Proton-Proton Near-Forward Hard Elastic Scattering
  We calculate the leading twist contribution to near-forward proton-proton (and proton-antiproton) elastic scattering with large momentum transfer, in the multiple scattering (Landshoff) mechanism. The amplitude in the near-forward region is dominated by singlet exchange for all three valence quark-quark scatterings. We assume the existence of a hard singlet quark-quark amplitude, which we estimate to be ${\cal O}(\alpha_s^2/t)$. For a three-quark state whose transverse size is less than $1/\Lambda_{\rm QCD}$, Sudakov resummation accounts for both approximate $\d \sigma^{pp}/ \d t \sim t^{-8}$ at moderate $t$, and $\d \sigma^{pp}/ \d t \sim t^{-10}$ at larger $t$. The transition from approximate $t^{-8}$ to $t^{-10}$ behavior is strongly correlated with the transverse size of the valence three-quark state in the proton. 
Michael G. Sotiropoulos and George Sterman