Light Front Quark Model Analysis Of Electroweak Decays Of Pseudoscalar And Vector Mesons

We present a relativistic constituent quark model to analyze the mass spectrum and hadronic properties of radially excited u and d quark sector mesons. Using a simple Gaussian function as a trial wave function for the variational principle together with a QCD motivated Hamiltonian, including not only the Coulomb and confining potential but also a relativistic corrected hyperfine interaction term, we obtain the mass spectrum consistent with the experimental data. To do the same for several observables such as decay constants and form factors it seems necessary to include bothDirac and Pauli form factors on the level of constituent quarks. Taking into account these quark form factors we thus present the generalized formulas for the rho meson decay constant and the rho meson form factors as well asthe $\pi\gamma$ transition form factor. We alsopredict several hadronic properties for the radially excited states.

We use the light-front quark model to investigate the structure of the scalar mesons, mainly focusing on the three heavy isoscalar states f0(1370), f0(1500), and f0(1710). We comput the spectrum of scalar mesons by diagonalizing a relativized, QCD-inspired model Hamiltonian written in a basis of 25 simple harmonic oscillator states. The masses are then used to perform a mixing analysis which assumes that the heavy isoscalars are mixtures of quarkonia and the scalar glueball. The resulting quark-glue content is used along with the meson wave functions determined from the spectrum to compute the decay rates to pairs of pseudoscalar mesons (two pions, two kaons, two eta mesons). We find that when the glueball contributions to the decays are ignored, the results are in poor agreement with the available data. However, when we estimate the effect of including the glueball contributions in the decays, a solution can be found that matches the data quite well. In this solution, the f0(1710) is mostly glueball (78%) while the f0(1500) and f0(1370) are mostly mixtures of quarkonia. Additionally, in this solution the glueball contributions to kaon and eta final states are significant, while the contributions to the pion final state is negligible. This finding is in agreement with Chanowitz who uses chiral perturbation theory to show that the amplitude for a scalar glueball to decay to a quark-antiquark pair is proportional to the quark mass. This results in a suppression of the pion decay channel compared to the kaon and eta decay channels.

Keywords: quark model, light front, scalar meson, glueball, mixing, hadronic decay, treacherous points, lfd, light front dynamics.