Infrared behavior of non-Abelian gauge theories

Abstract

Infrared singularities in non-Abelian gauge (Yang-Mills) theories are studied in the leading-logarithm approximation. In addition to the usual infrared limit in which the infrared cutoff $\ensuremath{\mu}$ approaches zero for fixed on-shell momenta, we consider high-energy wide-angle scattering and form factors at large momentum transfer $t$ in which infrared-induced powers of ${g}^{2}{\mathrm{ln}}^{2}t$ ($g=\mathrm{coupling}\mathrm{constant}$) typical of vector field theories appear in perturbation expansions. Our techniques include asymptotic estimates of Feynman integrals (to sixth order) and a nonperturbative approach based on a conjectured formula for soft-meson emission. Remarkably, the logarithms sum up into exponential factors much as in QED. Unlike QED, cross sections for production of nonsinglet particles, even including an indefinite number of soft gauge quanta, vanish as $\ensuremath{\mu}\ensuremath{\rightarrow}0$, a phenomenon we interpret as evidence of particle confinement. We discuss exclusive hadronic processes in the context of the non-Abelian quark-gluon theory based on color SU(3). We find justification for the scaling laws at large momentum transfers ("quark counting rules") in that the infrared logarithms cancel in the scaling pieces of hadronic amplitudes while providing a fast damping of the "pinch" contributions associated with Landshoff graphs.