Variational analysis of mass spectra and decay constants for ground state pseudoscalar and vector mesons in the light-front quark model

Abstract

Using the variational principle, we compute mass spectra and decay constants of ground state pseudoscalar and vector mesons in the light-front quark model (LFQM) with the QCD-motivated effective Hamiltonian including the hyperfine interaction. By smearing out the Dirac $\ensuremath{\delta}$ function in the hyperfine interaction, we avoid the issue of negative infinity in applying the variational principle to the computation of meson mass spectra and provide analytic expressions for the meson mass spectra. Our analysis with the smeared hyperfine interaction indicates that the interaction for the heavy meson sector including the bottom and charm quarks gets more point-like. We also consider the flavor mixing effect in our analysis and determine the mixing angles from the mass spectra of $(\ensuremath{\omega},\ensuremath{\phi})$ and $(\ensuremath{\eta},{\ensuremath{\eta}}^{\ensuremath{'}})$. Our variational analysis with the trial wave function including the two lowest order harmonic oscillator basis functions appears to improve the agreement with the data of meson decay constants and the heavy meson mass spectra over the previous computation handling the hyperfine interaction as perturbation.