Search

This report summarizes the recent progress and promising future directions in theoretical high-energy physics (HEP) identified within the Theory Frontier of the 2021 Snowmass Process., Comment: Contribution to the US Community Study on the Future of Particle Physics (Snowmass 2021), v2: fixed typos

Electroweak vector-boson production, accompanied by multiple jets, is an important background to searches for physics beyond the Standard Model. A precise and quantitative understanding of this process is helpful in constraining deviations from known physics. We study four key ratios in $W + n$-jet production at the LHC. We compute the ratio of cross sections for $W + n$- to $W + (n-1)$-jet production as a function of the minimum jet transverse momentum. We also study the ratio differentially, as a function of the $W$-boson transverse momentum; as a function of the scalar sum of the jet transverse energy, $H_T^{\rm jets}$; and as a function of certain jet transverse momenta. We show how to use such ratios to extrapolate differential cross sections to $W+6$-jet production at next-to-leading order, and we cross-check the method against a direct calculation at leading order. We predict the differential distribution in $H_T^{\rm jets}$ for $W+6$ jets at next-to-leading order using such an extrapolation. We use the BlackHat software library together with SHERPA to perform the computations., Comment: RevTex, 60 pages, 25 tables, 19 figures

We study $W$-boson production accompanied by multiple jets at 7 TeV at the LHC. We study the jet-production ratio, of total cross sections for $W$+$n$- to $W$+($n-1$)-jet production, and the ratio of distributions in the total transverse hadronic jet energy $H_{\rm T}^{\rm jets}$. We use the ratios to extrapolate the total cross section, and the differential distribution in $H_{\rm T}^{\rm jets}$, to $W$+6-jet production. We use the BlackHat software library in conjunction with SHERPA to perform the computations., Comment: Merge of Moriond 2014 and Loops & Legs 2014 proceedings, 6 pages, 2 figures

We present next-to-leading order QCD predictions for cross sections and for a comprehensive set of distributions in diphoton + 2-jet production at the Large Hadron Collider. We consider the contributions from loop amplitudes for two photons and four gluons, but we neglect top quarks. We use BlackHat together with SHERPA to carry out the computation. We use a Frixione cone isolation for the photons. We study standard sets of cuts on the jets and the photons, and also sets of cuts appropriate for studying backgrounds to Higgs-boson production via vector-boson fusion., Comment: RevTex, 20 figures, 16 tables

We present results from a recent calculation of prompt photon-pair production in association with two jets to next-to-leading order (NLO) at the LHC. The virtual contribution is evaluated using the BlackHat library, a numerical implementation of on-shell methods for one-loop amplitudes, in conjunction with SHERPA. We study four sets of cuts: standard jet cuts, a set of Higgs-related cuts suggested by ATLAS, and corresponding sets which isolate the kinematic region where the process becomes the largest background to Higgs production via vector-boson fusion., Comment: 10 pages, 4 figures, Presented at 11th International Symposium on Radiative Corrections (RADCOR 2013), 22-27 September 2013, Lumley Castle Hotel, Durham, UK

We present an event-file format for the dissemination of next-to-leading-order (NLO) predictions for QCD processes at hadron colliders. The files contain all information required to compute generic jet-based infrared-safe observables at fixed order (without showering or hadronization), and to recompute observables with different factorization and renormalization scales. The files also make it possible to evaluate cross sections and distributions with different parton distribution functions. This in turn makes it possible to estimate uncertainties in NLO predictions of a wide variety of observables without recomputing the short-distance matrix elements. The event files allow a user to choose among a wide range of commonly-used jet algorithms and jet-size parameters. We provide event files for a $W$ or $Z$ boson accompanied by up to four jets, and for pure-jet events with up to four jets. The files are for the Large Hadron Collider with a center of mass energy of 7 or 8 TeV. A C++ library along with a Python interface for handling these files are also provided and described in this article. The library allows a user to read the event files and recompute observables transparently for different pdf sets and factorization and renormalization scales., Comment: 43 pages, 6 tables

We present recent next-to-leading order (NLO) results in perturbative QCD obtained using the BlackHat software library. We discuss the use of n-tuples to separate the lengthy matrix-element computations from the analysis process. The use of n-tuples allows many analyses to be carried out on the same phase-space samples, and also allows experimenters to conduct their own analyses using the original NLO computation., Comment: Talk given at ACAT 2013, Beijing, China, May 16--21, 2013; 6 pages, 2 figures; added references

In these proceedings we present results from a recent calculation for the production of a W boson in conjunction with five jets at next-to-leading order in perturbative QCD. We also use results at lower multiplicities to extrapolate the cross section to the same process with six jets., Comment: 5 pages, Proceedings for the DIS2013 conference

We present next-to-leading order QCD predictions for the total cross section and for a comprehensive set of transverse-momentum distributions in W + 5-jet production at the Large Hadron Collider. We neglect the small contributions from subleading-color virtual terms, top quarks and some terms containing four quark pairs. We also present ratios of total cross sections, and use them to obtain an extrapolation formula to an even larger number of jets. We include the decay of the $W$ boson into leptons. This is the first such computation with six final-state vector bosons or jets. We use BlackHat together with SHERPA to carry out the computation., Comment: RevTex, 27 pages, 7 figures, v2 minor corrections and corrected references

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 useful for resolving the general ultraviolet behavior of supergravity theories., Comment: 5 pages, 4 figures, RevTex. Ancillary file included. v2 minor corrections, corrected references and overall phase in eq. (5), matching journal version

We extend our investigation of backgrounds to new physics signals, following CMS's data-driven search for supersymmetry at the LHC. The aim is to use different sets of cuts in gamma + 3-jet production to predict the irreducible Z + 3-jet background (with the Z boson decaying to neutrinos) to searches with missing transverse energy + 3-jet signal topologies. We compute ratios of Z + 3-jet to gamma + 3-jet production cross sections and kinematic distributions at next-to-leading order (NLO) in alpha_s. We compare these ratios with those obtained using a parton shower matched to leading-order matrix elements (ME+PS). This study extends our previous work [arXiv:1106.1423 [hep-ph]] on the Z + 2-jet to gamma + 2-jet ratio. We find excellent agreement with the ratio determined from the earlier NLO results involving two instead of three jets, and agreement to within 10% between the NLO and ME+PS results for the ratios. We also examine the possibility of large QCD logarithms in these processes. Ratios of Z + n-jet to gamma + n-jet cross sections are plausibly less sensitive to such corrections than the cross sections themselves. Their effect on estimates of Z + 3-jet to gamma + 3-jet ratios can be assessed experimentally by measuring the gamma + 3-jet to gamma + 2-jet production ratio in search regions. We partially address the question of potentially large electroweak logarithms by computing the real-emission part of the electroweak corrections to the ratio using ME+PS, and find that it is 1% or less. Our estimate of the remaining theoretical uncertainties in the Z to gamma ratio is in agreement with our earlier study., Comment: 32 pages, 10 figures, 8 tables, RevTeX

In this contribution we present recent progress in the computation of next-to-leading order (NLO) QCD corrections for the production of an electroweak vector boson in association with jets at hadron colliders. We focus on results obtained using the virtual matrix element library BLACKHAT in conjunction with SHERPA, focusing on results relevant to understanding the background to top production., Comment: 4+2 epsilon pages, Submitted for the proceedings of TOP2011 - 4th International Workshop on Top Quark Physics, 25-30th September 2011, Sant Feliu de Guixols, Spain

We use the duality between color and kinematics to simplify the construction of the complete four-loop four-point amplitude of N=4 super-Yang-Mills theory, including the nonplanar contributions. The duality completely determines the amplitude's integrand in terms of just two planar graphs. The existence of a manifestly dual gauge-theory amplitude trivializes the construction of the corresponding N=8 supergravity integrand, whose graph numerators are double copies (squares) of the N=4 super-Yang-Mills numerators. The success of this procedure provides further nontrivial evidence that the duality and double-copy properties hold at loop level. The new form of the four-loop four-point supergravity amplitude makes manifest the same ultraviolet power counting as the corresponding N=4 super-Yang-Mills amplitude. We determine the amplitude's ultraviolet pole in the critical dimension of D=11/2, the same dimension as for N=4 super-Yang-Mills theory. Strikingly, exactly the same combination of vacuum integrals (after simplification) describes the ultraviolet divergence of N=8 supergravity as the subleading-in-1/N_c^2 single-trace divergence in N=4 super-Yang-Mills theory., Comment: v2: PRD published version, fixed glitch in ancillary file. v1: 61 pages, 22 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., Comment: 5 pages, 2 figures, 2 tables. v2: references added, additional discussion of scale and PDF uncertainties, other minor clarifications

We present the cross section for production of a Z boson in association with four jets at the Large Hadron Collider, at next-to-leading order in the QCD coupling. When the Z decays to neutrinos, this process is a key irreducible background to many searches for new physics. Its computation has been made feasible through the development of the on-shell approach to perturbative quantum field theory. We present the total cross section for pp collisions at sqrt{s} = 7 TeV, after folding in the decay of the Z boson, or virtual photon, to a charged-lepton pair. We also provide distributions of the transverse momenta of the four jets, and we compare cross sections and distributions to the corresponding ones for the production of a W boson with accompanying jets., Comment: 5 pages, 3 figures, 1 table, RevTex, corrected Z+0 jet cross section

We expose simple and practical relations between the integrated four- and five-point one-loop amplitudes of N >= 4 supergravity and the corresponding (super-)Yang-Mills amplitudes. The link between the amplitudes is simply understood using the recently uncovered duality between color and kinematics that leads to a double-copy structure for gravity. These examples provide additional direct confirmations of the duality and double-copy properties at loop level for a sample of different theories., Comment: 25 pages, 4 figures, minor corrections

The prediction of backgrounds to new physics signals in topologies with large missing transverse energy and jets is important to new physics searches at the LHC. Following a CMS study, we investigate theoretical issues in using measurements of gamma + 2-jet production to predict the irreducible background to searches for missing energy plus two jets that originates from Z + 2-jet production where the Z boson decays to neutrinos. We compute ratios of gamma + 2-jet to Z + 2-jet production cross sections and kinematic distributions at next-to-leading order in alpha_s, as well as using a parton shower matched to leading-order matrix elements. We find that the ratios obtained in the two approximations are quite similar, making gamma + 2-jet production a theoretically reliable estimator for the missing energy plus two jets background. We employ a Frixione-style photon isolation, but we also show that for isolated prompt photon production at high transverse momentum the difference between this criterion and the standard cone isolation used by CMS is small., Comment: 27 pages, 9 figures, 3 tables, RevTex, v2 minor corrections and added references

The production of W bosons in association with jets is an important background to new physics at the LHC. Events in which the W carries large transverse momentum and decays leptonically lead to large missing energy and are of particular importance. We show that the left-handed nature of the W coupling, combined with valence quark domination at a pp machine, leads to a large left-handed polarization for both W^+ and W^- bosons at large transverse momenta. The polarization fractions are very stable with respect to QCD corrections. The leptonic decay of the W bosons translates the common left-handed polarization into a strong asymmetry in transverse momentum distributions between positrons and electrons, and between neutrinos and anti-neutrinos (missing transverse energy). Such asymmetries may provide an effective experimental handle on separating W + jets from top quark production, which exhibits very little asymmetry due to C invariance, and from various types of new physics., Comment: 32 pages, revtex, 17 figures, 3 tables, v2 minor corrections to ME+PS results, no changes to conclusions, added references

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 present the complete four-loop four-point amplitude in N=4 super-Yang-Mills theory, for a general gauge group and general D-dimensional covariant kinematics, and including all non-planar contributions. We use the method of maximal cuts --- an efficient application of the unitarity method --- to construct the result in terms of 50 four-loop integrals. We give graphical rules, valid in D-dimensions, for obtaining various non-planar contributions from previously-determined terms. We examine the ultraviolet behavior of the amplitude near D=11/2. The non-planar terms are as well-behaved in the ultraviolet as the planar terms. However, in the color decomposition of the three- and four-loop amplitude for an SU(N_c) gauge group, the coefficients of the double-trace terms are better behaved in the ultraviolet than are the single-trace terms. The results from this paper were an important step toward obtaining the corresponding amplitude in N=8 supergravity, which confirmed the existence of cancellations beyond those needed for ultraviolet finiteness at four loops in four dimensions. Evaluation of the loop integrals near D=4 would permit tests of recent conjectures and results concerning the infrared behavior of four-dimensional massless gauge theory., Comment: 108 pages, 37 figures

We review the recently discovered duality between color and kinematics in gauge theories. This duality leads to a remarkably simple double-copy relation between diagrammatic numerators of gravity scattering amplitudes and gauge-theory ones. We summarize nontrivial evidence that the duality and double-copy property holds to all loop orders. We also comment on other developments, including a proof that the gauge-theory duality leads to the gravity double-copy property, and the identification of gauge-theory Lagrangians whose double copies yield gravity Lagrangians., Comment: To appear in Proceedings of Loops and Legs in Quantum Field Theory, Woerlitz, Germany, April 25-30, 2010; 4 figures

We review recent NLO QCD results for W,Z + 3-jet production at hadron colliders, computed using BlackHat and SHERPA. We also include some new results for Z + 3-jet production at the LHC at 7 TeV. We report new progress towards the NLO cross section for W + 4-jet production. In particular, we show that the virtual matrix elements produced by BlackHat are numerically stable. We also show that with an improved integrator and tree-level matrix elements from BlackHat, SHERPA produces well-behaved real-emission contributions. As an illustration, we present the real-emission contributions -- including dipole-subtraction terms -- to the p_T distribution of the fourth jet, for a single subprocess with the maximum number of gluons., Comment: 6 pages, 4 figures, presented at Loops and Legs 2010

Using BlackHat in conjunction with SHERPA, we have computed next-to-leading order QCD predictions for a variety of distributions in Z,gamma*+1,2,3-jet production at the Tevatron, where the Z boson or off-shell photon decays into an electron-positron pair. We find good agreement between the NLO results for jet p_T distributions and measurements by CDF and D0. We also present jet-production ratios, or probabilities of finding one additional jet. As a function of vector-boson p_T, the ratios have distinctive features which we describe in terms of a simple model capturing leading logarithms and phase-space and parton-distribution-function suppression., Comment: 50 pages, RevTeX, 17 figures, v2 clarifications including commentary on threshold and other logarithms

We present several results obtained using the BlackHat next-to-leading order QCD program library, in conjunction with SHERPA. In particular, we present distributions for vector boson plus 1,2,3-jet production at the Tevatron and at the asymptotic running energy of the Large Hadron Collider, including new Z+3-jet distributions. The Z+2-jet predictions for the second-jet P_T distribution are compared to CDF data. We present the jet-emission probability at NLO in W+2-jet events at the LHC, where the tagging jets are taken to be the ones furthest apart in pseudorapidity. We analyze further the large left-handed W polarization, identified in our previous study, for W bosons produced at high P_T at the LHC., Comment: Presented at RADCOR 2009 - 9th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology), October 25 - 30 2009, Ascona, Switzerland}, 12 pages, 9 figures, LaTeX, v2 updated small correction to polarization effect plot

In this contribution we present results from the NLO computation of the production of a $W$ boson in association with three jets in hadronic collisions. The results are obtained by combining two programs: {\tt BlackHat} for the virtual one-loop matrix elements and {\tt Sherpa} for the real-emission contributions. We present results for the Tevatron and the LHC, and address the issue of the choice of a common factorization and renormalization scale for this process., Comment: Invited talk given at the European Physical Society Europhysics Conference on High Energy Physics, EPS-HEP 2009, July 16 - 22 2009, Krakow, Poland

We present next-to-leading order QCD predictions for a variety of distributions in W+3-jet production at both the Tevatron and the Large Hadron Collider. We include all subprocesses and incorporate the decay of the W boson into leptons. Our results are in excellent agreement with existing Tevatron data and provide the first quantitatively precise next-to-leading order predictions for the LHC. We include all terms in an expansion in the number of colors, confirming that the specific leading-color approximation used in our previous study is accurate to within three percent. The dependence of the cross section on renormalization and factorization scales is reduced significantly with respect to a leading-order calculation. We study different dynamical scale choices, and find that the total transverse energy is significantly better than choices used in previous phenomenological studies. We compute the one-loop matrix elements using on-shell methods, as numerically implemented in the BlackHat code. The remaining parts of the calculation, including generation of the real-emission contributions and integration over phase space, are handled by the SHERPA package., Comment: 64 pages, 37 figures, v2 minor changes in table X, cross sections and distributions unaffected; other minor corrections to text, references added

In this talk, we report on a recent next-to-leading order QCD calculation of the production of a W boson in association with three jets at hadron colliders. The computation is performed by combining two programs, BlackHat for the computation of the virtual one-loop matrix elements and Sherpa for the real emission part., Comment: 4 pages, contribution to the proceedings of the XLIIIth Rencontres de Moriond (QCD)

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

In this paper we describe algebraic and diagrammatic methods, related to the MHV generating function method, for evaluating and exposing the structure of supersymmetric sums over the states crossing generalized unitarity cuts of multi-loop amplitudes in four dimensions. We focus mainly on cuts of maximally supersymmetric Yang-Mills amplitudes. We provide various concrete examples, some of which are directly relevant for the calculation of four-loop amplitudes. Additionally, we discuss some cases with less than maximal supersymmetry. The results of these constructions carry over to generalized cuts of multi-loop supergravity amplitudes through use of the Kawai-Lewellen-Tye relations between gravity and gauge-theory tree amplitudes., Comment: Minor typographical errors corrected

In this lecture we summarize recent calculations pointing to the possible ultraviolet finiteness of N = 8 supergravity in four dimensions. We outline the modern unitarity method, which enables multiloop calculations in this theory and allows us to exploit a remarkable relation between tree-level gravity and gauge-theory amplitudes. We also describe a link between observed cancellations at loop level and improved behavior of tree-level amplitudes under large complex deformations of momenta., Comment: Invited lecture at International School of Subnuclear Physics, 46th Course, Erice Sicily, August 29-September 7, 2008. 20 pages, 8 figures, LaTeX, v2 references corrected

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

Using the method of maximal cuts, we obtain a form of the three-loop four-point scattering amplitude of N=8 supergravity in which all ultraviolet cancellations are made manifest. The Feynman loop integrals that appear have a graphical representation with only cubic vertices, and numerator factors that are quadratic in the loop momenta, rather than quartic as in the previous form. This quadratic behavior reflects cancellations beyond those required for finiteness, and matches the quadratic behavior of the three-loop four-point scattering amplitude in N=4 super-Yang-Mills theory. By direct integration we confirm that no additional cancellations remain in the N=8 supergravity amplitude, thus demonstrating that the critical dimension in which the first ultraviolet divergence occurs at three loops is D_c=6. We also give the values of the three-loop divergences in D=7,9,11. In addition, we present the explicitly color-dressed three-loop four-point amplitude of N=4 super-Yang-Mills theory., Comment: 38 pages, 10 figures, 3 tables

In this talk, we present the first, numerically stable, results for the one-loop amplitudes needed for computing W,Z + 3 jet cross sections at the LHC to next-to-leading order in the QCD coupling. We implemented these processes in BlackHat, an automated program based on on-shell methods. These methods scale very well with increasing numbers of external partons, and are applicable to a wide variety of problems of phenomenological interest at the LHC., Comment: Parallel talk in QCD session of the 34th International Conference on High Energy Physics, Philadelphia, USA, July 2008. 4 pages, LaTeX, 3 eps figures

We describe BlackHat, an automated C++ program for calculating one-loop amplitudes, and the techniques used in its construction. These include the unitarity method and on-shell recursion. The other ingredients are compact analytic formulae for tree amplitudes for four-dimensional helicity states. The program computes amplitudes numerically, using analytic formulae only for the tree amplitudes, the starting point for the recursion, and the loop integrals. We make use of recently developed on-shell methods for evaluating coefficients of loop integrals, in particular a discrete Fourier projection as a means of improving numerical stability. We illustrate the good numerical stability of this approach by computing six-, seven- and eight-gluon amplitudes in QCD and comparing against known analytic results., Comment: To appear in the proceedings of 9th Workshop on Elementary Particle Theory: Loops and Legs in Quantum Field Theory, Sondershausen, Germany, 20-25 Apr 2008

We present an identity satisfied by the kinematic factors of diagrams describing the tree amplitudes of massless gauge theories. This identity is a kinematic analog of the Jacobi identity for color factors. Using this we find new relations between color-ordered partial amplitudes. We discuss applications to multi-loop calculations via the unitarity method. In particular, we illustrate the relations between different contributions to a two-loop four-point QCD amplitude. We also use this identity to reorganize gravity tree amplitudes diagram by diagram, offering new insight into the structure of the KLT relations between gauge and gravity tree amplitudes. This can be used to obtain novel relations similar to the KLT ones. We expect this to be helpful in higher-loop studies of the ultraviolet properties of gravity theories., Comment: 40 pages, 7 figures, RevTex, v2 minor corrections

We present the first results from BlackHat, an automated C++ program for calculating one-loop amplitudes. The program implements the unitarity method and on-shell recursion to construct amplitudes. As input to the calculation, it uses compact analytic formulae for tree amplitudes for four-dimensional helicity states. The program performs all related computations numerically. We make use of recently developed on-shell methods for evaluating coefficients of loop integrals, introducing a discrete Fourier projection as a means of improving efficiency and numerical stability. We illustrate the numerical stability of our approach by computing and analyzing six-, seven- and eight-gluon amplitudes in QCD and comparing against previously-obtained analytic results., Comment: 38 pages, 10 figures, RevTex

We give a representation of the parity-even part of the planar two-loop six-gluon MHV amplitude of N=4 super-Yang-Mills theory, in terms of loop-momentum integrals with simple dual conformal properties. We evaluate the integrals numerically in order to test directly the ABDK/BDS all-loop ansatz for planar MHV amplitudes. We find that the ansatz requires an additive remainder function, in accord with previous indications from strong-coupling and Regge limits. The planar six-gluon amplitude can also be compared with the hexagonal Wilson loop computed by Drummond, Henn, Korchemsky and Sokatchev in arXiv:0803.1466 [hep-th]. After accounting for differing singularities and other constants independent of the kinematics, we find that the Wilson loop and MHV-amplitude remainders are identical, to within our numerical precision. This result provides non-trivial confirmation of a proposed n-point equivalence between Wilson loops and planar MHV amplitudes, and suggests that an additional mechanism besides dual conformal symmetry fixes their form at six points and beyond., Comment: 49 pages, RevTex, 2 figure file, v2 minor corrections

This report summarizes the activities of the NLM working group of the Workshop "Physics at TeV Colliders", Les Houches, France, 11-29 June, 2007., Comment: 119 pages, latex, many figures, summary report of the NLO multileg working group of the Les Houches 2007 workshop "Physics at TeV Colliders", Les Houches, France, 11-29 June, 2007; some references added or corrected

Recent computations of scattering amplitudes show that N=8 supergravity is surprisingly well behaved in the ultraviolet and may even be ultraviolet finite in perturbation theory. The novel cancellations necessary for ultraviolet finiteness first appear at one loop in the guise of the "no-triangle hypothesis". We study one-loop amplitudes in pure Einstein gravity and point out the existence of cancellations similar to those found previously in N=8 supergravity. These cancellations go beyond those found in the one-loop effective action. Using unitarity, this suggests that generic theories of quantum gravity based on the Einstein-Hilbert action may be better behaved in the ultraviolet at higher loops than suggested by naive power counting, though without additional (supersymmetric) cancellations they diverge. We comment on future studies that should be performed to support this proposal., Comment: 40 pages, 6 figures. v2 minor corrections, removed comment on absence of rational terms in N=4 supergravity

We present an ansatz for the planar five-loop four-point amplitude in maximally supersymmetric Yang-Mills theory in terms of loop integrals. This ansatz exploits the recently observed correspondence between integrals with simple conformal properties and those found in the four-point amplitudes of the theory through four loops. We explain how to identify all such integrals systematically. We make use of generalized unitarity in both four and D dimensions to determine the coefficients of each of these integrals in the amplitude. Maximal cuts, in which we cut all propagators of a given integral, are an especially effective means for determining these coefficients. The set of integrals and coefficients determined here will be useful for computing the five-loop cusp anomalous dimension of the theory which is of interest for non-trivial checks of the AdS/CFT duality conjecture. It will also be useful for checking a conjecture that the amplitudes have an iterative structure allowing for their all-loop resummation, whose link to a recent string-side computation by Alday and Maldacena opens a new venue for quantitative AdS/CFT comparisons., Comment: 52 pages, 20 figures, revtex

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., Comment: 5 pages, 4 figures. In v2 references and minor clarifications added

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 ref.~[1]. This confirmation of the iteration relation provides further evidence suggesting that N=4 gauge theory is solvable., Comment: 4 pages, 3 figures

We review how (dimensionally regulated) scattering amplitudes in N=4 super-Yang-Mills theory provide a useful testing ground for perturbative QCD calculations relevant to collider physics, as well as another avenue for investigating the AdS/CFT correspondence. We describe the iterative relation for two-loop scattering amplitudes in N=4 super-Yang-Mills theory found in C. Anastasiou et al., Phys. Rev. Lett. 91:251602 (2003), and discuss recent progress toward extending it to three loops., Comment: 17 pages, 9 figures. Talk presented by LD at Strings 2004

We discuss the calculation of two-loop helicity amplitudes for quark-quark scattering in QCD and four-gluino scattering in N=1 supersymmetric Yang-Mills theory. We study the dependence of the results on different variants of dimensional regularization. In particular, we consider the 't Hooft-Veltman and four-dimensional helicity (FDH) schemes. We also discuss ambiguities in continuing the Dirac algebra to D dimensions. For the four-gluino case, once the infrared divergent part of the amplitude is subtracted, the finite remainder is free of these ambiguities., Comment: Presented at 7th DESY Workshop on Elementary Particle Theory: Loops and Legs in Quantum Field Theory, Zinnowitz, Germany, 25-30 Apr 2004

Splitting amplitudes govern the behavior of scattering amplitudes at the momenta of external legs become collinear. In this talk we outline the calculation of two-loop splitting amplitudes via the unitarity sewing method. This method retains the simple factorization properties of light-cone gauge, but avoids the need for prescriptions such as the principal value or Mandelstam-Leibbrandt ones. The encountered loop momentum integrals are then evaluated using integration-by-parts and Lorentz invariance identities. We outline a variety of applications for these splitting amplitudes., Comment: Contribution to the Proceedings of "Loops and Legs in Quantum Field Theory 2004", Zinnowitz, Usedom Island, Germany, April 2004. 5 pages, latex, espcrc2, 5 figures

Using twistor space intuition, Cachazo, Svrcek and Witten presented novel diagrammatic rules for gauge-theory amplitudes, expressed in terms of maximally helicity-violating (MHV) vertices. We define non-MHV vertices, and show how to use them to give a recursive construction of these amplitudes. We also use them to illustrate the equivalence of various twistor-space prescriptions, and to determine the associated combinatoric factors., Comment: 28 pages, 13 figures, ReVTeX; updated references, cosmetic changes to figures, minor changes to text

The anti-de Sitter/conformal field theory duality conjecture raises the question of how the perturbative expansion in the conformal field theory can resum to a simple function. We exhibit a relation between the one-loop and two-loop amplitudes whose generalization to higher-point and higher-loop amplitudes would answer this question. We also provide evidence for the first of these generalizations., Comment: 6 pages, talk given at the 3rd International Symposium on Quantum Theory and Symmetries, Cincinnati, OH, Sept 10-14, 2003; v2: Mispositioned figure in eqn. 1 fixed

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., Comment: 5 pages, 2 figures, uses revtex. v2: references added. v3: reference added, normalizations corrected

We present the two-loop QCD helicity amplitudes for quark-gluon scattering, and for quark-antiquark annihilation into two gluons. These amplitudes are relevant for next-to-next-to-leading order corrections to (polarized) jet production at hadron colliders. We give the results in the `t Hooft-Veltman and four-dimensional helicity (FDH) variants of dimensional regularization. The transition rules for converting the amplitudes between the different variants are much more intricate than for the previously discussed case of gluon-gluon scattering. Summing our two-loop expressions over helicities and colors, and converting to conventional dimensional regularization, gives results in complete agreement with those of Anastasiou, Glover, Oleari and Tejeda-Yeomans. We describe the amplitudes for 2 to 2 scattering in pure N=1 supersymmetric Yang-Mills theory, obtained from the QCD amplitudes by modifying the color representation and multiplicities, and verify supersymmetry Ward identities in the FDH scheme., Comment: 77 pages. v2: corrected errors in eqs. (3.7) and (3.8) for one-loop assembly; remaining results unaffected