Pseudoscalar Decay Constants Research Articles

Pion and kaon physics with improved staggered quarks

Abstract We compute pseudoscalar meson masses and decay constants using staggered quarks on lattices with three flavors of sea quarks and lattice spacing ≈ 0.12 fm and ≈ 0.09 fm. We fit partially quenched results to “staggered chiral perturbation theory” formulae, thereby taking into account the effects of taste-symmetry violations. Chiral logarithms are observed. From the fits we calculate f π and f ϰ, extract Gasser-Leutwyler parameters of the chiral Lagrangian, and (modulo rather large perturbative errors) find the light and strange quark masses.

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.

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.

Kaon B-parameter using overlap fermions

I present first results from an in-progress calculation of B K in quenched approximation using overlap fermions. My particular implementation of the overlap uses a kernel with nearest and next-nearest neighbor interactions and HYP-blocked gauge connections. Matching to the continuum NDR regularization is done perturbatively. I present preliminary results at β = 5.9 and 6.1 (lattice spacings 0.125 and 0.09 fm) for quark masses, pseudoscalar decay constants, and B-parameter− B K (NDR)(μ = 2GeV) ⋍ 0.66(3 − 4).

Low energy chiral lagrangian parameters for scalar and pseudoscalar mesons

We present results of a high-statistics study of scalar and pseudoscalar meson propagators in quenched QCD at two values of lattice spacing,β = 5.7 and 5.9, with clover-improved Wilson fermions. The study of the chiral limit is facilitated by the pole-shifting ansatz of the modified quenched approximation. Pseudoscalar masses and decay constants are determined as a function of quark mass and quenched chiral log effects are estimated. A study of the flavor singlet ν′ hairpin diagram yields a precise determination of the ν′ mass insertion. The corresponding value of the quenched chiral log parameter b is compared with the observed QCL effects. Removal of QCL effects from the scalar propagator allows a determination of the mass of the lowest lying isovector scalar qq meson.

Light hardon properties with improved staggered quarks

Preliminary results from simulations with 2+1 dynamical quark flavors at a lattice spacing of 0.09 fm are combined with earlier results at a = 0.13 fm. We examine the approach to the continuum limit and investigate the dependence of the pseudoscalar masses and decay constants as the sea and valence quark masses are separately varied.

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.

Masses and decay constants of heavy–light flavour mesons in a variational scheme

The hadronic properties of heavy–light flavour mesons, vis a vis B, Bs, D and Ds, are investigated by treating the light flavour relativistically and the heavy flavour non-relativistically with an effective quark–antiquark interaction potential of the form −αc/r + Arν. The Fermi momentum parameter generally used for experimental analysis, ground state masses, the ratio of the pseudoscalar decay constants and the vector–pseudoscalar mass differences and their ratios are computed for values of the potential index ν varying from 0.5 to 2.0. The excellent agreement of the properties calculated here with the experimental values suggest the most suitable potential form to be ν = 0.5.

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.

A nonperturbative determination of C A and the scaling of fπ and m[formula omitted

We calculate the O( a) improvement coefficient for the axial-vector current using the nonperturbative method proposed by the LANL group. Results for the coefficient in the range β = 5.93 to 6.2 are presented. We find c A is close to the 1-loop tadpole-improved perturbative value. In addition, scaling of the pseudoscalar decay constant and renormalised quark mass is improved compared to that obtained using the (larger) c A values obtained by the ALPHA collaboration.

Chiral properties of pseudoscalar mesons on a quenched204lattice with overlap fermions

The chiral properties of the pseudoscalar mesons are studied numerically on a quenched ${20}^{4}$ lattice with the overlap fermion. We elucidate the role of the zero modes in the meson propagators, particularly that of the pseudoscalar meson. The non-perturbative renormalization constant ${Z}_{A}$ is determined from the axial Ward identity and is found to be almost independent of the quark mass for the range of quark masses we study; this implies that the ${O(a}^{2})$ error is small. The pion decay constant ${f}_{\ensuremath{\pi}}$ is calculated from which we determine the lattice spacing to be 0.148 fm. We look for the quenched chiral log in the pseudoscalar decay constants and the pseudoscalar masses and we find clear evidence for its presence. The chiral log parameter $\ensuremath{\delta}$ is determined to be in the range 0.15--0.4, which is consistent with that predicted from 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.

Masses of S and P wave mesons and pseudoscalar decay constants using a confinement scheme

In the framework of relativistic harmonic confinement model for quarks and antiquarks, the masses of S- and P-wave mesons and pseudoscalar decay constants from light flavour to heavy flavour sectors are computed. The residual two-body Coulomb interaction and the spin-dependent interaction of the confined one gluon exchange effects (COGEP) such as spin-spin and spin-orbit interactions are perturbatively incorporated with the confinement energy to get the respective vector-pseudoscalar meson mass differences. Here we employ the same parametrization and model parameters as used in a recent study of low-lying hadron masses and leptonic decay widths. The results are being compared with the values obtained from other theoretical models and the experimental values.

QCD isospin breaking in meson masses, decay constants and quark mass ratios

The procedure to calculate masses and matrix-elements in the presence of mixing of the basis states is explained in detail. We then apply this procedure to the two-loop calculation in Chiral Perturbation Theory of pseudoscalar masses and decay constants including quark mass isospin breaking. These results are used to update our analysis of $K_{\ell4}$ done previously and obtain a value of $m_u/m_d$ in addition to values for the low-energy-constants $L_i^r$.

Zweig rule violation in the scalar sector and values of low-energy constants

We discuss the role of the Zweig rule (ZR) violation in the scalar channel for the determination of low-energy constants and condensates arising in the effective chiral lagrangian of QCD. The analysis of the Goldstone boson masses and decay constants shows that the three-flavor condensate and some low-energy constants are very sensitive to the value of the ZR violating constant L6. A similar study is performed in the case of the decay constants. A chiral sum rule based on experimental data in the 0++ channel is used to constrain L6, indicating a significant decrease between the two- and the three-flavor condensates. The analysis of the scalar form factors of the pion at zero momentum suggests that the pseudoscalar decay constant could also be suppressed from Nf = 2 to 3.

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.

FB for various actions: approaching the continuum limit with dynamical fermions

We present results for pseudoscalar decay constants of heavy-light mesons using both quenched and N f = 2 dynamical fermion configurations. A variety of fermion actions is investigated: Wilson, nonperturbative clover, and fat-link clover. For heavy quarks the Fermilab formalism is applied. In the quenched approximation, results with the nonperturbatively improved clover action of the Alpha collaboration allow us to study the systematic error of the continuum extrapolation from the Wilson action. In addition, we use quenched configurations to explore the effects of fattening. The lessons from the quenched analyses are then applied to data with dynamical fermions, where both Wilson and fat-link clover actions have been used. This allows us to attempt a continuum extrapolation of the dynamical results.

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.