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

We study the exclusive double-photon annihilation processes, $e^+ e^- \to γγ^\ast\to γV^0$ and $e^+ e^- \to γ^\ast γ^\ast \to V^0_a V^0_b,$ where the $V^0_i$ is a neutral vector meson produced in the forward kinematical region: $s \gg -t$ and $-t \gg Λ_{\rm QCD}^2$. We show how the differential cross sections $\frac{dσ}{dt}$, 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-$θ_{\rm CM}$ scaling laws. However, even though they are exclusive channels and not associated with the conventional electron-positron annihilation process $e^+ e^- \to γ^\ast \to q \bar q,$ these total cross sections $σ(e^+ e^- \to γV^0)$ and $σ(e^+ e^- \to V^0_a V^0_b),$ integrated over the dominant forward- and backward-$θ_{\rm CM}$ 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 $e^+ e^- \to W^-ρ^+$. 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.

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