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

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 $\delta$ 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 $(\omega ,\varphi )$ and $(\eta ,{\eta }^{\prime })$. 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.

Figure 1

The masses (and hyperfine splittings) and the corresponding decay constants of heavy quarkonia depending on the variation of the multiplicative factor $\lambda$, i.e., $\left(c\overline{c}\right)$ [(a) and (b)] with two different $\lambda \sigma =(1,2)\sigma$ and $\left(b\overline{b}\right)$ [(c) and (d)] with two different $\lambda \sigma =(1,3)\sigma$ values, respectively.

Figure 2

Fit of the ground state meson masses [MeV] with the parameters given in Tables 2 and 1 compared with the fit from our previous calculations using the CJ model [15] as well as the experimental values. The $(\pi ,\rho )$ masses are our input data. The $(\eta ,{\eta }^{\prime },\omega ,\varphi )$ masses are also used as input to find the $(\eta -{\eta }^{\prime })$ and $(\omega -\varphi )$ mixing angles. The theoretical error bars for $(c\overline{c},b\overline{c},b\overline{b})$ sectors are due to the usage of $\lambda =(2_{-1}^{+1},2.3_{-1}^{+1},3_{-2}^{+2})$ values, respectively.