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

We present a factorization theorem valid near the kinematic threshold z= Q²/ ŝ → 1 of the partonic Drell-Yan process qq¯ → γ^∗+ 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) 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.