Coherently coupled two-component Bose-Einstein condensates (BEC) exhibit vortex confinement resembling quark confinement in quantum chromodynamics (QCD). Fractionally quantized vortices winding only in one of two components are attached by solitons, and they cannot stably exist alone. Possible stable states are "hadrons"either of mesonic type, i.e., molecules made of a vortex and antivortex in the same component connected by a soliton, or of baryonic type, i.e., molecules made of two vortices winding in two different components connected by a soliton. Mesonic molecules move straight with a constant velocity while baryonic molecules rotate. We numerically simulate collision dynamics of mesonic and baryonic molecules and find that the molecules swap partners in collisions in general like chemical and nuclear reactions, as well as summarizing all collisions as vortex reactions, and describe those by Feynman diagrams. We find a selection rule for final states after collisions of vortex molecules, analogous to that for collisions of hadrons in QCD.
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