Decay Constants Of Pseudoscalar Mesons Research Articles

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.

Decay constants of pseudoscalar mesons in a relativistic quark model

The decay constants of pseudoscalar mesons are calculated in a relativistic quark model which assumes that mesons are made of a valence quark antiquark pair and of an effective vacuum like component. The results are given in terms of quark masses and of some free parameters entering the expression of the internal wave functions of the mesons. By using the pion and kaon decay constants $F_{\pi^+}=130.7~MeV,~F_{K^+}=159.8~MeV$ to fix the parameters of the model one gets $60~MeV\leq F_{D^+}\leq 185~MeV,~95~MeV\leq F_{D_s}\leq230~MeV,~80~MeV\leq F_{B^+}\leq205~MeV$ for the light quark masses $m_u=5.1~MeV,~m_d=9.3~MeV,~m_s=175~MeV$ and the heavy quark masses in the range: $1.~GeV\leq m_c\leq1.6~GeV,~4.1~GeV\leq m_b\leq4.5~GeV$. In the case of light neutral mesons one obtains with the same set of parameters $F_{\pi^0}\approx 138~MeV,~F_\eta\approx~130~MeV,F_{\eta'} \approx~78~MeV$. The values are in agreement with the experimental data and other theoretical results.

Radiative corrections to πl2 and Kl2 decays

We reexamine radiative corrections to π l2 and K l2 decays. We perform a matching calculation, including vector and axial vector resonances as explicit degrees of freedom in the long distance part. By considering the dependence on the matching scale and on the hadronic parameters, and by comparing with model independent estimates, we scrutinize the model dependence of the results. For the pseudoscalar meson decay constants, we extract the values f π = (92.1 ± 0.3) MeV and f K = (112.4 ± 0.9) MeV. For the ratios R π and R K of the electronic and muonic decay modes, we predict R π = (1.2354 ± 0.0002) × 10 −4 and R K = (2.472 ± 0.001) × 10 −5.

Heavy-flavour phenomenology from lattice QCD

The latest results on several weak hadronic amplitudes that have been computed in numerical simulations are reviewed. Many of these results have already had, or are expected to have, a significant impact on the phenomenology of weak interactions, and in particular on our understanding ofCP violation. The main topics discussed in this review are: leptonic decay constants of pseudoscalar heavy-light mesons, B-\(\bar B\) mixing amplitudes, semi-leptonic decays of D and B mesons, radiative decays of B mesons and the Isgur-Wise function.

Static and dynamic properties of pseudoscalar mesons

We report the results of form factors, charge radii and decay constants of both light and heavy flavoured pseudoscalar mesons in a QCD inspired quark model. We use the quantum mechanical perturbation theory and discuss its limitations in the present problem. Several predictions are also made for bottom and top flavours.

Current renormalization constants with an O(a)-improved fermion action.

Using chiral Ward identities, we determine the renormalisation constants of bilinear quark operators for the Sheikholeslami-Wohlert action lattice at beta=6.2. The results are obtained with a high degree of accuracy. For the vector current renormalisation constant we obtain Z_V=0.817(2)(8), where the first error is statistical and the second is due to mass dependence of Z_V. This is close to the perturbative value of 0.83. For the axial current renormalisation constant we obtain Z_A = 1.045(+10 -14), significantly higher than the value obtained in perturbation theory. This is shown to reduce the difference between lattice estimates and the experimental values for the pseudoscalar meson decay constants, but a significant discrepancy remains. The ratio of pseudoscalar to scalar renormalisation constants, Z_P/Z_S, is less well determined, but seems to be slightly lower than the perturbative value.

Chiral Lagrangian with Higher Resonances and Flavour SU(3) Breaking

A chiral Lagrangian with SU(3) breaking and higher resonances is proposed. In this model, the SU(3) breaking structure in vector-pseudoscalar sector is realized with the decay constants of pseudoscalar mesons and the masses of vector mesons used as inputs. We examine whether the resulting SU(3) breaking effect in the charge radii of pseudoscalar mesons is consistent with the experimental facts.

Decay constants and masses of octet pseudoscalar mesons.

The masses and decay constants of the octet pseudoscalar mesons are calculated to all orders of quark mass in terms of the effective meson theory. Consequently, the analytic functions of quark masses for the masses and decay constants are obtained. The decay constant ${\mathit{F}}_{\mathrm{\ensuremath{\eta}}}$ has been predicted and the three light quark masses are determined.

Decay constants of heavy-light mesons

The decay constants of the heavy-light pseudoscalar mesons are studied in a high statistics run using the Wilson action at β = 6.0 and β = 6.2, and the clover action at β = 6.0. The systematics of O(a) discretisation errors are discussed.. Our best estimates of the decay constant are: f D = 218(9) MeV, f D / f D s = 1.11(1) and we obtain preliminary values for f B .

Chiral Lagrangian with Higher Resonances and Flavour SU(3) Breaking

A chiral Lagrangian with $ SU(3) $ breaking and higher resonances is proposed. In this model, the $ SU(3) $ breaking structure in vector-pseudoscalar sector is realized with the decay constants of pseudoscalar mesons and the masses of vector mesons used as inputs. We examine whether the resulting $ SU(3) $ breaking effect in the charge radii of pseudoscalar mesons is consistent with the experimental facts.

Renormalization of bilinears in nonrelativistic QCD.

We calculate the $O({\ensuremath{\alpha}}_{s})$ corrections to bilinear lattice vertex operators in nonrelativistic QCD (NRQCD) on the lattice. We use the lowest-order (in $\frac{1}{M}$) NRQCD action which includes the time derivative and kinetic energy terms, but we ignore spin effects. We give the correction required to convert a lattice calculation of the pseudoscalar heavy-light meson decay constant into a value appropriate for the continuum. For the light fermion we have used ordinary Wilson fermions, improved Wilson fermions, and naive fermions. We also give the correction required for a calculation of the vector heavy-heavy meson leptonic width. This is unfortunately large.

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 ).

Light 0- Meson Solution of Bethe-Salpeter Equation Involving the Vacuum Condensates in QCD11The project supported by National Natural Science Foundation of China

We discuss the Bethe-Salpeter equation involving the vacuum condensates in QCD in the background fields. The bound state equation for the light 0- meson (π and K) is solved in the ladder approximation of single gluon exchange, where the gluon propagator is calculated in tree level of a gluon condensate and a quark condensate. The kernel is divided into two parts: perturbative and non-perturbative. The non-perturbative part is determined by the vacuum condensate. Pseudo-scalar meson spectrum and decay constants are in good agreement with data.

Decay constants of heavy mesons

Results of two different calculations of the decay constants ( f P ) of heavy pseudoscalar mesons ( P) are presented. The first calculation uses the static approximation for the heavy-quark propagator, and the second uses the conventional technique where the decay constants are obtained from fully propagating quark fields. Both methods give a substantial negative correction to the asymptotic scaling law f P √ M P = constant, at the mass of the charm quark. This is the main result of this talk. The result for the decay constant using the static quark method is however significantly larger than that obtained using the conventional method. A discussion of the systematic errors likely to be responsible for this difference is presented, together with a description of work in progress designed to reduce these errors.

A lattice computation of the decay constant of the B-meson

We compute the decay constant of the B-meson, ƒ B, on a 10 2 × 20 × 40 lattice at β = 6.0, with Wilson fermions, using 30 gauge field configurations, generated in the quenched approximation. For the propagator of the b-quark we keep only the leading term in the 1/ m b expansion. To improve our results we use, as the interpolating fields for the B-meson, lattice operators which are “smeared” over several lattice sites. We observe a clear signal for the lightest B-meson state, and obtain the value ƒ B = 310 ± 25 ± 50 MeV , where the first error is statistical and the second represents our uncertainty in the value of the lattice spacing. This result, combined with earlier lattice measurements of ƒ D (ƒ D ⋍ 180 MeV , demonstrates that the asymptotic scaling law for the decay constants of heavy pseudoscalar mesons P, (i.e. ƒ P √M P ∼ constant ), has large corrections for charmed mesons. We estimate that the non-scaling corrections will reduce the above value of ƒ B by about 25%.

Heavy meson decay constants. [formula omitted] corrections

The coefficients of the 1 m -suppressed dimension-five operators in the static effective field theory lagrangian have been calculated to one loop order. In this paper we calculate to order α s the coefficients of the 1 m -suppressed operators in the expansion of the vector and axial vector currents containing one light and one heavy quark field. The matrix element of the time component of the axial vector current determines the decay constants of pseudoscalar heavy-light mesons.

Pions and kaons in QCD.

From reliable numerical solutions of an approximate Dyson-Schwinger equation for the quark propagator, we obtain values of the pion and kaon decay constants that differ significantly from those obtained recently by Munczek and McKay using ad hoc quark mass functions. We present arguments that the Pagels-Stokar formula should not be used to estimate the pseudoscalar-meson decay constants when chiral symmetry is broken.

Generalized SU(3) Nambu-Jona-Lasinio model: (I). Mesonic modes

We present calculations of mesonic (quark-antiquark) modes in a generalized Nambu-Jona-Lasinio model with three quark flavours. The effective interaction between quarks is symmetric under chiral SU(3) L⊗ SU(3) R and incorporates a U(1) A-breaking six-point interaction as suggested by 't Hooft. We concentrate on the evaluation of masses and decay constants of pseudoscalar mesons, with special emphasis on the underlying symmetry breaking patterns. Scalar, vector and axial vector mesonic modes are also discussed.

Analysis of finite size effects on the decay constants of heavy mesons

Finite size effects on the decay constants of heavy pseudoscalar mesons (D and B mesons) are analyzed in the continuum limit. This study applies to the scaling limit of lattice QCD with dynamical light fermions. For large enough volume it is possible to determine the finite size effects by means of an effective field theory for both light and heavy mesons (chiral perturbation theory). The finite size effects are due to the presence of the light mesons (pions). It is shown that the existence of excited states in the heavy meson system can lead to important contributions to the effects. This is analyzed by including heavy vector mesons.