Three-hadron form factor via quark-triangle loop

An explicit construction in a manifestly Lorentz-invariant and cyclically symmetric form is given for a three-hadron (H) coupling through their respective (q) constituents interacting via a quark triangle loop under the most general conditions of unequal mass kinematics atboth the elementary quark and composite-hadron levels. The only ansatz employed is that theHq vertex function ΓH at each vertexi is a function ofi, the relative momentumtransverse to the corresponding hadron momentumPi, an assumption which can be justified from several independent angles. The resulting structure, withD() being a model-independent function, has proved crucial for an explicit integration over the time-like component of the loop momentum, and thus provided an analytical, cyclically symmetric structure free of overlapping pole singularities. The applicational potential of this quantity is outlined.