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

Abstract

We study the exclusive double-photon annihilation processes, $e^{+}{e}^{-}\to \gamma {\gamma }^{\ast }\to \gamma V^0$ and $e^{+}{e}^{-}\to {\gamma }^{\ast }{\gamma }^{\ast }\to V_a^0{V}_b^0,$ where the $V_i^0$ is a neutral vector meson produced in the forward kinematical region: $s\gg -t$ and $-t\gg {\Lambda }_{\mathrm{QCD}}^2$. 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-${\theta }_{\mathrm{CM}}$ 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 $\sigma (e^{+}{e}^{-}\to V_a^0{V}_b^0),$ integrated over the dominant forward- and backward-${\theta }_{\mathrm{CM}}$ 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.

Comments: 10 pages