Deep inelastic scattering near the endpoint in soft-collinear effective theory

Abstract

We apply the soft-collinear effective theory to deep inelastic scattering near the endpoint region. The forward scattering amplitude and the structure functions are shown to factorize as a convolution of the Wilson coefficients, the jet functions, and the parton distribution functions. The behavior of the parton distribution functions near the endpoint region is considered. It turns out that it evolves with the Altarelli-Parisi kernel even in the endpoint region, and the parton distribution function can be factorized further into a collinear part and the soft Wilson line. The factorized form for the structure functions is obtained by the two-step matching, and the radiative corrections or the evolution for each factorized part can be computed in perturbation theory. We present the radiative corrections of each factorized part to leading order in ${\ensuremath{\alpha}}_{s}$, including the zero-bin subtraction for the collinear part.