Helicity selection rules and tests of gluon spin in exclusive quantum-chromodynamic processes

Abstract

We show how the helicity and angular dependence of large-momentum-transfer exclusive processes can be used to test the gluon spin and other basic elements of perturbative quantum chromodynamics (QCD). Unlike inclusive reactions, these processes isolate QCD hard-scattering subprocesses in situations where the helicities of all the interacting quarks are controlled. The predictions can be summarized in terms of a general spin selection rule which states that the total hadron helicity is conserved ($\Sigma {\mathrm{initial}}^{}{\lambda }_H=\Sigma {\mathrm{final}}^{}{\lambda }_H$) up to corrections falling as an inverse power in the momentum transfer. In particular, the hadrons in $e^{+}{e}^{-}\to {\gamma }^{*}\to h_A+{\overline{h}}_B$ are produced at large $Q^2$ with opposite helicity ${\lambda }_A+{\lambda }_B=0\mathrm{}$, and $\left|{\lambda }_i\right|\le \frac{1}{2}$. This also implies $\frac{d\sigma }{d}cos\theta \propto (1+{cos}^2\theta )$ for all baryon pairs and $\frac{d\sigma }{d}cos\theta \propto {sin}^2\theta$ for all meson pairs, to leading order in $\frac{1}{Q}$. Applications to many processes are given, including electroweak form factors, two-photon processes, hadron-hadron scattering, and heavy-quark decays (e.g., $\psi \to p\overline{p}$).