arXiv subjects

L. J. Dixon

Publications and source records attributed to L. J. Dixon.

At least 37 records · Page 2Linked to original sources

arXiv2011

Precise Predictions for W + 4 Jet Production at the Large Hadron Collider

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.

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arXiv2010

Next-to-Leading Order Jet Physics with BlackHat

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.

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arXiv2010

The Complete Four-Loop Four-Point Amplitude in N=4 Super-Yang-Mills Theory

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.

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arXiv2010

Next-to-Leading Order QCD Predictions for Z,gamma^*+3-Jet Distributions at the Tevatron

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.

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arXiv2010

Vector Boson + Jets with BlackHat and Sherpa

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.

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arXiv2010

R^4 counterterm and E7(7) symmetry in maximal supergravity

The coefficient of a potential R^4 counterterm in N=8 supergravity has been shown previously to vanish in an explicit three-loop calculation. The R^4 term respects N=8 supersymmetry; hence this result poses the question of whether another symmetry could be responsible for the cancellation of the three-loop divergence. In this article we investigate possible restrictions from the coset symmetry E7(7)/SU(8), exploring the limits as a single scalar becomes soft, as well as a double-soft scalar limit relation derived recently by Arkani-Hamed et al. We implement these relations for the matrix elements of the R^4 term that occurs in the low-energy expansion of closed-string tree-level amplitudes. We find that the matrix elements of R^4 that we investigated all obey the double-soft scalar limit relation, including certain non-maximally-helicity-violating six-point amplitudes. However, the single-soft limit does not vanish for this latter set of amplitudes, which suggests that the E7(7) symmetry is broken by the R^4 term.

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arXiv2009

Next-to-Leading Order QCD Predictions for W+3-Jet Distributions at Hadron Colliders

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.

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arXiv2009

NLO QCD Predictions for W+3 jets

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.

hep-ph↗

arXiv2009

Multi-jet cross sections at NLO with BlackHat and Sherpa

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.

hep-ph↗

arXiv2009

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 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.

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arXiv2008

Manifest Ultraviolet Behavior for the Three-Loop Four-Point Amplitude of N=8 Supergravity

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.

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arXiv2008

The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory

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.

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arXiv2008

One-Loop Multi-Parton Amplitudes with a Vector Boson for the LHC

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.

hep-ph↗

arXiv2008

One-Loop Calculations with BlackHat

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.

hep-ph↗

arXiv2008

An Automated Implementation of On-Shell Methods for One-Loop Amplitudes

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.

hep-ph↗

arXiv2007

Three-Loop Superfiniteness of N=8 Supergravity

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.

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arXiv2004

N=4 Super-Yang-Mills Theory, QCD and Collider Physics

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.

hep-th↗

arXiv2004

Two-loop Splitting Amplitudes

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.

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