  PHENIX has measured the azimuthal correlations of muon pairs from charm and
bottom semi-leptonic decays in $p$+$p$ collisions at $\sqrt{s}=200$ GeV, using
a novel analysis technique utilizing both unlike- and like-sign muon pairs to
separate charm, bottom and Drell-Yan contributions. The dimuon measurements
combined with the previous electron-muon and dielectron measurements span a
wide range in rapidity, and are well described by PYTHIA Tune A. Through a
Bayesian analysis based on PYTHIA Tune A, we show that leading order pair
creation is the dominant $(76\%\pm^{14}_{19}\%)$ contribution for $b\bar{b}$
production, whereas the data favor the scenario in which next-to-leading-order
processes dominate $c\bar{c}$ production. The small contribution of
next-to-leading-order processes in $b\bar{b}$ production at the collision
energies of the Relativistic Heavy Ion Collider contrasts with the case at
Large-Hadron-Collider energies, where next-to-leading-order processes are
expected to dominate.
