Relativistic effects and the constituent quark model of heavy quarkonia

Abstract

Charmonium$c\bar c$ and bottomonium$b\bar b$ are investigated in the framework of a constituent quark model. A scalar confining and a one-gluon exchange (OGE) potential are used in a nonrelativistic reduction to order (p/m)². Therefore the model includes spin dependent as well as spin independent terms. Their influence on the meson mass spectra and decay widths is analysed. We find that the experimental spectra can be reproduced by using a full model as well as by using a reduced version neglecting the spin independent terms. For both versions we calculate leptonic and radiative decay widths including relativistic corrections for the current operators. We find that for leptonic decays inclusion of all terms of the OGE potential gives better results than the non-relativistic formulas. For radiative transitions relativistic corrections are important.