Soft Wilson lines in the soft-collinear effective theory

Abstract

The effects of the soft gluon emission in hard scattering processes at the phase boundary are resummed in the soft-collinear effective theory (SCET). In SCET, the soft gluon emission is decoupled from the energetic collinear part, and is obtained by the vacuum expectation value of the soft Wilson-line operator. The form of the soft Wilson lines is universal in deep inelastic scattering, in the Drell-Yan process, in the jet production from ${e}^{+}{e}^{\ensuremath{-}}$ collisions, and in the ${\ensuremath{\gamma}}^{*}{\ensuremath{\gamma}}^{*}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}$ process, but its analytic structure is slightly different in each process. The anomalous dimensions of the soft Wilson-line operators for these processes are computed along the lightlike path at leading order in SCET and to first order in ${\ensuremath{\alpha}}_{s}$, and the renormalization group behavior of the soft Wilson lines is discussed.