Soft function for exclusiveN-jet production at hadron colliders

Abstract

The N -jettiness event shape divides phase space into N + 2 regions, each containing one jet or beam. Using a geometric measure these regions correspond to jets with circular boundaries. We give a factorization theorem for the cross section fully differential in the mass of each jet, and compute the corresponding soft function at next-to-leading order (NLO). The ultraviolet divergences are analytically extracted by exploiting hemispheres for interactions between each pair of hard partons, leaving only convergent integrals that are sensitive to the precise boundaries. This hemisphere decomposition can also be applied to other N -jet soft functions, including other observables. For N -jettiness, the final result for the soft function involves stable one-dimensional numerical integrals, and all ingredients are now available to extend NLO cross sections to resummed predictions at next-to-next-to-leading logarithmic order.

Jet mass spectra in Higgs boson plus one jet at next-to-next-to-leading logarithmic order

“…An illustration of the more irregular regions that appear for the invariant mass measure can be found in Ref. [48]. We now study how the jet mass spectrum is affected by these different jet definitions as well as by their jet area (R dependence).…”

“…[62][63][64][65], and the one-loop soft function in Ref. [48]. We also require the cusp anomalous dimension to three loops [66,67], and the non-cusp anomalous dimensions to two loops, which are known from Refs.…”

“…Therefore, the structure of the perturbation theory, which is simultaneously differential in these two kinematic variables, is simpler. In particular, there is a QCD factorization formula for this cross section [47,48], obtained by making use of Soft-Collinear Effective Theory (SCET) [20,[49][50][51]. For the experimentally more realistic case of measuring m J with a p T veto variable one must simultaneously deal with a thrust-like invariant mass resummation and a p T -type resummation.…”

Gauge theory webs and surfaces

“…The imaginary parts for timeline configurations have been discussed recently in Ref. [18] Corrections to partonic scattering [19][20][21][22][23][24][25][26][27][28][29] involve the coupling of more than two ordered exponentials at a point [30,31]. In this paper we study the all-orders properties of the single cusp and of polygons with sequential cusps, computed perturbatively in coordinate space.…”

Z-Boson Production in Association with a Jet at Next-To-Next-To-Leading Order in Perturbative QCD

“…[15,16]. The determination of the p i is insensitive to the choice of jet algorithm in the small-T cut N limit [15].…”