Threshold factorization of the Drell-Yan process at next-to-leading power

Abstract

Abstract We present a factorization theorem valid near the kinematic threshold z = Q 2 / s ̂ → 1 $$ z={Q}^2/\hat{s}\to 1 $$ of the partonic Drell-Yan process q q ¯ → γ ∗ + X $$ q\overline{q}\to {\gamma}^{\ast }+X $$ for general subleading powers in the (1 − z) expansion. We then consider the specific case of next-to-leading power. We discuss the emergence of collinear functions, which are a key ingredient to factorization starting at next-to-leading power. We calculate the relevant collinear functions at O α s $$ \mathcal{O}\left({\alpha}_s\right) $$ by employing an operator matching equation and we compare our results to the expansion-by- regions computation up to the next-to-next-to-leading order, finding agreement. Factorization holds only before the dimensional regulator is removed, due to a divergent convolution when the collinear and soft functions are first expanded around d = 4 before the convolution is performed. This demonstrates an issue for threshold resummation beyond the leading-logarithmic accuracy at next-to-leading power.

Keywords

• Effective Field Theories
• Perturbative QCD
• Resummation