A Tree-Loop Duality Relation at Two Loops and Beyond

The duality relation between one-loop integrals and phase-space integrals, developed in a previous work, is extended to higher-order loops. The duality relation is realized by a modification of the customary +i0 prescription of the Feynman propagators, which compensates for the absence of the multiple-cut contributions that appear in the Feynman tree theorem. We rederive the duality theorem at one-loop order in a form that is more suitable for its iterative extension to higher-loop orders. We explicitly show its application to two- and three-loop scalar master integrals, and we discuss the structure of the occurring cuts and the ensuing results in detail.Comment: 20 pages. Few typos corrected, some additional comments included, Appendix B and one reference added. Final version as published in JHE

A general method for the resummation of event-shape distributions in e⁺ e− annihilation

We present a novel method for resummation of event shapes to next-to-next-to-leading-logarithmic (NNLL) accuracy. We discuss the technique and describe its implementation in a numerical program in the case of e + e − collisions where the resummed prediction is matched to NNLO. We reproduce all the existing predictions and present new results for oblateness and thrust major

Giant QCD K-factors beyond NLO

Hadronic observables in Z+jet events can be subject to large NLO corrections at TeV scales, with K-factors that even reach values of order 50 in some cases. We develop a method, LoopSim, by which approximate NNLO predictions can be obtained for such observables, supplementing NLO Z+jet and NLO Z+2-jet results with a unitarity-based approximation for missing higher loop terms. We first test the method against known NNLO results for Drell-Yan lepton pt spectra. We then show our approximate NNLO results for the Z+jet observables. Finally we examine whether the LoopSim method can provide useful information even in cases without giant K-factors, with results for observables in dijet events that can be compared to early LHC data.Comment: 38 pages, 13 figures; v2 includes additional reference

NLL+NNLO predictions for jet-veto efficiencies in Higgs-boson and Drell-Yan production

Using the technology of the CAESAR approach to resummation, we examine the jet-veto efficiency in Higgs-boson and Drell-Yan production at hadron colliders and show that at next-to-leading logarithmic (NLL) accuracy the resummation reduces to just a Sudakov form factor. Matching with NNLO calculations results in stable predictions for the case of Drell-Yan production, but reveals substantial uncertainties in gluon-fusion Higgs production, connected in part with the poor behaviour of the perturbative series for the total cross section. We compare our results to those from POWHEG with and without reweighting by HqT, as used experimentally, and observe acceptable agreement. In an appendix we derive the part of the NNLL resummation corrections associated with the radius dependence of the jet algorithm.Comment: 30 pages, 8 figures; v2 as published in JHE

Non-global Structure of the O({\alpha}_s^2) Dijet Soft Function

High energy scattering processes involving jets generically involve matrix elements of light- like Wilson lines, known as soft functions. These describe the structure of soft contributions to observables and encode color and kinematic correlations between jets. We compute the dijet soft function to O({\alpha}_s^2) as a function of the two jet invariant masses, focusing on terms not determined by its renormalization group evolution that have a non-separable dependence on these masses. Our results include non-global single and double logarithms, and analytic results for the full set of non-logarithmic contributions as well. Using a recent result for the thrust constant, we present the complete O({\alpha}_s^2) soft function for dijet production in both position and momentum space.Comment: 55 pages, 8 figures. v2: extended discussion of double logs in the hard regime. v3: minor typos corrected, version published in JHEP. v4: typos in Eq. (3.33), (3.39), (3.43) corrected; this does not affect the main result, numerical results, or conclusion

On the breaking of collinear factorization in QCD

We investigate the breakdown of collinear factorization for non-inclusive observables in hadron-hadron collisions. For pure QCD processes, factorization is violated at the three-loop level and it has a structure identical to that encountered previously in the case of super-leading logarithms. In particular, it is driven by the non-commutation of Coulomb/Glauber gluon exchanges with other soft exchanges. Beyond QCD, factorization may be violated at the two-loop level provided that the hard subprocess contains matrix element contributions with phase differences between different colour topologies.Comment: Version 2: minor improvements for journal publicatio

Non-global logarithms and jet algorithms in high-pT jet shapes

We consider jet-shape observables of the type proposed recently, where the shapes of one or more high-pT jets, produced in a multi-jet event with definite jet multiplicity, may be measured leaving other jets in the event unmeasured. We point out the structure of the full next-to-leading logarithmic resummation specifically including resummation of non-global logarithms in the leading-Nc limit and emphasising their properties. We also point out differences between jet algorithms in the context of soft gluon resummation for such observables.Comment: 22 pages, 4 figures. Title and a few words changed. Several typos corrected. Version accepted by JHE

Next-to-leading order QCD predictions for W+W+jj production at the LHC

Because the LHC is a proton-proton collider, sizable production of two positively charged W-bosons in association with two jets is possible. This process leads to a distinct signature of same sign high-pt leptons, missing energy and jets. We compute the NLO QCD corrections to the QCD-mediated part of pp -> W+W+jj. These corrections reduce the dependence of the production cross-section on the renormalization and factorization scale to about +- 10 percent. We find that a large number of W+W+jj events contain a relatively hard third jet. The presence of this jet should help to either pick up the W+W+jj signal or to reject it as an unwanted background.Comment: 15 pages, 5 (lovely) figures, v3 accepted for publication in JHEP, corrects tables in appendi

On the singular behaviour of scattering amplitudes in quantum field theory

We analyse the singular behaviour of one-loop integrals and scattering amplitudes in the framework of the loop-tree duality approach. We show that there is a partial cancellation of singularities at the loop integrand level among the different components of the corresponding dual representation that can be interpreted in terms of causality. The remaining threshold and infrared singularities are restricted to a finite region of the loop momentum space, which is of the size of the external momenta and can be mapped to the phase-space of real corrections to cancel the soft and collinear divergences

Two-Loop Soft Corrections and Resummation of the Thrust Distribution in the Dijet Region

The thrust distribution in electron-positron annihilation is a classical precision QCD observable. Using renormalization group (RG) evolution in Laplace space, we perform the resummation of logarithmically enhanced corrections in the dijet limit, $T\to 1$ to next-to-next-to-leading logarithmic (NNLL) accuracy. We independently derive the two-loop soft function for the thrust distribution and extract an analytical expression for the NNLL resummation coefficient $g_3$. To combine the resummed expressions with the fixed-order results, we derive the $\log(R)$-matching and $R$-matching of the NNLL approximation to the fixed-order NNLO distribution.Comment: 50 pages, 12 figures, 1 table. Few minor changes. Version accepted for publication in JHE