Polarized deep inelastic scattering as x → 1 using soft collinear effective theory

A bstract We use Soft Collinear Effective Theory (SCET) to factorize the polarized Deep Inelastic Scattering (DIS) structure functions g 1 ( x ) and g 2 ( x ), and to sum Sudakov double logarithms of 1 − x . The analysis is done both in terms of lightcone parton distributions and their moments. Computing g 2 requires subleading SCET operators which contain gluons. We calculate the one-loop matching coefficients from QCD onto these subleading SCET operators, and the one-loop matching from SCET onto the parton distribution function (PDF). The PDF in SCET is given by a bilocal operator, rather than the trilocal operator used in the QCD analysis of g 2 for generic x . We compute the one-loop anomalous dimension of the PDF operator for any x , and show that as x → 1, it factors into a single-variable evolution. We comment on the QCD anomalous dimensions of twist-three operators, their equation-of-motion relation, and connection to the SCET analysis. We briefly discuss the definition of axial operators in the BMHV scheme. As a side result, we derive the 1/ N dependence of the QCD coefficient functions for F 1 , F L and g 1 in the N → ∞ limit, where N is the moment, which is expected to hold to all orders in α s .