Update on the Light-Front Quark Model and Mass Spectrum Calculations for Ground State Pseudoscalar and Vector Mesons

TL;DR

This paper updates the light-front quark model for meson mass spectra, improving accuracy by smearing the hyperfine interaction and expanding the basis, leading to better agreement with experimental data.

Contribution

It introduces a novel approach to handle hyperfine interactions in the light-front quark model, enhancing the accuracy of meson mass and decay constant calculations.

Findings

Improved fit for ground state pseudoscalar and vector meson masses.

Decay constants show better agreement with experimental data.

Smearing hyperfine interaction avoids divergence issues.

Abstract

We present an update on the meson mass spectra calculation with the light-front quark model constrained by the variational principle for the QCD-motivated effective Hamiltonian. By smearing out the Dirac delta function in the hyperfine interaction, we were able to avoid the negative infinity that one encounters when using variational principle for the entire Hamiltonian. We obtained a better fitting for the mass spectra of ground state pseudoscalar and vector mesons from $\pi$ to $\Upsilon$, compared to the previous calculation that handled the hyperfine interaction as a perturbation rather than including it in the parameterization process. Our new parameters are further tested in decay constant calculation. We showed that by taking a larger harmonic oscillator basis in our trial wave function, the decay constants calculated from our model can be improved to agree reasonably well with the experimental data.