Hard scattering factorization from effective field theory

Abstract

In this paper we show how gauge symmetries in an effective theory can be used to simplify proofs of factorization formulas in highly energetic hadronic processes. We use the soft-collinear effective theory, generalized to deal with back-to-back jets of collinear particles. Our proofs do not depend on the choice of a particular gauge, and the formalism is applicable to both exclusive and inclusive factorization. As examples we treat the $\ensuremath{\pi}\ensuremath{-}\ensuremath{\gamma}$ form factor $(\ensuremath{\gamma}{\ensuremath{\gamma}}^{*}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}),$ light meson form factors $({\ensuremath{\gamma}}^{*}\stackrel{\ensuremath{\rightarrow}}{M}M),$ as well as deep inelastic scattering ${(e}^{\ensuremath{-}}\stackrel{\ensuremath{\rightarrow}}{p}{e}^{\ensuremath{-}}X),$ the Drell-Yan process $(p\overline{p}\ensuremath{\rightarrow}{\mathrm{Xl}}^{+}{l}^{\ensuremath{-}}),$ and deeply virtual Compton scattering $({\ensuremath{\gamma}}^{*}\stackrel{\ensuremath{\rightarrow}}{p}{\ensuremath{\gamma}}^{(*)}p).$