Radiative Scalar Meson Decays in the Light-Front Quark Model

Abstract

We construct a relativistic $^3P_0$ wavefunction for scalar mesons within the framework of light-front quark model(LFQM). This scalar wavefunction is used to perform relativistic calculations of absolute widths for the radiative decay processes$(0^{++})\toγγ,(0^{++})\toϕγ$, and $(0^{++})\toργ$ which incorporate the effects of glueball-$q\bar{q}$ mixing. The mixed physical states are assumed to be $f_0(1370),f_0(1500)$,and $f_0(1710)$ for which the flavor-glue content is taken from the mixing calculations of other works. Since experimental data for these processes are poor, our results are compared with those of a recent non-relativistic model calculation. We find that while the relativistic corrections introduced by the LFQM reduce the magnitudes of the decay widths by 50-70%, the relative strengths between different decay processes are fairly well preserved. We also calculate decay widths for the processes $ϕ\to(0^{++})γ$ and $(0^{++})\toγ\gamm$ involving the light scalars $f_0(980)$ and $a_0(980)$ to test the simple $q\bar{q}$ model of these mesons. Our results of $q\bar{q}$ model for these processes are not quite consistent with well-established data, further supporting the idea that $f_0(980)$ and $a_0(980)$ are not conventional $q\bar{q}$ states.