Three-hadron form factor via quark-triangle loop

Abstract

An explicit construction in a manifestly Lorentz-invariant and cyclically symmetric form is given for a three-hadron (H) coupling through their respective (qq̅) constituents interacting via a quark triangle loop under the most general conditions of unequal mass kinematics at both the elementary quark and composite-hadron levels. The only ansatz employed is that the Hqq̅ vertex function Γ_H at each vertex i is a function of q^{^}_i, the relative momentum transverse to the corresponding hadron momentum P _i, an assumption which can be justified from several independent angles. The resulting structure Γ _H≈D(q^{^})⊗Ψ(q^{^}), with D(q^{^}) 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.