Five-loop four-point amplitude of N=4 super-Yang-Mills theory

Using the method of maximal cuts, we construct the complete D-dimensional integrand of the five-loop four-point amplitude of N=4 super-Yang-Mills theory, including nonplanar contributions. In the critical dimension where this amplitude becomes ultraviolet divergent, we present a compact explicit expression for the nonvanishing ultraviolet divergence in terms of three vacuum integrals. This construction provides a crucial step towards obtaining the corresponding amplitude of N=8 supergravity required to resolve the general ultraviolet behavior of supergravity theories.

Four-jet production at the Large Hadron Collider at next-to-leading order in QCD

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 multijet events in pp collisions at √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.

Color dual form for gauge-theory amplitudes

Recently a duality between color and kinematics has been proposed, exposing a new unexpected structure in gauge theory and gravity scattering amplitudes. Here we propose that the relation goes deeper, allowing us to reorganize amplitudes into a form reminiscent of the standard color decomposition in terms of traces over generators, but with the role of color and kinematics swapped. By imposing additional conditions similar to Kleiss-Kuijf relations between partial amplitudes, the relationship between the earlier form satisfying the duality and the current one is invertible. We comment on extensions to loop level.

Precise predictions for W+4-jet production at the large hadron collider

We present the next-to-leading order (NLO) QCD results for W+4-jet production at hadron colliders. This is the first hadron-collider process with five final-state objects to be computed at NLO. It represents an important background to many searches for new physics at the energy frontier. Total cross sections, as well as distributions in the jet transverse momenta, are provided for the initial LHC energy of √s = 7  TeV. We use a leading-color approximation, known to be accurate to 3% for W production with fewer jets. The calculation uses the BLACKHAT library along with the SHERPA package.

Ultraviolet behavior of N = 8 supergravity at four loops

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 nontrivial evidence that N=8 supergravity in four dimensions may be ultraviolet finite to all orders of perturbation theory.

Precise predictions for w+3 jet production at hadron colliders

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 data from the Tevatron and find excellent agreement. 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.

Cancellations beyond finiteness in N=8 supergravity at three loops

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 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.

Two-loop iteration of five-point N=4 super-Yang-Mills amplitudes

We confirm by explicit computation the conjectured all-orders iteration of planar maximally supersymmetric N=4 Yang-Mills theory in the nontrivial case of five-point two-loop amplitudes. We compute the required unitarity cuts of the integrand and evaluate the resulting integrals numerically using a Mellin-Barnes representation and the automated package of Czakon [Comput. Phys. Commun. 175, 559 (2006)]. This confirmation of the iteration relation provides further evidence suggesting that N=4 gauge theory is solvable.

Planar amplitudes in maximally supersymmetric Yang-Mills theory

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 anti-de Sitter/conformal field theory correspondence that the form of the large-N(c) L-loop amplitudes should be simple enough to allow a resummation to all orders.

Coupling gravitons to matter

Using relationships between open and closed strings, we present a construction of tree-level scattering amplitudes for gravitons minimally coupled to matter in terms of gauge theory partial amplitudes. In particular, we present examples of amplitudes with gravitons coupled to vectors or to a single fermion pair. We also present two examples with massive graviton exchange, as would arise in the presence of large compact dimensions. The gauge charges are represented by flavors of dynamical scalars or fermions. This also leads to an unconventional decomposition of color and kinematics in gauge theories.