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

摘要

We study the exclusive double-photon annihilation processes, $e^+ e^- \to\gamma \gamma^\ast\to \gamma V^0$ and $e^+ e^- \to \gamma^\ast \gamma^\ast \toV^0_a V^0_b,$ where the $V^0_i$ is a neutral vector meson produced in theforward kinematical region: $s \gg -t$ and $-t \gg \Lambda_{\rm QCD}^2$. Weshow how the differential cross sections $\frac{d\sigma}{dt}$, as predicted byQCD, have additional falloff in the momentum transfer squared $t$ due to theQCD compositeness of the hadrons, consistent with the leading-twistfixed-$\theta_{\rm CM} $ scaling laws. However, even though they are exclusivechannels and not associated with the conventional electron-positronannihilation process $e^+ e^- \to \gamma^\ast \to q \bar q,$ these total crosssections $\sigma(e^+ e^- \to \gamma V^0) $ and $\sigma(e^+ e^- \to V^0_aV^0_b),$ integrated over the dominant forward- and backward-$\theta_{\rm CM}$angular domains, scale as $1/s$, and thus contribute to the leading-twistscaling behavior of the ratio $R_{e^+ e^-}$. We generalize these results toexclusive double-electroweak vector-boson annihilation processes accompanied bythe 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 productionof exotic hadrons such as tetraquarks, where the cross-section scaling behaviorcan reveal their multiquark nature.