QCD constituent counting rules for neutral vector mesons

QCD constituent counting rules define the scaling behavior of exclusive hadronic scattering and electromagnetic scattering amplitudes at high momentum transfer in terms of the total number of fundamental constituents in the initial and final states participating in the hard subprocess. The scaling laws reflect the twist of the leading Fock state for each hadron and hence the leading operator that creates the composite state from the vacuum. Thus, the constituent counting scaling laws can be used to identify the twist of exotic hadronic candidates such as tetraquarks and pentaquarks. Effective field theories must consistently implement the scaling rules in order to be consistent with the fundamental theory. Here, we examine how one can apply constituent counting rules for the exclusive production of one or two neutral vector mesons V0 in e+e- annihilation, processes in which the V0 can couple via intermediate photons. In the case of a (narrow) real V0, the photon virtuality is fixed to a precise value s1=mV02, thus treating the V0 as a single fundamental particle. Each real V0 thus contributes to the constituent counting rules with NV0=1. In effect, the leading operator underlying the V0 has twist 1. Thus, in the specific physical case of single or double on-shell V0 production via intermediate photons, the predicted scaling from counting rules coincides with vector-meson dominance (VMD), an effective theory that treats V0 as an elementary field. However, the VMD prediction fails in the general case where the V0 is not coupled through an elementary photon field, and then the leading-twist interpolating operator has twist NV0=2. Analogous effects appear in pp scattering processes.