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We study the maximally-helicity-violating six-gluon scattering amplitude in planar N=4 super-Yang-Mills theory at finite coupling when all three cross ratios are small. It exhibits a double logarithmic scaling in the cross ratios, controlled by a handful of “anomalous dimensions” that are functions of the coupling constant alone. Inspired by known seven-loop results at weak coupling and the integrability-based pentagon operator product expansion, we present conjectures for the all-order resummation of these anomalous dimensions. At strong coupling, our predictions agree perfectly with the string theory analysis. Intriguingly, the simplest of these anomalous dimensions coincides with one describing the lightlike limit of the octagon, namely, the four-point function of large-charge Bogomol’nyi–Prasad–Sommerfield (BPS) operators.

We compute the symbol of the two-loop five-point scattering amplitude in N=4 supersymmetric Yang-Mills theory, including its full color dependence. This requires constructing the symbol of all two-loop five-point nonplanar massless master integrals, for which we give explicit results.

The energy-energy correlation (EEC) between two detectors in e+e− annihilation was computed analytically at leading order in QCD almost 40 years ago, and numerically at next-to-leading order (NLO) starting in the 1980s. We present the first analytical result for the EEC at NLO, which is remarkably simple, and facilitates analytical study of the perturbative structure of the EEC. We provide the expansion of the EEC in the collinear and back-to-back regions through next-to-leading power, information which should aid resummation in these regions.

We calculate the rate for e{sup +}e{sup -} annihilation into four jets at next-to-leading order in perturbative QCD, but omitting terms that are suppressed by one or more powers of 1/N{sup 2}{sub c}, where N{sub c} is the number of colors. The O({alpha}{sup 3}{sub s}) corrections depend strongly on the jet resolution parameter y{sub cut} and on the clustering and recombination schemes, and they substantially improve the agreement between theory and data. {copyright} {ital 1997} {ital The American Physical Society}

We study the change in the di-photon invariant mass distribution for Higgs boson decays to two photons, due to interference between the Higgs resonance in gluon fusion and the continuum background amplitude for gluon pair to photon pair. Previously, the apparent Higgs mass was found to shift by around 100 MeV in the Standard Model in the leading order approximation, which may potentially be experimentally observable. We compute the next-to-leading order QCD corrections to the apparent mass shift, which reduce it by about 40%. The apparent mass shift may provide a way to measure, or at least bound, the Higgs boson width at the Large Hadron Collider through "interferometry." We investigate how the shift depends on the Higgs width, in a model that maintains constant Higgs boson signal yields. At Higgs widths above 30 MeV the mass shift is over 200 MeV and increases with the square root of the width. The apparent mass shift could be measured by comparing with the ZZ* channel, where the shift is much smaller. It might be possible to measure the shift more accurately by exploiting its strong dependence on the Higgs transverse momentum., 5 pages 6 figures

We present the cross sections for production of up to four jets at the Large Hadron Collider, at next-to-leading order in the QCD coupling. We use the BlackHat library in conjunction with SHERPA and a recently developed algorithm for assembling primitive amplitudes into color-dressed amplitudes. We adopt the cuts used by ATLAS in their study of multi-jet events in pp collisions at \sqrt{s} = 7 TeV. We include estimates of nonperturbative corrections and compare to ATLAS data. We store intermediate results in a framework that allows the inexpensive computation of additional results for different choices of scale or parton distributions., 5 pages, 2 figures, 2 tables. v2: references added, additional discussion of scale and PDF uncertainties, other minor clarifications

We present the first next-to-leading order QCD results for W + 4-jet production at hadron colliders. Total cross sections, as well as distributions in the jet transverse momenta and in the total transverse energy H_T are provided for the initial LHC energy of \sqrt{s} = 7 TeV. We use a leading-color approximation, known to be accurate to 3% for W production with fewer jets. The virtual matrix elements and the most complicated real-emission matrix elements are handled by the BlackHat library, based on on-shell methods. The remaining parts of the calculation, including the integration over phase space, are performed by the SHERPA package., Comment: 5 pages, 3 figures, 2 tables. v2: W^+ + 4 jets NLO results added, plus minor typo corrections

We describe the construction of the complete four-loop four-particle amplitude of N=8 supergravity. The amplitude is ultraviolet finite, not only in four dimensions, but in five dimensions as well. The observed extra cancellations provide additional non-trivial evidence that N=8 supergravity in four dimensions may be ultraviolet finite to all orders of perturbation theory., Comment: 5 pages, 4 figures. v2 contains minor corrections, including flipping sign of eq. (1). Complete results, including mathematica readable form, presented in the directory aux/ included in the source of this manuscript. As certain computer operating systems (e.g. Windows) preclude the naming of directories "aux" we also host this data at: http://www.physics.ucla.edu/~jjmc/auxiliaryData.tgz

We report on the first next-to-leading order QCD computation of W + 3-jet production in hadronic collisions including all partonic subprocesses. We compare the results with CDF data from the Tevatron, and find excellent agreement. The renormalization and factorization scale dependence is reduced substantially compared to leading-order calculations. The required one-loop matrix elements are computed using on-shell methods, implemented in a numerical program, BlackHat. We use the SHERPA package to generate the real-emission contributions and to integrate the various contributions over phase space. We use a leading-color (large-N_c) approximation for the virtual part, which we confirm in W + 1,2-jet production to be valid to within three percent. The present calculation demonstrates the utility of on-shell methods for computing next-to-leading-order corrections to processes important to physics analyses at the Large Hadron Collider., Comment: 5 pages, 3 figures, RevTex, v3 small change in values, no changes in conclusions

We construct the three-loop four-point amplitude of N = 8 supergravity using the unitarity method. The amplitude is ultraviolet finite in four dimensions. Novel cancellations, not predicted by traditional superspace power-counting arguments, render its degree of divergence in D dimensions to be no worse than that of N = 4 super-Yang-Mills theory--a finite theory in four dimensions. Similar cancellations can be identified at all loop orders in certain unitarity cuts, suggesting that N = 8 supergravity may be a perturbatively finite theory of quantum gravity.

The collinear factorization properties of two-loop scattering amplitudes in dimensionally-regulated N=4 super-Yang-Mills theory suggest that, in the planar ('t Hooft) limit, higher-loop contributions can be expressed entirely in terms of one-loop amplitudes. We demonstrate this relation explicitly for the two-loop four-point amplitude and, based on the collinear limits, conjecture an analogous relation for n-point amplitudes. The simplicity of the relation is consistent with intuition based on the AdS/CFT correspondence that the form of the large N_c L-loop amplitudes should be simple enough to allow a resummation to all orders., 5 pages, 2 figures, uses revtex. v2: references added. v3: reference added, normalizations corrected

We compute the rapidity distribution of the virtual photon produced in the Drell-Yan process through next-to-next-to-leading order in perturbative QCD. We introduce a powerful new method for calculating differential distributions in hard scattering processes. This method is based upon a generalization of the optical theorem; it allows the integration-by-parts technology developed for multiloop diagrams to be applied to noninclusive phase-space integrals, and permits a high degree of automation. We apply our results to the analysis of fixed-target experiments.

A low mass Standard Model Higgs boson should be visible at the Large Hadron Collider through its production via gluon-gluon fusion and its decay to two photons. We compute the interference of this resonant process, gg -> H -> gamma gamma, with the continuum QCD background, gg -> gamma gamma induced by quark loops. Helicity selection rules suppress the effect, which is dominantly due to the imaginary part of the two-loop gg -> gamma gamma scattering amplitude. The interference is destructive, but only of order 5% in the Standard Model, which is still below the 10-20% present accuracy of the total cross section prediction. We comment on the potential size of such effects in other Higgs models., 10 pages, 2 figures