Z -> b b-bar b b-bar in the light gluino and light sbottom scenario

The light gluino (12 - 16 GeV) and light sbottom (2 - 6 GeV) scenario has been used to explain the apparent overproduction of b-quarks at the Tevatron. This scenario also predicts the decay Z -> b b-bar ~g ~g where the gluinos subsequently decay into b-quarks and sbottoms. We show that this can contribute to the width Gamma_4b = Gamma(Z -> b b-bar b b-bar) since most of the sbottoms and b-quarks arising from gluino decay have a small angular separation. We find that while no excess in Gamma_4b is observable due to large uncertainties in experimental measurements, the ratio Gamma(Z -> b b-bar ~g ~g)/Gamma(Z -> b b-bar b b-bar) can be large due to sensitivity to b-quark mass, the sbottom mixing angle and the gluino mass. We calculate it to be in the range 0.05 - 0.41 inclusive of the entire parameter space.