Gauge invariance of the resummation approach to evolution equations

Abstract

We show that the Collins-Soper-Sterman resummation approach to the derivation of the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi equation is gauge invariant. The special gauge-dependent parton distribution function employed in the resummation technique is expressed as the convolution of an infrared finite function with the standard distribution function. By means of this convolution relation, we explain how the technique works in summing large logarithmic corrections, and how the gauge invariance of the special distribution function is restored.