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

Abstract

We present a factorization theorem valid near the kinematic threshold z = Q 2 /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-byregions 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.

Factorization at subleading power and endpoint divergences in h → γγ decay. Part II. Renormalization and scale evolution

“…We have derived the corresponding evolution equations at two-loop order in two recent papers. For the jet function one finds [25,31] 8) which in this form holds for both space-like and time-like values of p 2 . The anomalous dimension is given by…”

“…Much recent work has focused on exploring the structure of factorization at subleading order in power counting -a problem that turns out to be unexpectedly subtle and full of complexities. Specific applications discussed in the literature include the study of power corrections to event shapes [4] and transverse-momentum distributions [5,6], the threshold factorization for the Drell-Yan process [7,8], and the factorization of power-suppressed contributions to Higgs-boson decays [9,10]. One finds that such factorization theorems contain a sum over convolutions of Wilson coefficients with operator matrix elements, where the relevant SCET operators mix under renormalization.…”

“…Several new complications arise, which do not occur at leading power. The most puzzling one is the appearance of endpoint-divergent convolution integrals over products of component functions each depending on a single scale [6,[8][9][10][11][12][13][14]. In some sense, such endpoint divergences indicate a failure of dimensional regularization and the MS subtraction scheme, because some of the 1/ n pole terms are not removed by renormalizing the individual component functions, and hence naive scale separation is violated.…”

On next to soft threshold corrections to DIS and SIA processes

“…It was found that the structure of corresponding leading log(1 − z) terms in the kernel can be constrained [63] allowing them to predict certain next to SV logarithms at higher orders in a s . The next to SV corrections to various inclusive processes were studied in a series of papers [65][66][67][68][69][70][71][72][73] JHEP04(2021)131…”

Asymptotic dynamics on the worldline for spinning particles

“…Building on this work, and motivated by the rising interest in the field of next-toleading power (NLP) corrections to the soft and collinear limits both in phenomenology [35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53] and in more formal contexts [54][55][56][57][58][59][60][61][62][63][64][65][66][67][68][69][70], the worldline description of [28] has proved to be a valuable tool to derive factorization theorems at NLP [71,72]. The asymptotic dressed propagator defined in this way at NLP has been dubbed Generalized Wilson Line (GWL), and it is defined for a semi-infinite straight line starting from the origin in the JHEP02(2021)007…”