Dynamical relativistic corrections to the leptonic decay width of heavy quarkonia

Abstract

We calculate the dynamical relativistic corrections, originating from radiative one-gluon-exchange, to the leptonic decay width of heavy quarkonia in the framework of a covariant formulation of Light-Front Dynamics. Comparison with the non-relativistic calculations of the leptonic decay width of J=1 charmonium and bottomonium S-ground states shows that relativistic corrections are large. Most importantly, the calculation of these dynamical relativistic corrections legitimate a perturbative expansion in $α_s$, even in the charmonium sector. This is in contrast with the ongoing belief based on calculations in the non-relativistic limit. Consequences for the ability of several phenomenological potential to describe these decays are drawn.