Role of QCD compositeness in the production of scalar and tensor mesons through single-photon annihilation $e^+ e^- \to \gamma^* \to \gamma S(T)$

TL;DR

This paper investigates the production of scalar and tensor mesons via single-photon annihilation, deriving their cross section scaling laws based on QCD compositeness, and compares different internal structures like quark-antiquark and tetraquark models.

Contribution

It provides theoretical predictions for the scaling behavior of meson production cross sections and transition form factors considering various internal meson structures.

Findings

Differential cross section scales as 1/s^3 at large s.

Transition form factors scale as 1/s for scalar and 1/s^2 for tensor mesons.

Tetraquark configurations exhibit similar falloff behaviors as quark-antiquark models.

Abstract

We study the exclusive production of scalar $S = 0^{++}$ and tensor $T = 2^{++}$ mesons through single-photon annihilation $e^+ e^- \to \gamma^* \to \gamma S(T)$. Using QCD compositeness of the involved hadrons considered as quark-antiquark systems, the prediction for the scaling of the differential cross sections of these processes is $d\sigma/dt \sim 1/s^3$ at large $s$. We further derive the scaling of the $\gamma^\ast \to \gamma S$ and $\gamma^\ast \to \gamma T$ transition form factors: $F_{\gamma^\ast\gamma S}(s) \sim 1/s$ and $F_{\gamma^\ast\gamma T}(s) \sim 1/s^2$. Results for the respective cross sections of the scalar and tensor meson production are presented. Note, when scalar and tensor mesons are considered as tetraquark systems of two tightly bound color diquarks, corresponding to them transition form factors and differential cross sections have the same falloffs as in case of quark-antiquark picture. For other tetraquark or two-hadron molecules configurations the transition form factors $F_{\gamma^\ast\gamma S(T)}(s)$ and the differential cross section $d\sigma/dt$ have additional $1/s$ and $1/s^2$ falloffs, respectively.