Soft gluon resummation of Drell–Yan rapidity distributions: Theory and phenomenology

Abstract

We examine critically the theoretical underpinnings and phenomenological implications of soft gluon (threshold) resummation of rapidity distributions at a hadron collider, taking Drell-Yan production at the Tevatron and the LHC as a reference test case. First, we show that in perturbative QCD soft gluon resummation is necessary whenever the partonic (rather the hadronic) center-of-mass energy is close enough to threshold, and we provide tools to assess when resummation is relevant for a given process. Then, we compare different prescriptions for handling the divergent nature of the series of resummed perturbative corrections, specifically the minimal and Borel prescriptions. We assess the intrinsic ambiguities of resummed results, both due to the asymptotic nature of their perturbative expansion, and to the treatment of subleading terms. Turning to phenomenology, we introduce a fast and accurate method for the implementation of resummation with the minimal and Borel prescriptions using an expansion on a basis of Chebyshev polynomials. We then present results for W and Z production as well as both high-and low-mass dilepton pairs at the LHC, and show that soft gluon resummation effects are generally comparable in size to NNLO corrections, but sometimes affected by substantial ambiguities.

Resummed Higgs cross section at N3LL

“…[49], and refined and extended in refs. [50][51][52][53]. This prescription, called Borel Prescription (BP), is typically slower but more flexible.…”

“…[49][50][51][52][53]. This prescription adopts a Borel method for summing the divergent series, and it is therefore called Borel Prescription (BP).…”

“…This shows that the series is not Borel summable. The Borel Prescription is now formulated as [49][50][51][52][53] where the w integral has been cut off, and W is minimally W = 2 (corresponding to the inclusion of twist 4 terms). This cut-off makes the integral convergent, because the cut extends always on a finite range.…”

An extensive survey of the estimation of uncertainties from missing higher orders in perturbative calculations

“…This approach is viable because one can show that at least in some cases (see e.g. [15,16]), such a dominant Mellin moment exists and gives a good approximation to the full result.…”

“…The other partonic channels, which only enter at NLO and at NNLO order, turn out to only give subleading contributions. We calculate the dominant moment of the Higgs coefficient functions in Mellin space given in [41] using a saddle-point approximation [15,16]. We find that N 0 = 2 gives the best approximation of the full Mellin inversion integral.…”