Meson Decay Constants Research Articles

Exciting flavored bound states

We study ground and radial excitations of flavor singlet and flavored pseudoscalar mesons within the framework of the rainbow-ladder truncation using an infrared massive and finite interaction in agreement with recent results for the gluon-dressing function from lattice QCD and Dyson-Schwinger equations. Whereas the ground-state masses and decay constants of the light mesons as well as charmonia are well described, we confirm previous observations that this truncation is inadequate to provide realistic predictions for the spectrum of excited and exotic states. Moreover, we find a complex conjugate pair of eigenvalues for the excited ${D}_{(s)}$ mesons, which indicates a non-Hermiticity of the interaction kernel in the case of heavy-light systems and the present truncation. Nevertheless, limiting ourselves to the leading contributions of the Bethe-Salpeter amplitudes, we find a reasonable description of the charmed ground states and their respective decay constants.

Masses and decay constants of the heavy tensor mesons with QCD sum rules

In this article, we calculate the contributions of the vacuum condensates up to dimension-6 in the operator product expansion, study the masses and decay constants of the heavy tensor mesons $D_2^*(2460)$, $D_{s2}^*(2573)$, $B_2^*(5747)$, $B_{s2}^*(5840)$ using the QCD sum rules. The predicted masses are in excellent agreement with the experimental data, while the ratios of the decay constants $\frac{f_{D_{s2}^*}}{f_{D_{2}^*}}\approx\frac{f_{B_{s2}^*}}{f_{B_{2}^*}}\approx\frac{f_{D_{s}}}{f_{D}}\mid_{\rm exp}$, where the exp denotes the experimental value.

Review of lattice results concerning low-energy particle physics

We review lattice results related to pion, kaon, D- and B-meson physics with the aim of making them easily accessible to the particle-physics community. More specifically, we report on the determination of the light-quark masses, the form factor f_+(0), arising in semileptonic K rightarrow pi transition at zero momentum transfer, as well as the decay-constant ratio f_K/f_pi of decay constants and its consequences for the CKM matrix elements V_{us} and V_{ud}. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of hbox {SU}(2)_Ltimes hbox {SU}(2)_R and hbox {SU}(3)_Ltimes hbox {SU}(3)_R Chiral Perturbation Theory and review the determination of the B_K parameter of neutral kaon mixing. The inclusion of heavy-quark quantities significantly expands the FLAG scope with respect to the previous review. Therefore, we focus here on D- and B-meson decay constants, form factors, and mixing parameters, since these are most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. In addition we review the status of lattice determinations of the strong coupling constant alpha _mathrm{s}.

A model of duality violations

A realistic model for the spin-one correlators guided by the large-Nc limit of QCD is elaborated in terms of the meson decay constants, masses and energy-dependent widths, which are expanded in 1/n, where n is the radial excitation number. The matching onto OPE is performed up to NLO in 1/Nc. After applying the resulting constraints, the remaining free parameters are fitted to ALEPH and OPAL data on the related spectral functions. Excellent agreement with the data is found and the model yields, at large n, a spectrum of overlapping states coupling with essentially equal strength, in agreement with the large-Nc predictions. This model provides a consistent and appropriate way to compute the impact of duality violations on the moments of the related spectral functions computed along the circle in the complex s-plane, and therefore to quantify its importance in the extraction of physical parameters like αS(Mτ2).

Relevance of various Dirac covariants in hadronic Bethe-Salpeter wave functions in electromagnetic decays of ground state vector mesons

In this work we have employed Bethe-Salpeter equation (BSE) under covariant instantaneous ansatz (CIA) to study electromagnetic decays of ground state equal mass vector mesons: $\rho$, $\omega$, $\phi$, $\psi$ and $Y$ through the process $V\rightarrow\gamma*\rightarrow e^+ + e^-$. We employ the generalized structure of hadron-quark vertex function $\Gamma$ which incorporates various Dirac structures from their complete set order-by-order in powers of inverse of meson mass. The electromagnetic decay constants for the above mesons are calculated using the leading order (LO) and the next-to-leading order (NLO) Dirac structures. The relevance of various Dirac structures in this calculation is studied.

Leptonic decays of vector mesons in a power-law potential model of independent quarks

A relativistic power-law potential model of independent quarks is used to study the leptonic decays of neutral vector mesons. Here, the transition probability amplitude for leptonic decay of meson is determined from the momentum distribution function which is found from the assumption of a strong correlation existing between the momenta of quark and antiquark inside the meson. The model parameters are first determined from the application of the model to study the ground state spectra of ρ, ω, ϕ, ψ and ϒ mesons together with the radiative decay widths of mesons. The same model with no adjustable parameters is then used to evaluate the leptonic decay widths and the electromagnetic decay constants for the vector mesons ρ, ω, ϕ, ψ and ϒ. The calculated results are in remarkable agreement with the corresponding experimental values.

Erratum: Decay constants of heavy-light vector mesons from QCD sum rules [Phys. Rev. D 88, 014015 (2013)

Erratum: Decay constants of heavy-light vector mesons from QCD sum rules [Phys. Rev. D 88, 014015 (2013)

LEPTONIC DECAY WIDTHS OF VECTOR MESONS IN A RELATIVISTIC POTENTIAL MODEL

Leptonic decay widths and the corresponding decay constants of neutral vector mesons are calculated in the framework of a square-root potential model of independent quarks. Starting with the assumption that a strong correlation exists between the momenta of the quark and anti-quark inside the meson so as to have their total momenta identically zero in the center-of-mass frame of the meson, we find the quark and anti-quark momentum distribution amplitude which is used to determine the transition probability amplitude for the leptonic decay of mesons. The calculated results for leptonic decay widths and the electromagnetic decay constants for the vector mesons \rho, \omega, \phi and \psi are in good agrement with the corresponding experimental values. The results for the heavy meson \Upsilon are somewhat lower than the experimental values.

Determination of the mass spectrum and the decay constant mesons consisting of c and b quarks

On the basis of an investigation into the asymptotic behavior of the correlation functions of the corresponding field currents with the necessary quantum numbers, an analytic method for determining the mass spectrum and decay constants of mesons consisting of c and b quarks with relativistic corrections is proposed. The dependence of the constituent mass of quarks on the current mass and on the orbital and radial quantum numbers is analytically derived. The mass and the wave function (WF) mesons are determined from the Schrodinger equation with a mass of constituent components particles. We calculate the splitting of the mass spectrum for the singlet and triplet states mesons, as well as to determine the width of the lepton and radiation decays due E1 transition for \(\left( {\bar cc} \right)\), \(\left( {\bar bb} \right)\), \(\left( {\bar bc} \right)\) systems. Our results for the mass spectrum of mesons consisting of c and b quarks are in satisfactory agreement with the available experimental data.

Self-consistent covariant description of vector meson decay constants and chirality-even quark-antiquark distribution amplitudes up to twist 3 in the light-front quark model

Although the meson decay amplitude described by a two-point function may be regarded as one of the simplest possible physical observable, it is interesting that this apparently simple amplitude bears abundant fundamental informations on QCD vacuum dynamics and chiral symmetry. The light-front zero-mode issue of the vector meson decay constant $f_V$ is in this respect highly non-trivial and deserves careful analyses. We discuss the zero-mode issue in the light-front quark model (LFQM) prediction of $f_V$ from the perspective of the vacuum fluctuation consistent with the chiral symmetry of QCD. We extend the exactly solvable manifestly covariant Bethe-Salpeter model calculation to the more phenomenologically accessible realistic LFQM and present a self-consistent covariant description of $f_V$ analyzing the twist-2 and twist-3 quark-antiquark distribution amplitudes with even chirality.

Approximating chiral $${SU}(3)$$ S U ( 3 ) amplitudes

We construct large-N_c motivated approximate chiral SU(3) amplitudes of next-to-next-to-leading order. The amplitudes are independent of the renormalization scale. Fitting lattice data with those amplitudes allows for the extraction of chiral coupling constants with the correct scale dependence. The differences between approximate and full amplitudes are required to be at most of the order of N^3LO contributions numerically. Applying the approximate expressions to recent lattice data for meson decay constants, we determine several chiral couplings with good precision. In particular, we obtain a value for F_0, the meson decay constant in the chiral SU(3) limit, that is more precise than all presently available determinations.

Decay Constants of Beauty Mesons from QCD Sum Rules

Our recently completed analysis of the decay constants of both pseudoscalar and vector beauty mesons reveals that in the bottom-quark sector two specific features of the sum-rule predictions show up: (i) For the input value of the bottom-quark mass in the $\overline{\rm MS}$ scheme $\overline{m}_b(\overline{m}_b)\approx4.18\;\mbox{GeV},$ the sum-rule result $f_B\approx210$-$220\;\mbox{MeV}$ for the $B$ meson decay constant is substantially larger than the recent lattice-QCD finding $f_B\approx190\;\mbox{MeV}.$ Requiring QCD sum rules to reproduce the lattice-QCD value of $f_B$ yields a significantly larger $b$-quark mass: $\overline{m}_b(\overline{m}_b)=4.247\;\mbox{GeV}.$ (ii) Whereas QCD sum-rule predictions for the charmed-meson decay constants $f_D,$ $f_{D_s},$ $f_{D^*}$ and $f_{D_s^*}$ are practically independent of the choice of renormalization scale, in the beauty sector the results for the decay constants - and especially for the ratio $f_{B^*}/f_B$ - prove to be very sensitive to the specific scale setting.

Two-loop sunset integrals at finite volume

We show how to compute the two-loop sunset integrals at finite volume, for non-degenerate masses and non-zero momentum. We present results for all integrals that appear in the Chiral Perturbation Theory (χPT) calculation of the pseudoscalar meson masses and decay constants at next-to-next-to-leading order, including the case of Partially Quenched χPT. We also provide numerical implementations of the finite-volume sunset integrals, and review the results for one-loop integrals at finite volume.

Light-Front Zero-Mode Issue on the Vector Meson Decay Constant

We discuss the light-front zero-mode issue in the light-front quark model (LFQM) prediction of a vector meson decay constant from the perspective of the vacuum fluctuation consistent with the chiral symmetry of QCD. We extend the exactly solvable manifestly covariant Bethe-Salpeter model calculation to the more phenomenologically accessible realistic LFQM and present a self-consistent covariant description of the vector meson decay constant analyzing the twist-2 and twist-3 quark-antiquark distribution amplitudes with even chirality.

Dynamic AdS/QCD and the spectrum of walking gauge theories

We present a simple AdS/QCD model in which the formation of the chiral condensate is dynamically determined. The gauge dynamics is input through the running of the quark bilinear's anomalous dimension, gamma. The condensate provides a dynamically generated infra-red wall in the computation of mesonic bound state masses and decay constants. As an example, we use the model, with perturbative computations of the running of gamma, to study SU(3) gauge theory with a continuous number of quark flavours, Nf. We follow the behaviour of the spectrum as we approach the conformal window through a walking gauge theory regime. We show such walking theories display a BKT phase transition, with Miransky scaling, as one approaches the edge of the conformal window at the critical value of Nf. We show that these walking theories possess an enhanced quark condensate, a light Higgs like excitation and argue that the non-perturbative contribution to S falls to zero. We also study the deformation of the BKT transition when the quarks have a current mass which may be of use for understanding lattice simulations of walking theories.

Analysis of the decay constants of the heavy pseudoscalar mesons with QCD sum rules

In this article, we recalculate the contributions of all vacuum condensates up to dimension-6, in particular the one-loop corrections to the quark condensates $\alpha_s<\bar{q}q>$ and partial one-loop corrections to the four-quark condensates $\alpha_s^2<\bar{q}q>^2$, in the operator product expansion. Then we study the masses and decay constants of the heavy pseudoscalar mesons $D$, $D_s$, $B$ and $B_s$ using the QCD sum rules with two choices: {\bf I} we choose the $\bar{MS}$ masses by setting $m=m(\mu)$ and take perturbative corrections up to the order $\mathcal{O}(\alpha_s)$; {\bf II} we choose the pole masses $m$, take perturbative corrections up to the order $\mathcal{O}(\alpha_s^2)$ and set the energy-scale to be the heavy quark pole mass $\mu=m_Q$. In the case of {\bf I}, the predictions $f_D=(208\pm11)\,\rm{MeV}$ and $f_B=(189\pm15)\,\rm{MeV}$ are consistent with the experimental data within uncertainties, while the prediction $f_{D_s}=(241\pm12)\,\rm{MeV}$ is below the lower bound of the experimental data $f_{D_s}=(260.0\pm5.4)\,\rm{MeV}$. In the case of {\bf II}, the predictions $f_D=(211\pm14)\,\rm{MeV}$, $f_B=(190\pm17)\,\rm{MeV}$, $f_{D_s}=(258\pm13)\,\rm{MeV}$ and $f_{D_s}/f_D=1.22\pm0.08$ are all in excellent agreements with the experimental data within uncertainties.

LOW-ENERGY QCD II — STATUS OF LATTICE CALCULATIONS

The current status of lattice calculations is reviewed, with a particular emphasis on the question whether lattice simulations have matured to a stage where there is full interaction with experiment. Particular examples include the hadron spectrum, mesonic form factors and decay constants, the axial charge of the nucleon, and the hadronic vacuum polarization contribution to the muon (g-2).

Decay constants of heavy-light vector mesons from QCD sum rules

We revisit QCD sum rules for the decay constants of heavy-light mesons. In the sum rules for the vector mesons ${B}_{(s)}^{*}$ and ${D}_{(s)}^{*}$ we improve the accuracy of OPE, taking into account the $O({\ensuremath{\alpha}}_{s}^{2})$ terms in the perturbative part and calculating the $O({\ensuremath{\alpha}}_{s})$ corrections to the quark-condensate contribution. With this accuracy, we obtain the ratios of decay constants: ${f}_{{B}^{*}}/{f}_{B}={1.02}_{\ensuremath{-}0.03}^{+0.07}$, ${f}_{{D}^{*}}/{f}_{D}={1.20}_{\ensuremath{-}0.07}^{+0.10}$. The sum rule predictions for the decay constants of pseudoscalar mesons are updated with the results ${f}_{B}=({207}_{\ensuremath{-}9}^{+17})\text{ }\text{ }\mathrm{MeV}$, ${f}_{{B}_{s}}=({242}_{\ensuremath{-}12}^{+17})\text{ }\text{ }\mathrm{MeV}$, ${f}_{D}=({201}_{\ensuremath{-}13}^{+12})\text{ }\text{ }\mathrm{MeV}$, ${f}_{{D}_{s}}=({238}_{\ensuremath{-}23}^{+13})\text{ }\text{ }\mathrm{MeV}$. In order to assess the sensitivity of our calculation to the form of the sum rule, we consider alternative versions such as the power moments and Borel sum rules with different weights of the spectral density. We also investigated the heavy-quark limit of the sum rules for vector and pseudoscalar mesons, estimating the violations of the heavy-quark spin and flavor symmetry.

Mesons in large-N QCD

We present the results of a systematic, first-principles study of the spectrum and decay constants of mesons for different numbers of color charges N, via lattice computations. We restrict our attention to states in the non-zero isospin sector, evaluating the masses associated with the ground-state and first excitation in the pseudoscalar, vector, scalar, and axial vector channels. Our results are based on a new set of simulations of four dimensional SU(N) Yang-Mills theories with the number of colors ranging from N=2 to N=17; the spectra and the decay constants are computed in the quenched approximation (which becomes exact in the 't Hooft limit) using Wilson fermions. After discussing the extrapolations to the chiral and large-N limits, we present a comparison of our results to some of the numerical computations and analytical predictions available in the literature - including, in particular, those from holographic computations.

DecaysB(s)→a1(b1)D(s),a1(b1)D(s)*in the perturbative QCD approach

Within the framework of the perturbative QCD approach, we study the branching ratios of the two-body charmed decays ${B}_{(s)}\ensuremath{\rightarrow}{a}_{1}({b}_{1}){D}_{(s)}$, ${a}_{1}({b}_{1}){D}_{(s)}^{*}$, which, including Cabibbo-Kobayashi-Maskawa, allowed and suppressed decays. Our calculations are consistent with the currently available data and the experimental upper limits. Certainly, many of these predicted channels have not been measured by experiments and can be confronted with the future experimental data. We also discuss the polarization factions of the decays ${B}_{(s)}\ensuremath{\rightarrow}{a}_{1}({b}_{1}){D}_{(s)}^{*}$, some of which are sensitive to the distinct Gegenbauer moments of the wave functions and the decay constants of mesons ${a}_{1}$ and ${b}_{1}$.