  We propose two new analysis strategies for studying charm and beauty quarks
at colliders. The first strategy is aimed at testing the kinematics of
heavy-flavor quarks within an identified jet. Here, we use the SoftDrop
jet-declustering algorithm to identify two subjets within a large-radius jet,
using subjet flavor tagging to test the heavy-quark splitting functions of QCD.
For subjets containing a $J / \psi$ or $\Upsilon$, this declustering technique
can also help probe the mechanism for quarkonium production. The second
strategy is aimed at isolating heavy-flavor production from gluon splitting.
Here, we introduce a new FlavorCone algorithm, which smoothly interpolates from
well-separated heavy-quark jets to the gluon-splitting regime where jets
overlap. Because of its excellent ability to identify charm and beauty hadrons,
the LHCb detector is ideally suited to pursue these strategies, though similar
measurements should also be possible at ATLAS and CMS. Together, these SoftDrop
and FlavorCone studies should clarify a number of aspects of heavy-flavor
physics at colliders, and provide crucial information needed to improve
heavy-flavor modeling in parton-shower generators.
