Two-gluino bound states and heavy quarkonium

Abstract

A supersymmetric octet QCD, incorporating interacting gluons and gluinos, is formulated and used to discuss the features of two-gluino bound states. The short-range gluino-gluino potential is calculated and it is assumed that the complete potential, including the color-confining part, has the same form as the quark-antiquark potential but multiplied by the color factor derived for the short-range part. A spin-dependent mass formula based on a quark-antiquark potential of the Martin single-power type is fitted to the known triplet and singlet states of heavy quarkonia and is then used to make predictions of the mass spectra of $^{3}S$, $^{1}P$, and $^{3}D$ gluino-gluino bound states. It is found that the relative energy spacings of these states are almost independent of gluino mass ${m}_{\ensuremath{\lambda}}$ for ${m}_{\ensuremath{\lambda}}\ensuremath{\gtrsim}5$ GeV, the experimental lower limit.