QCD Compositeness as Revealed in Exclusive Vector Boson Reactions through Double-Photon Annihilation: $e^+ e^- \to \gamma \gamma^\ast \to \gamma V^0 $ and $e^+ e^- \to \gamma^\ast \gamma^\ast \to V^0 V^0$

TL;DR

This paper investigates how exclusive double-photon annihilation processes in electron-positron collisions reveal QCD compositeness through specific scaling laws and cross-section behaviors, including potential insights into exotic hadrons.

Contribution

It demonstrates the QCD-based scaling laws for exclusive vector meson production and extends the analysis to electroweak processes and exotic hadron production.

Findings

Differential cross sections exhibit additional falloff due to QCD compositeness.

Total cross sections scale as 1/s, contributing to leading-twist behavior.

Results applicable to exotic hadron production and multiquark states.

Abstract

We study the exclusive double-photon annihilation processes, $e^+ e^- \to \gamma \gamma^\ast\to \gamma V^0$ and $e^+ e^- \to \gamma^\ast \gamma^\ast \to V^0_a V^0_b,$ where the $V^0_i$ is a neutral vector meson produced in the forward kinematical region: $s \gg -t$ and $-t \gg \Lambda_{\rm QCD}^2$. We show how the differential cross sections $\frac{d\sigma}{dt}$, as predicted by QCD, have additional falloff in the momentum transfer squared $t$ due to the QCD compositeness of the hadrons, consistent with the leading-twist fixed-$\theta_{\rm CM} $ scaling laws. However, even though they are exclusive channels and not associated with the conventional electron-positron annihilation process $e^+ e^- \to \gamma^\ast \to q \bar q,$ these total cross sections $\sigma(e^+ e^- \to \gamma V^0) $ and $\sigma(e^+ e^- \to V^0_a V^0_b),$ integrated over the dominant forward- and backward-$\theta_{\rm CM}$ angular domains, scale as $1/s$, and thus contribute to the leading-twist scaling behavior of the ratio $R_{e^+ e^-}$. We generalize these results to exclusive double-electroweak vector-boson annihilation processes accompanied by the forward production of hadrons, such as $e^+ e^- \to Z^0 V^0$ and $e^+ e^- \to W^-\rho^+$. These results can also be applied to the exclusive production of exotic hadrons such as tetraquarks, where the cross-section scaling behavior can reveal their multiquark nature.