QCD constituent counting rules for neutral vector mesons

Abstract

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 V 0 in e þ e − annihilation, processes in which the V 0 can couple via intermediate photons.In the case of a (narrow) real V 0 , the photon virtuality is fixed to a precise value s 1 ¼ m 2 V 0 , thus treating the V 0 as a single fundamental particle. Each real V 0 thus contributes to the constituent counting rules withIn effect, the leading operator underlying the V 0 has twist 1. Thus, in the specific physical case of single or double on-shell V 0 production via intermediate photons, the predicted scaling from counting rules coincides with vector-meson dominance (VMD), an effective theory that treats V 0 as an elementary field.However, the VMD prediction fails in the general case where the V 0 is not coupled through an elementary photon field, and then the leading-twist interpolating operator has twist N V 0 ¼ 2.

Using QCD counting rules to identify the production of gluonium

“…This would increase the counting rate as the neutral decays of the recoiling f 0 would be included. Multiparticle decays of the f 0 would not change the counting here, as the most likely quasi-collinear emission, not involving another highly virtual particle, does not cost an additional power of s, as recently emphasized [46].…”

Constituent Counting Rules and Exotic Hadrons

“…Away from this special point, the original expectations of [20] remain valid [21]. In particular, the inclusive forward cross section σ(e + e − → γγ * → γqq) scales as 1/|t| 2 , while V 0 created by hadronic processes (e.g., in pp scattering) no longer behave as though composed of a single constituent.…”

“…[20] that additional suppressions by α EM κ 2 /|t| or α 2 EM κ 4 /|t| 2 , respectively [where κ = O(Λ QCD )], arise when one or both of the photons convert to neutral vector mesons V 0 , are the cost of constraining the qq components of V 0 both to propagate in the forward direction. However, this result must be reassessed in light of the objection noted above, that obtaining the full naive scaling behavior requires all relevant lines in the diagram to carry large momentum transfers; if not, then the twist of the corresponding operator is smaller [21]. Such is the case (anticipated in [24]) when the photon couples solely to a single V 0 of fixed squared mass m 2 V 0 ≡ s 1 ; then the photon-which generically would have O(|t|) virtuality-carries a precisely fixed virtuality, s 1 .…”

“…This paper focuses upon the use of one of the earliest diagnostics of QCD, the constituent counting rules [17,18] developed in its first decade, and specifically upon their use to reveal the multiquark nature of heavy-quark states, as recently discussed in Refs. [19,20,21]. The counting rules are an expression of the approximate conformality and scale independence of QCD at high energies; formally, they give the leading-order scaling behavior of scattering amplitudes in terms of the twist dimension of the operator responsible for the process amplitude.…”

The Constituent Counting Rule and Omega Photoproduction

“…We will be looking at a kinematical range comparable to these previous studies. Recently, there has been a discussion in the literature about the applicability, limitations, and necessary conditions for the CCR [10,11]. Ref.…”