Mixing angles and electromagnetic properties of ground state pseudoscalar and vector meson nonets in the light-cone quark model

Abstract

Both the mass spectra and the wave functions of the light pseudoscalar ($\pi ,K,\eta ,{\eta }^{\prime }$) and vector($\rho ,K^{\ast },\omega ,\varphi$) mesons are analyzed within the framework of the light-cone constituent quark model. A gaussian radial wave function is used as a trial function of the variational principle for a QCD motivated Hamiltonian which includes not only the Coulomb plus confining potential but also the hyperfine interaction to obtain the correct $\rho -\pi$ splitting. For the confining potential, we use (1) harmonic oscillator potential and (2) linear potential and compare the numerical results for these two cases. The mixing angles of $\omega -\varphi$ and $\eta -{\eta }^{\prime }$ are predicted and various physical observables such as decay constants, charge radii, and radiative decay rates $etc.$ are calculated. Our numerical results in two cases (1) and (2) are overall not much different from each other and have a good agreement with the available experimental data. use (1) harmonic oscillator potential and (2) linear potential and compare the numerical results for these two cases. The mixing angles of $\omega -\varphi$ and $\eta -{\eta }^{\prime }$ are predicted and various physical observables such as decay constants, charge radii, and radiative decay rates $etc.$ are calculated. Our numerical results in two cases (1) and (2) are overall not much different from each other and have a good agreement with the available experimental data.

Comments: 22 pages, 10 figures, to appear in Phys. Rev. D