Second-Order QCD Corrections to Jet Production at Hadron Colliders: The All-Gluon Contribution

Abstract

We report the calculation of next-to-next-to-leading order (NNLO) QCD corrections in the purely gluonic channel to dijet production and related observables at hadron colliders. Our result represents the first NNLO calculation of a massless jet observable at hadron colliders, and opens the path towards precision QCD phenomenology with the LHC.PACS numbers: 13.87. Ce,12.38Bx Single inclusive jet and dijet observables are the most fundamental QCD processes measured at hadron colliders. They probe the basic parton-parton scattering in 2 → 2 kinematics, and thus allow for a determination of the parton distribution functions in the proton and for a direct probe of the strong coupling constant α s up to the highest energy scales that can be attained in collider experiments.Precision measurements of single jet and dijet cross Theoretical predictions for these observables are accurate to next-to-leading order (NLO) in QCD [6][7][8][9][10] and the electroweak theory [11]. The estimated uncertainty from missing higher order corrections on the NLO QCD predictions is substantially larger than the experimental errors on single jet and dijet data, and is thus the dominant source of error in the determination of α s . A consistent inclusion of jet data in global fits of parton distributions is also feasible only to NLO. These theoretical limitations to precision phenomenology provide a very strong motivation for computing next-to-next-to-leading order (NNLO) corrections to jet production at hadron colliders.At this perturbative order, three types of parton-level processes contribute to jet production: the two-loop virtual corrections to the basic 2 → 2 process [12], the one-loop virtual corrections to the single real radiation 2 → 3 process [13] and the double real radiation 2 → 4 process at tree-level [14]. Each contribution is infrared divergent, and only their sum yields a finite and meaningful result. After ultraviolet renormalization, both virtual contributions contain explicit infrared singularities, which are compensated by infrared singularities from single or double real radiation. These become explicit only after integrating out the real radiation contributions over the phase space relevant to single jet or dijet production.This interplay with the jet definition complicates the extraction of infrared singularities from the real radiation process. It is typically done by subtracting an infrared approximation from the corresponding matrix elements. These infrared subtraction terms are sufficiently simple to be integrated analytically, such that they can be combined with the virtual contributions to obtain the cancellation of all infrared singularities. Several generic methods for the construction of subtraction terms are available at NLO [15][16][17].The development of subtraction methods for NNLO calculations is a very active field of research. Up to now, various methods were constructed and applied to specific NNLO calculations of exclusive observables: sector decomposition [18] The antenna subtraction method [27,...

Statistical issues in the parton distribution analysis of the Tevatron jet data

“…While the present paper was under review, a new estimate of the K-factor at the level of 15-20% for the NNLO QCD corrections to inclusive jet hadro-production appeared in [26]. This correction nicely matches with the the coherent 3σ excess in the luminosity nuisance parameters for the D0 and CDF experiments.…”

Electroweak production of top-quark pairs ine+e−annihilation at NNLO in QCD: The vector current contributions

“…At NLO, this is relatively straightforward to do and both phase-space slicing [33][34][35][36][37][38][39] and subtraction [40][41][42][43][44][45] techniques which solve the problem were worked out long time ago. However, as is clear from the massive amount of literature on the subject [46,47,, analogous techniques at NNLO are considerably more complicated to develop and complete solutions took much longer to emerge. For example, in the important case of massless dijet production, it took more than a decade for the first physical predictions to appear [46,47] from the time that the relevant two-loop virtual amplitudes were first calculated [48][49][50][51][52][53][54][55][56][57].…”

“…However, as is clear from the massive amount of literature on the subject [46,47,, analogous techniques at NNLO are considerably more complicated to develop and complete solutions took much longer to emerge. For example, in the important case of massless dijet production, it took more than a decade for the first physical predictions to appear [46,47] from the time that the relevant two-loop virtual amplitudes were first calculated [48][49][50][51][52][53][54][55][56][57]. As a result of significant theoretical efforts during the past decade, a number of important "benchmark processes"…”

CT10 next-to-next-to-leading order global analysis of QCD

“…NNLO matrix elements are unknown for several other processes in the global analysis. Most notably, the key input theoretical cross section for inclusive jet production in p p ð−Þ collisions is still evaluated at NLO, although some of the NNLO radiative contributions have already been computed [22,23]. 1 Various NNLO PDF sets have been published in the literature [24][25][26][27][28][29] that make use of NNLO matrix elements when available.…”