• Corpus ID: 119255272

Sharpening The Leading Singularity

@article{Cachazo2008SharpeningTL,
  title={Sharpening The Leading Singularity},
  author={Freddy Cachazo},
  journal={arXiv: High Energy Physics - Theory},
  year={2008}
}
  • F. Cachazo
  • Published 13 March 2008
  • Physics
  • arXiv: High Energy Physics - Theory
W e show how studying leading singularitiesofFeynm an diagram s,when allm om enta are com plex,givesa sim ple way ofwriting m ulti-loop and m ulti-particle scattering am plitudesin N = 4 superYang-M ills.Thesim plicity ofthem ethod isequivalenttothatofthequadruplecuttechnique introduced in hep-th/0412103 atone-loop. The new technique only involves the com putation of residuesand the solution oflinear equations. In our technique both parity even and parity odd 

Prescriptive unitarity with elliptic leading singularities

We investigate the consequences of elliptic leading singularities for the unitarity-based representations of two-loop amplitudes in planar, maximally supersymmetric Yang-Mills theory. We show that

Nonplanar on-shell diagrams and leading singularities of scattering amplitudes

Bipartite on-shell diagrams are the latest tool in constructing scattering amplitudes. In this paper we prove that a Britto–Cachazo–Feng–Witten (BCFW) decomposable on-shell diagram process a rational

Nonplanar on-shell diagrams and leading singularities of scattering amplitudes

Bipartite on-shell diagrams are the latest tool in constructing scattering amplitudes. In this paper we prove that a Britto–Cachazo–Feng–Witten (BCFW) decomposable on-shell diagram process a rational

Global residues and two-loop hepta-cuts

A bstractWe examine maximal unitarity in the nonplanar case and derive remarkably compact analytic expressions for coefficients of master integrals with two-loop crossed box topology in massless

Traintrack Calabi-Yaus from twistor geometry

We describe the geometry of the leading singularity locus of the traintrack integral family directly in momentum twistor space. For the two-loop case, known as the elliptic double box, the leading

Landau Singularities and Higher-Order Roots

Landau’s work on the singularities of Feynman diagrams suggests that they can only be of three types: either poles, logarithmic divergences, or the roots of quadratic polynomials. On the other hand,

The Yangian origin of the Grassmannian integral

In this paper we analyse formulas which reproduce leading singularities of scattering amplitudes in $ \mathcal{N} = 4 $ super Yang-Mills theory through a Grassmannian integral. Recently their Yangian

Inverse soft factors and grassmannian residues

The action of holomorphic inverse soft factors on scattering amplitudes in $ \mathcal{N} = 4 $ SYM is shown to take a remarkably simple form in momentum twistor space. This is used to identify

Multivariate residues and maximal unitarity

A bstractWe extend the maximal unitarity method to amplitude contributions whose cuts define multidimensional algebraic varieties. The technique is valid to all orders and is explicitly demonstrated

UV cancellations in gravity loop integrands

A bstractIn this work we explore the properties of four-dimensional gravity integrands at large loop momenta. This analysis can not be done directly for the full off-shell integrand but only becomes
...

References

SHOWING 1-10 OF 33 REFERENCES

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

This confirmation of the iteration relation provides further evidence suggesting that N=4 gauge theory is solvable.

On the structure of scattering amplitudes in N=4 super Yang-Mills and N=8 supergravity

Exploiting singularities in Feynman integrals to get information about scattering amplitudes has been particularly useful at one-loop in theories where no triangles or bubbles appear. At higher loops

Dimensionally-regulated pentagon integrals☆

Two-loop amplitudes of gluons and octa-cuts in Script N = 4 super Yang-Mills

After reduction techniques, two-loop amplitudes in = 4 super Yang-Mills theory can be written in a basis of integrals containing scalar double-box integrals with rational coefficients, though the

One-loop n-point gauge theory amplitudes, unitarity and collinear limits

MASSIVE LOOP AMPLITUDES FROM UNITARITY

Iterative structure within the five-particle two-loop amplitude

We find an unexpected iterative structure within the two-loop five-gluon amplitude in $\mathcal{N}=4$ supersymmetric Yang-Mills theory. Specifically, we show that a subset of diagrams contributing to

Generalized unitarity and one-loop amplitudes in N=4 super-Yang-Mills

ONE-LOOP AMPLITUDES FOR E+E- TO FOUR PARTONS