  Coherently coupled two-component Bose-Einstein condensates (BEC) exhibit
vortex confinement resembling quark confinement in Quantum Chromo Dynamics
(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 anti-vortex 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 a
partner in collisions in general like chemical and nuclear reactions, summarize
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.
