QCD Constituent Counting Rules for Neutral Vector Mesons

TL;DR

This paper explores how QCD constituent counting rules apply to the production of neutral vector mesons in electron-positron annihilation, highlighting the conditions under which these rules align with or differ from vector meson dominance models.

Contribution

It clarifies the application of constituent counting rules to neutral vector meson production and distinguishes between scenarios where VMD predictions hold or fail.

Findings

Counting rules match VMD when V^0 is treated as an elementary particle.

For off-shell or non-elementary V^0, the scaling differs, with twist 2 operators dominating.

Analogous effects are observed in proton-proton scattering processes.

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 $e^+ e^-$ annihilation, processes in which the $V^0$ can couple via intermediate photons. In case of a (narrow) real $V^0$, the photon virtuality is fixed to a precise value $s_1 = m_{V^0}^2$, in effect treating the $V^0$ as a single fundamental particle. Each real $V^0$ thus contributes to the constituent counting rules with $N_{V_0} = 1$. In 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 $N_{V_0} = 2$. Analogous effects appear in $pp$ scattering processes.