Probing quarkonium production mechanisms with jet substructure

We use fragmenting jet functions (FJFs) in the context of quarkonia to study the production channels predicted by NRQCD (³S₁ ⁽¹⁾, ³S₁ ⁽⁸⁾, ¹S₀ ⁽⁸⁾, ³P_J ⁽⁸⁾). We choose a set of FJFs that give the probability to find a quarkonium with a given momentum fraction inside a cone-algorithm jet with fixed cone size and energy. This observable gives several lever arms that allow one to distinguish different production channels. In particular, we show that at fixed momentum fraction the individual production mechanisms have distinct behaviors as a function of the the jet energy. As a consequence of this fact, we arrive at the robust prediction that if the depolarizing ¹S₀ ⁽⁸⁾ matrix element dominates, then the gluon FJF will diminish with increasing energy for fixed momentum fraction, z, and z >0.5.