Annihilation rates of 3D2(2−−) and 3D3(3−−) heavy quarkonia

Abstract

We calculate the annihilation decay rates of the [Formula: see text] and [Formula: see text] charmonia and bottomonia by using the instantaneous Bethe–Salpeter (BS) method. The wave functions of states with quantum numbers [Formula: see text] and [Formula: see text] are constructed. By solving the corresponding instantaneous BS equations, we obtain the mass spectra and wave functions of the quarkonia. The annihilation amplitude is written within Mandelstam formalism and the relativistic corrections are taken into account properly. This is important, especially for high excited states, since their relativistic corrections are large. The results for the [Formula: see text] channel are as follows: [Formula: see text] keV, [Formula: see text] keV, [Formula: see text] keV and [Formula: see text] keV.