Publications (91)
Vector Boson + Jets with BlackHat and Sherpa
C. F. Berger, Z. Bern, L. J. Dixon +6
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 th…
Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops
Z. Bern, J. J. M. Carrasco, H. Johansson +1
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 obser…
Recent Progress in One-Loop Multi-Parton Calculations
Z. Bern, L. Dixon, D. C. Dunbar +1
We describe techniques that simplify the calculation of one-loop QCD amplitudes with many external legs, which are needed for next-to-leading-order (NLO) corrections to multi-jet p…
Two-loop helicity amplitudes for fermion-fermion scattering
A. De Freitas, Z. Bern
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 depend…
Cross-Order Relations in N=4 Supersymmetric Gauge Theories
C. Anastasiou, Z. Bern, L. J. Dixon +1
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…
Neutralino Annihilation into Two Photons
Z. Bern, P. Gondolo, M. Perelstein
We compute the annihilation cross-section of two neutralinos at rest into two photons, which is of importance for the indirect detection of neutralino dark matter in the galactic h…
Precise Predictions for Z + 4 Jets at Hadron Colliders
H. Ita, Z. Bern, L. J. Dixon +3
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…
Next-to-Leading Order QCD Predictions for W+3-Jet Distributions at Hadron Colliders
C. F. Berger, Z. Bern, L. J. Dixon +6
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 subprocesse…
New Relations for Gauge-Theory Amplitudes
Z. Bern, J. J. M. Carrasco, H. Johansson
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 i…
NLO vector boson production with light jets
Z. Bern, G. Diana, L. J. Dixon +8
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 w…
Two-Loop N=4 Supersymmetric Amplitudes and QCD
Z. Bern, J. Rozowsky, B. Yan
Two-loop four-gluon N=4 susy amplitudes are evaluated via cutting techniques as a testing ground for QCD. A conjecture for four-point amplitudes to all loop orders is described. We…
Supersymmetry Relations Between Contributions To One-Loop Gauge Boson Amplitudes
Z. Bern, A. G. Morgan
We apply ideas motivated by string theory to improve the calculational efficiency of one-loop weak interaction processes with massive external gauge bosons. In certain cases ``supe…
The Five Gluon Amplitude and One-Loop Integrals
Z. Bern, L. Dixon, D. A. Kosower
We review the conventional field theory description of the string motivated technique. This technique is applied to the one-loop five-gluon amplitude. To evaluate the amplitude a g…
The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
Z. Bern, L. J. Dixon, D. A. Kosower +4
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…
One-Loop N Gluon Amplitudes with Maximal Helicity Violation via Collinear Limits
Z. Bern, G. Chalmers, L. Dixon +1
We present a conjecture for the -gluon one-loop amplitudes with maximal helicity violation. The conjecture emerges from the powerful requirement that the amplitudes have the cor…
Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge Theory and Gravity Amplitudes
Z. Bern, J. J. M. Carrasco, L. J. Dixon +2
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…
A Two-Loop Four-Gluon Helicity Amplitude in QCD
Z. Bern, L. Dixon, D. A. Kosower
We present the two-loop pure gauge contribution to the gluon-gluon scattering amplitude with maximal helicity violation. Our construction of the amplitude does not rely directly on…
Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory
C. Anastasiou, Z. Bern, L. Dixon +1
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…
Two-loop Splitting Amplitudes
Z. Bern, L. J. Dixon, D. A. Kosower
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 am…
Next-to-Leading Order QCD Predictions for Z,gamma^*+3-Jet Distributions at the Tevatron
C. F. Berger, Z. Bern, L. J. Dixon +6
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, w…
One-Loop Amplitudes for e^+ e^- to Four Partons
Z. Bern, L. Dixon, D. A. Kosower
We present the first explicit formulae for the complete set of one-loop helicity amplitudes necessary for computing next-to-leading order corrections for e^+ e^- annihilation into…
Counterterms in Supergravity
Z. Bern, D. Dunbar, L. Dixon +5
We examine the ultraviolet behaviour of supergravity theories as a function of dimension and number of supercharges. We do so by the computation of one and two-loop physical on-she…
Progress in One-Loop QCD Computations
Z. Bern, L. Dixon, D. A. Kosower
We review progress in calculating one-loop scattering amplitudes required for next-to-leading-order corrections to QCD processes. The underlying technical developments include the…
Two-Loop Amplitudes for Gluon Fusion into Two Photons
Z. Bern, A. De Freitas, L. Dixon
We present the two-loop matrix elements for the scattering of two gluons into two photons in QCD. These matrix elements will enter into improved estimates of the QCD background to…
The Structure of Multiloop Amplitudes in Gauge and Gravity Theories
Z. Bern, J. J. M. Carrasco, H. Johansson
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 numera…
The Five-Loop Four-Point Amplitude of N=4 super-Yang-Mills Theory
Z. Bern, J. J. M. Carrasco, H. Johansson +1
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 cont…
Two-Loop Four-Gluon Amplitudes in N=4 Super-Yang-Mills
Z. Bern, J. S. Rozowsky, B. Yan
Using cutting techniques we obtain the two-loop N=4 super-Yang-Mills helicity amplitudes for four-gluon scattering in terms of scalar integral functions. The N=4 amplitudes are con…
The Infrared Behavior of One-Loop QCD Amplitudes at Next-to-Next-to-Leading Order
Z. Bern, V. Del Duca, W. B. Kilgore +1
We present universal factorization formulas describing the behavior of one-loop QCD amplitudes as external momenta become either soft or collinear. Our results are valid to all ord…
One-Loop Self-Dual and N=4 Super Yang-Mills
Z. Bern, L. Dixon, D. C. Dunbar +1
We conjecture a simple relationship between the one-loop maximally helicity violating gluon amplitudes of ordinary QCD (all helicities identical) and those of N=4 supersymmetric Ya…
Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes
Z. Bern, L. Dixon, D. C. Dunbar +1
We identify a large class of one-loop amplitudes for massless particles that can be constructed via unitarity from tree amplitudes, without any ambiguities. One-loop amplitudes for…
Two-Loop Helicity Amplitudes for Quark-Gluon Scattering in QCD and Gluino-Gluon Scattering in Supersymmetric Yang-Mills Theory
Z. Bern, A. De Freitas, L. Dixon
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-…
Next-to-Leading Order W + 5-Jet Production at the LHC
Z. Bern, L. J. Dixon, F. Febres Cordero +5
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 H…
Snowmass Theory Frontier Report
N. Craig, C. Csáki, A. X. El-Khadra +38
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 Proce…
Two-loop corrections to
Z. Bern, A. De Freitas, L. Dixon
An overview of the calculation of the two-loop helicity amplitudes for scattering of two gluons into two photons is presented. These matrix elements enter into the recent improved…
New QCD Results from String Theory
Z. Bern, L. Dixon, D. A. Kosower
We discuss new results in QCD obtained with string-based methods. These methods were originally derived from superstring theory and are significantly more efficient than convention…
One-Loop Corrections to Two-Quark Three-Gluon Amplitudes
Z. Bern, L. Dixon, D. A. Kosower
We present the one-loop QCD amplitudes for two external massless quarks and three external gluons (). This completes the set of one-loop amplitudes needed for the next…
High multiplicity W+jets predictions at NLO
Z. Bern, L. J. Dixon, F. Febres Cordero +5
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 als…
EFFICIENT ANALYTIC COMPUTATION OF HIGHER-ORDER QCD AMPLITUDES
Z. Bern, G. Chalmers, L. Dixon +2
We review techniques simplifying the analytic calculation of one-loop QCD amplitudes with many external legs, for use in next-to-leading-order corrections to multi-jet processes. P…
Four-Jet Production at the Large Hadron Collider at Next-to-Leading Order in QCD
Z. Bern, G. Diana, L. J. Dixon +6
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 conjuncti…
The Ultraviolet Behavior of N=8 Supergravity at Four Loops
Z. Bern, J. J. Carrasco, L. J. Dixon +2
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 di…
On the Structure of Supersymmetric Sums in Multi-Loop Unitarity Cuts
Z. Bern, J. J. M. Carrasco, H. Ita +2
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 t…
Massive Loop Amplitudes from Unitarity
Z. Bern, A. G. Morgan
We show, for previously uncalculated examples containing a uniform mass in the loop, that it is possible to obtain complete massive one-loop gauge theory amplitudes solely from uni…
Left-Handed W Bosons at the LHC
Z. Bern, G. Diana, L. J. Dixon +8
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 leptoni…
One-Loop n-Point Helicity Amplitudes in (Self-Dual) Gravity
Z. Bern, L. Dixon, M. Perelstein +1
We present an ansatz for all one-loop amplitudes in pure Einstein gravity for which the n external gravitons have the same outgoing helicity. These loop amplitudes, which are ratio…
Precise Predictions for W + 3 Jet Production at Hadron Colliders
C. F. Berger, Z. Bern, L. J. Dixon +6
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 dat…
N >= 4 Supergravity Amplitudes from Gauge Theory at One Loop
Z. Bern, C. Boucher-Veronneau, H. Johansson
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.…
Unitarity-based Techniques for One-Loop Calculations in QCD
Z. Bern, L. Dixon, D. A. Kosower
We discuss new techniques developed in recent years for performing one-loop calculations in QCD, and present an example of results from the process 0 -> V q q-bar g g. Talk present…
Driving Missing Data at Next-to-Leading Order
Z. Bern, G. Diana, L. J. Dixon +6
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 st…
Next-to-Leading Order Jet Physics with BlackHat
C. F. Berger, Z. Bern, L. J. Dixon +6
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 bos…
On the Coupling of Gravitons to Matter
Z. Bern, A. De Freitas, H. L. Wong
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 theor…
Two-Loop Iteration of Five-Point N=4 Super-Yang-Mills Amplitudes
Z. Bern, M. Czakon, D. A. Kosower +2
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 ampli…
Next-to-Leading Order Gamma Gamma + 2-Jet Production at the LHC
Z. Bern, L. J. Dixon, F. Febres Cordero +5
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 con…
Multi-jet cross sections at NLO with BlackHat and Sherpa
C. F. Berger, Z. Bern, L. J. Dixon +6
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 perf…
Perturbative Gravity from QCD Amplitudes
Z. Bern, A. K. Grant
We demonstrate that QCD gluon amplitudes can be used to construct a Lagrangian for gravity. This procedure makes use of perturbative `squaring' relations between gravity and gauge…
Twistor-Space Recursive Formulation of Gauge-Theory Amplitudes
I. Bena, Z. Bern, D. A. Kosower
Using twistor space intuition, Cachazo, Svrcek and Witten presented novel diagrammatic rules for gauge-theory amplitudes, expressed in terms of maximally helicity-violating (MHV) v…
One-Loop Corrections to Five-Gluon Amplitudes
Z. Bern, L. Dixon, D. A. Kosower
We present the one-loop helicity amplitudes with five external gluons. The computation employs string-based methods, new techniques for performing tensor integrals, and improvement…
One-Loop Amplitudes for e^+ e^- to q-bar q Q-bar Q
Z. Bern, L. Dixon, D. A. Kosower +1
We present the one-loop helicity amplitudes for processes involving a vector boson V (V=W,Z, or gamma^*) and four massless quarks, 0 to V q-bar q Q-bar Q, where V couples to a mass…
Supersymmetric Regularization, Two-Loop QCD Amplitudes and Coupling Shifts
Z. Bern, A. De Freitas, L. Dixon +1
We present a definition of the four-dimensional helicity (FDH) regularization scheme valid for two or more loops. This scheme was previously defined and utilized at one loop. It am…
Three-Loop Superfiniteness of N=8 Supergravity
Z. Bern, J. J. Carrasco, L. J. Dixon +3
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 pr…
Ntuples for NLO Events at Hadron Colliders
Z. Bern, L. J. Dixon, F. Febres Cordero +4
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 t…
Perturbative Relations between Gravity and Gauge Theory
Z. Bern, L. Dixon, D. C. Dunbar +2
We review the relations that have been found between multi-loop scattering amplitudes in gauge theory and gravity, and their implications for ultraviolet divergences in supergravit…
Multi-Leg One-Loop Gravity Amplitudes from Gauge Theory
Z. Bern, L. Dixon, M. Perelstein +1
By exploiting relations between gravity and gauge theories, we present two infinite sequences of one-loop n-graviton scattering amplitudes: the `maximally helicity-violating' ampli…
The NLO multileg working group: summary report
Z. Bern, S. Dittmaier, L. Dixon +44
This report summarizes the activities of the NLM working group of the Workshop "Physics at TeV Colliders", Les Houches, France, 11-29 June, 2007.
An Automated Implementation of On-Shell Methods for One-Loop Amplitudes
C. F. Berger, Z. Bern, L. J. Dixon +5
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 cons…
Extrapolating W-Associated Jet-Production Ratios at the LHC
Z. Bern, L. J. Dixon, F. Febres Cordero +4
Electroweak vector-boson production, accompanied by multiple jets, is an important background to searches for physics beyond the Standard Model. A precise and quantitative understa…
Next-to-leading order diphoton+2-jet production at the LHC
Z. Bern, L. J. Dixon, F. Febres Cordero +5
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 ev…
NLO QCD Predictions for W+3 jets
C. F. Berger, Z. Bern, L. J. Dixon +6
In this contribution we present results from the NLO computation of the production of a boson in association with three jets in hadronic collisions. The results are obtained by…
Multi-Parton Loop Amplitudes and Next-to-Leading Order Jet Cross-Sections
Z. Bern, L. Dixon, D. A. Kosower +1
We review recent developments in the calculation of QCD loop amplitudes with several external legs, and their application to next-to-leading order jet production cross-sections. Wh…
Manifest Ultraviolet Behavior for the Three-Loop Four-Point Amplitude of N=8 Supergravity
Z. Bern, J. J. M. Carrasco, L. J. Dixon +2
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. T…
One-Loop Calculations with BlackHat
C. F. Berger, Z. Bern, L. J. Dixon +5
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 rec…
Unexpected Cancellations in Gravity Theories
Z. Bern, J. J. Carrasco, D. Forde +2
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. T…
Universality in W+Multijet Production
Z. Bern, L. J. Dixon, F. Febres Cordero +5
We study -boson production accompanied by multiple jets at 7 TeV at the LHC. We study the jet-production ratio, of total cross sections for +- to +()-jet productio…
The Complete Four-Loop Four-Point Amplitude in N=4 Super-Yang-Mills Theory
Z. Bern, J. J. M. Carrasco, L. J. Dixon +2
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 n…
Progress on Ultraviolet Finiteness of Supergravity
Z. Bern, J. J. M. Carrasco, H. Johansson
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, w…
QCD and QED Corrections to Light-by-Light Scattering
Z. Bern, A. De Freitas, L. Dixon +2
We present the QCD and QED corrections to the fermion-loop contributions to light-by-light scattering, gamma gamma to gamma gamma, in the ultrarelativistic limit where the kinemati…
Perturbative Relationships Between QCD and Gravity and Some Implications
Z. Bern, L. Dixon, D. C. Dunbar +2
We discuss nontrivial examples illustrating that perturbative gravity is in some sense the `square' of gauge theory. This statement can be made precise at tree-level using the Kawa…
On Perturbative Gravity and Gauge Theory
Z. Bern, L. Dixon, D. C. Dunbar +3
We review some applications of tree-level (classical) relations between gravity and gauge theory that follow from string theory. Together with -dimensional unitarity, these rela…
One-Loop Multi-Parton Amplitudes with a Vector Boson for the LHC
C. F. Berger, Z. Bern, L. J. Dixon +5
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 t…
Two-Loop Correction to Bhabha Scattering
Z. Bern, L. Dixon, A. Ghinculov
We present the two-loop virtual QED corrections to e^+ e^- to mu^+ mu^- and Bhabha scattering in dimensional regularization. The results are expressed in terms of polylogarithms. T…
Perturbative Quantization of Gravity Theories
Z. Bern
We discuss string theory relations between gravity and gauge theory tree amplitudes. Together with -dimensional unitarity, these relations can be used to perturbatively quantize…
Dimensionally Regulated One-Loop Integrals
Z. Bern, L. Dixon, D. A. Kosower
We describe methods for evaluating one-loop integrals in $4-2\e$ dimensions. We give a recursion relation that expresses the scalar -point integral as a cyclicly symmetric combi…
String-Based Methods in Perturbative Gravity
Z. Bern, D. C. Dunbar, T. Shimada
String theory implies a relatively modest growth in computational complexity for perturbative gravity calculations as compared to gauge theory calculations, contrary to field theor…
On the Relationship between Yang-Mills Theory and Gravity and its Implication for Ultraviolet Divergences
Z. Bern, L. Dixon, D. C. Dunbar +2
String theory implies that field theories containing gravity are in a certain sense `products' of gauge theories. We make this product structure explicit up to two loops for the re…
One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
Z. Bern, L. Dixon, D. C. Dunbar +1
We present a technique which utilizes unitarity and collinear limits to construct ansatze for one-loop amplitudes in gauge theory. As an example, we obtain the one-loop contributio…
Missing Energy and Jets for Supersymmetry Searches
Z. Bern, G. Diana, L. J. Dixon +6
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 gamm…
Factorization in One-Loop Gauge Theory
Z. Bern, G. Chalmers
Factorization properties of one-loop gauge theory amplitudes have been used as checks on explicitly computed amplitudes and in the construction of ansatze for higher-point ones. In…
Precise Predictions for W + 4 Jet Production at the Large Hadron Collider
C. F. Berger, Z. Bern, L. J. Dixon +6
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 an…
N=4 Super-Yang-Mills Theory, QCD and Collider Physics
Z. Bern, L. J. Dixon, D. A. Kosower
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…
The BlackHat Library for One-Loop Amplitudes
Z. Bern, L. J. Dixon, F. Febres Cordero +5
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 matri…
One-Loop Gauge Theory Amplitudes with an Arbitrary Number of External Legs
Z. Bern, L. Dixon, D. Dunbar +1
We review recent progress in calculations of one-loop QCD amplitudes. By imposing the consistency requirements of unitarity and correct behavior as the momenta of two legs become c…
Dimensionally Regulated Pentagon Integrals
Z. Bern, L. Dixon, D. A. Kosower
We present methods for evaluating the Feynman parameter integrals associated with the pentagon diagram in 4-2 epsilon dimensions, along with explicit results for the integrals with…