Decay constants and mixing parameters in a relativistic model for aqQ¯system

Abstract

We extend our recent work, in which the Dirac equation with a "(asymptotically free) Coulomb + (Lorentz scalar γ 0 σr) linear " potential is used to obtain the light quark wavefunction for qQ mesons in the limit m Q → ∞, to estimate the decay constant f P and the mixing parameter B of the pseudoscalar mesons. We compare our results for the evolution of f P and B with the meson mass M P to the non-relativistic formulas for these quantities and show that there is a significant correction in the subasymptotic region. For σ = 0.14 GeV −2 and Λ M S = 0.240 GeV we obtain: f D = 0.371 , f Ds = 0.442 , f B = 0.301 , f Bs = 0.368 GeV and B D = 0.88 , B Ds = 0.89 , B B = 0.95 , B Bs = 0.96 , and B K = 0.60.

The dependence of the emission size on the hadron mass

“…which is widely used to derive the wave functions and decay constants of hadrons [17]. This can be seen by comparing in Fig.…”

“…(13) to an equality and evaluating Eq. (14) with the V (r) parameter values of κ = 0.14 GeV 2 = 0.70 GeV/fm and α s = 2π/9 ln(δ + γ/r) with δ = 2 and γ = 1.87 GeV −1 = 0.37 fm obtained from the hadron wave functions and decay constants [17].…”

Bose Einstein and Fermi Dirac interferometry in particle physics

“…widely used to derive the wave functions and decay constants of hadrons [111,112]. Setting the potential parameters values to κ = 0.14 GeV 2 = 0.70 GeV/fm , α s = 2π/9 ln(δ + γ/r) with δ = 2 and γ = 1.87 GeV −1 = 0.37 fm as derived from hadron wave functions and decay constants [111], the resulting dependence of r on the hadron mass, given by the solid thick line in Fig. 14, is seen to follow rather well the the data.…”

Parton-hadron duality in QCD sum rules: Quantum-mechanical examples

“…Since we do not wish to introduce any uncertainty due to the logarithm factorisation, we fix the running coupling constant α s at some value. A special choice of the parameters is not important for our analysis, but to be concrete we choose some quasi-realistic ones [22]: the string tension α = 0.14 GeV 2 ; δ = 2; γ = 1.87 GeV −1 ; for the constituent mass we take m = 0.35 GeV. When related problems are investigated within QCD the running coupling constant α s is usually of order 0.3.…”