Weak leptonic decay of light and heavy pseudoscalar mesons in an independent quark model

Abstract

Weak leptonic decays of light and heavy pseudoscalar mesons are studied in a field-theoretic frame-work based on the independent quark model with a scalar-vector harmonic potential. Defining the quark-antiquark momentum distribution amplitude obtainable from the bound quark eigenmodes of the model with the assumption of a strong correlation between quark-antiquark momenta inside the decaying meson in its rest frame, we derive the partial decay width with correct kinematical factors from which we extract an expression for the pseudoscalar decay constants ${f}_{M}$. Using the model parameters determined from earlier studies in the light-flavor sector and heavy-quark masses ${m}_{c}$ and ${m}_{b}$ from the hyperfine splitting of (${D}^{*}, D$) and (${B}^{*}, B$), we calculate the pseudoscalar decay constants. We find that while $({f}_{\ensuremath{\pi}}, {f}_{K})\ensuremath{\equiv}(138, 157 \mathrm{MeV})$; $({f}_{D}, {{f}_{D}}_{s})\ensuremath{\equiv}(161, 205 \mathrm{MeV})$, $({f}_{B}, {{f}_{B}}_{s})\ensuremath{\equiv}(122, 154 \mathrm{MeV})$, and ${{f}_{B}}_{c}=221$ MeV. We also obtain the partial decay widths and branching ratios for some kinematically allowed weak leptonic decay processes.