalar mesons: the sequel

We present further tests and applications of the new η– η′ mixing scheme recently proposed by us. The particle states are decomposed into orthonormal basis vectors in a light-cone Fock representation. Because of flavor symmetry breaking the mixing of the decay constants can be identical to the mixing of particle states at most for a specific choice of this basis. Theoretical and phenomenological considerations show that the quark flavor basis has this property and allows, therefore, for a reduction of the number of mixing parameters. A detailed comparison with other mixing schemes is also presented.

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 $0<~x<~1.$ 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.

Mixing and decay constants of pseudoscalar mesons

We propose a new eta-eta' mixing scheme where we start from the quark flavor basis and assume that the decay constants in that basis follow the pattern of particle state mixing. On exploiting the divergences of the axial vector currents - which embody the axial vector anomaly - all basic parameters are fixed to first order of flavor symmetry breaking. That approach naturally leads to a mass matrix, quadratic in the masses, with specified elements. We also test our mixing scheme against experiment and determine corrections to the first order values of the basic parameters from phenomenology. Finally, we generalize the mixing scheme to include the eta(c). Again the divergences of the axial vector currents fix the mass matrix and, hence, mixing angles and the charm content of the eta and eta'.

Decay constants of heavy-light pseudoscalar mesons in the Fermilab formalism

We present new results from the Fermilab weak matrix-element project. The decay constants of heavy-light pseudoscalar mesons are calculated using the Fermilab formalism for heavy quarks and a tadpole-improved SW action for light quarks. Improvement allows the bottom quark to be simulated directly on the lattice removing the need for large extrapolations. The dependence on the lattice spacing is discussed for 5.7 ≤ β ≤ 6.1.

The linear meson model and chiral perturbation theory

We compare the linear meson model and chiral perturbation theory in next to leading order in the quark mass expansion. In particular, we compute the couplings \(L_4\)–\(L_8\) of chiral perturbation theory as functions of the parameters of the linear model. They are induced by the exchange of \(0^{++}\) scalar mesons. We use a phenomenological analysis of the effective vertices of the linear model in terms of pseudoscalar meson masses and decay constants. Our results for the \(L_i\) agree with previous phenomenological estimates.

Heavy-light decay constants — MILC results with the Wilson action

We present the current status of our ongoing calculations of pseudoscalar meson decay constants for mesons that contain one light and one heavy quark (f_B, f_{B_s}, f_D, f_{D_s}). We are currently generating new gauge configurations that include dynamical quarks and calculating the decay constants. In addition, we have several new results for the static approximation. Those results, as well as several refinements to the analysis, are new since Lattice '96. Our current (still preliminary) value for f_B is 156 +- 11 +- 30 +- 14 MeV, where the first error is from statistical and fitting errors, the second error is an estimate of other systematic errors within the quenched approximation and the third error is an estimate of the quenching error. For the ratio f_{B_s}/f_B, we get 1.11 +- 0.02 +- 0.03 +- 0.07.