On the constituent counting rule for hard exclusive processes involving multi-quark states

At high energy, the cross section at finite scattering angle of a hard exclusive process falls off as a power of the Manderstam variable s. If all involved quark-gluon compositions undergo hard momentum transfers, the fall-off scaling is determined by the underlying valence structures of the initial and final hadrons, known as the constituent counting rule. In spite of the complication due to helicity conservation, it has been argued that when applied to exclusive process with exotic multiquark states, the counting rule is a powerful way to determine the valence degrees of freedom inside hadron exotics. In this work, we demonstrate that for hadrons with hidden flavors, the naive application of the constituent counting rule is problematic, since it is not mandatory for all components to participate in hard scattering at the scale sqrts. We illustrate the problems in the viewpoint based on effective field theory. We clarify the misleading results that may be obtained from the constituent counting rule in exclusive processes with exotic candidates such as Z_c^±(ccud/ccdu), Z_b^±(bbud/bbdu), X(3872), etc.