Soft-gluon resummation for boosted top-quark production at hadron colliders

Abstract

We investigate the production of highly energetic top-quark pairs at hadron colliders, focusing on the case where the invariant mass of the pair is much larger than the mass of the top quark. In particular, we set up a factorization formalism appropriate for describing the differential partonic cross section in the double soft and small-mass limit, and explain how to resum simultaneously logarithmic corrections arising from soft gluon emission and from the ratio of the pair-invariant mass to that of the top quark to next-to-next-to-leading logarithmic accuracy. We explore the implications of our results on approximate next-to-next-to-leading order formulas for the differential cross section in the soft limit, pointing out that they offer a simplified calculational procedure for determining the currently unknown delta-function terms in the limit of high invariant mass.using the results of [9][10][11][12]. A fully resummed cross section appropriate for both limits is then obtained by deriving and solving the renormalization-group (RG) evolution equations for the different functions separately. The anomalous dimensions appearing in the RG equations are known to the level sufficient for resummation of both mass and soft logarithms to NNLL accuracy. As simple and obvious as this approach is, it has yet to be fully worked out for any particular observable in top-quark pair production at hadron collider experiments.This formalism for the simultaneous resummation of soft and mass logarithms in the invariant-mass distribution is interesting in its own right. Moreover, with use of a proper matching procedure, it provides supplemental information to the current state-of-the-art predictions based on soft-gluon resummation with the counting m t ∼ M [5]. Particularly important in this regard is its use as a tool to calculate, up to easily quantifiable power corrections in m t /M, the full NNLO corrections to the massive hard and soft functions. Together, these pieces determine the coefficient of the delta-function coefficient in the fixed-order expansion at NNLO, a missing piece in currently available "approximate NNLO" formulas for generic values of the top-quark mass. Using our factorization formula for the double soft and smallmass limit, we can calculate the pieces of the NNLO delta-function correction enhanced by logarithms of the ratio m t /M. Furthermore, using the explicit NNLO results for the heavyquark fragmentation function [13] and the virtual corrections to massless qq → q ′q′ [14] and gg → qq [15] scattering, we can very nearly determine the piece of the delta-function coefficients which is constant in the limit m t /M → 0. The missing piece is the NNLO soft function for massless partons, related to double real emission for gg → qq and qq → qq scattering in the soft limit. We do not calculate this function here, but plan to return to it in future work. While these delta-function pieces of the NNLO partonic cross section are of N 3 LL in the counting of soft-gluon resummation, including them can only make the pred...

NNLL Resummation for Jet Broadening

“…Among the mixed virtual-real and double real emissions, only the diagrams in Figure 3 give nonvanishing contributions. The same matrix elements also arise in other two-loop computations of soft functions [24][25][26][27][28][29][30][31][32], what makes our case different are the phase-space constraints and the necessity of working with an additional analytic regulator. In the following, we denote the individual contributions of these diagrams to the soft function by…”

NNLO corrections to top-pair production at hadron colliders: the all-fermionic scattering channels

“…which has been discussed in the literature on heavy flavor fragmentation [48,49]. To derive the partonic reaction (2.5) we use the collinear subtraction term eq.…”

Resummed Differential Cross Sections for Top-Quark Pairs at the LHC

“…[5]. The technical details will be given in a forthcoming paper, although the main elements have already been sketched out in Ref.…”

“…The technical details will be given in a forthcoming paper, although the main elements have already been sketched out in Ref. [6]. In the kinematic situation where the top quarks are highly boosted and the events are dominated by softgluon emissions, the resummed partonic differential cross section in Mellin space can be written as…”

“…In Ref. [5], some of the authors of the current work developed a formalism for the simultaneous resummation of both type of logarithms to all orders in the strong coupling constant α s . In this Letter, we report the first phenomenological applications of that formalism, giving predictions for the t=t p T and the tt invariant mass distributions at the 8 TeV LHC and comparing with experimental measurements as well as the NNLO calculations when possible.…”