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 pointlike. We also consider the flavor mixing effect in our analysis and determine the mixing angles from the mass spectra of (ω, φ ) and (η, η ). 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.

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We investigate the QCD magnetic susceptibility χ at the finite quark-chemical potential (µ = 0) and at zero temperature (T = 0) to explore the pattern of the magnetic phase transition of the QCD vacuum. For this purpose, we employ the nonlocal chiral quark model derived from the instanton vacuum in the presence of the chemical potential in the chiral limit. Focusing on the Nambu-Goldstone phase, we find that the magnetic susceptibility remains almost stable to µ ≈ 200 MeV, and falls down drastically until the the quark-chemical potential reaches the critical point µ c ≈ 320 MeV. Then, the strength of the χ is reduced to be about a half of that at µ = 0, and the first-order magnetic phase transition takes place, corresponding to the chiral restoration. From these observations, we conclude that the response of the QCD vacuum becomes weak and unstable to the external electromagnetic field near the critical point, in comparison to that for vacuum. It is also shown that the breakdown of Lorentz invariance for the magnetic susceptibility, caused by the finite chemical potential, turns out to be small.

We investigate the (π 0 , η, η ) → γ * γ transitions both for the spacelike region and the timelike region using the light-front quark model (LFQM). In particular, we present the new direct method to explore the timelike region without resorting to mere analytic continuation from the spacelike region to the timelike region. Our direct calculation in timelike region shows the complete agreement not only with the analytic continuation result from the spacelike region but also with the result from the dispersion relation between the real and imaginary parts of the form factor. For the low energy regime, we compare our LFQM results of the transition form factors (TFFs) for the low timelike momentum transfer region and the slope parameters at q 2 = 0 with the recent experimental data from the Dalitz decays of (π 0 , η, η ). For the high energy regime, we incorporate the QCD factorization in our LFQM to examine the asymptotic behavior of TFFs both for the spacelike region and the timelike region. We compare our results with the available experimental data.