The fine and hyperfine structure and dipole transitions of charmonium and bottonium in the two-step potential model

Abstract

The fine and hyperfine structure and dipole transitions of the charmonium\((c\bar c)\) and bottonium\((b\bar b)\) systems are investigated in a simple quark-confining, analytically solvable, nonrelativistic quarkantiquark (two-step) potential,V=Vv+Vs, whereVv is the fourth component of a vector potential andVs is a scalar potential. Our predictions for the splittings of theP-state multiplets and for the absolute masses of the vacious3PJ(Ξ) states of\((c\bar c)\) and\((b\bar b)\) systems are in good agreement with the data. For the hyperfine splittings of\((b\bar b)\) system we obtain\(M_\Upsilon - M_{\eta _b } = 42MeV\) and\(M_{\Upsilon '} - M_{\eta '_b } = 34MeV\), which are comparable with the other theoretical predictions. Our results for the dipole transition rates are also comparable with the available experimental data and with other theoretical predictions.