Generalized Counting Rule for Hard Exclusive Processes

Abstract

We derive a generalized counting rule for hard exclusive processes involving parton orbital angular momentum and hadron helicity flip. We start with a systematic way to enumerate the Fock components of a hadronic light-cone wave function with $n$ partons and orbital angular momentum projection ${l}_{z}$. We show that the wave-function amplitude ${\ensuremath{\psi}}_{n}({x}_{i},{k}_{i\ensuremath{\perp}},{l}_{zi})$ has a leading behavior $1/({k}_{\ensuremath{\perp}}^{2}{)}^{[n+|{l}_{z}|+\mathrm{m}\mathrm{i}\mathrm{n}({n}^{\ensuremath{'}}+|{l}_{z}^{\ensuremath{'}}|)]/2\ensuremath{-}1}$ when all parton transverse momenta are uniformly large, where ${n}^{\ensuremath{'}}$ and ${l}_{z}^{\ensuremath{'}}$ are the number of partons and orbital angular momentum projection, respectively, of an amplitude that mixes under renormalization. Besides the generalized counting rule, the result can be used as a constraint in modeling the hadronic light-cone wave functions.