Factorization of Power Corrections in the Drell-Yan Process in EFT

We examine the quark-induced Drell-Yan process at next-to-leading power (NLP) in Soft-Collinear Effective Theory. Using an approach with no explicit soft or collinear modes, we discuss the factorization of the differential cross section in the small-$q_T$ hierarchy with $q^2\gg q_T^2\gg\Lambda_{\mathrm{QCD}}^2$. We show that the cross section may be written in terms of matrix elements of power-suppressed operators $T_{(i,j)}$, which contribute to $O(q_T^2/q^2)$ coefficients of the usual parton distribution functions. We derive a factorization for this observable at NLP which allows the large logarithms in each of the relevant factors to be resummed. We discuss the cancellation of rapidity divergences and the overlap subtractions required to eliminate double counting at next-to-leading power.