Decay constants of the pseudoscalar mesons in the framework of the coupled Schwinger-Dyson equation and Bethe-Salpeter equation

Abstract

In this article, we investigate the structures of the pseudoscalar mesons ($\pi$, $K$, $D$, $D_s$, $B$ and $B_s$) in the framework of the coupled rainbow Schwinger-Dyson equation and ladder Bethe-Salpeter equation with the confining effective potential (infrared modified flat bottom potential). The Schwinger-Dyson functions for the $u$, $d$ and $s$ quarks are greatly renormalized at small momentum region and the curves are steep at about $q^2=1Ge{V}^2$ which indicates an explicitly dynamical symmetry breaking. The Euclidean time fourier transformed quark propagators have no mass poles in the time-like region which naturally implements confinement. As for the $c$ and $b$ quarks, the current masses are very large, the renormalization are more tender, however, mass poles in the time-like region are also absent. The Bethe-Salpeter wavefunctions for those mesons have the same type (Gaussian type) momentum dependence and center around small momentum which indicate that the bound states exist in the infrared region. The decay constants for those pseudoscalar mesons are compatible with the values of experimental extractions and theoretical calculations, such as lattice simulations and QCD sum rules.

10 pages, 4 figures, Revised Version

References in corpus (24)

• Heavy Quark Symmetry
• Dyson-Schwinger Equations and the Application to Hadronic Physics
• Dyson-Schwinger Equations: Density, Temperature and Continuum Strong QCD
• Dyson-Schwinger equations: a tool for hadron physics
• pi- and K-meson Bethe-Salpeter Amplitudes
• Bethe-Salpeter Study of Vector Meson Masses and Decay Constants
• Pion mass and decay constant
• Hadron Physics from the Global Color Model of QCD
• Analysis of a quenched lattice-QCD dressed-quark propagator
• Confinement and complex singularities in QED3
• q\bar q$ bound states in the Bethe-Salpeter formalism
• Survey of heavy-meson observables
• Predictions on $B\to \pi \bar{l}{\nu }_l$, $D\to \pi \bar{l}{\nu }_l$ and $D\to K\bar{l}{\nu }_l$ from QCD Light-Cone Sum Rules
• f_B and f_B_s from QCD sum rules
• Heavy-Light Meson Decay Constant from QCD Sum Rules in Three-Loop Approximation
• c,b quark masses and f_D_(s), f_B_(s) decay constants from pseudoscalar sum rules in full QCD to order alpha_s^2
• Perturbative QCD Correction to the Light-Cone Sum Rule for the $B^{\ast }B\pi$ and $D^{\ast }D\pi$ Couplings
• Semileptonic decays of heavy mesons
• Heavy- to light-meson transition form factors
• Heavy--light decay constants in the continuum limit of quenched lattice QCD
• Decay constants of the pion and B mesons with the Bethe-Salpeter equation
• Calculation of some properties of the vacuum
• Dynamical symmetry breaking, confinement with flat-bottom potential
• Dyson-Schwinger studies of meson masses and decay constants

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