Related papers: Efficient integrand reduction for particles with s…
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 the integrals possess subtle…
The calculation of scattering amplitudes in Yang-Mills theory at loop level is important for the analysis of background processes at particle colliders as well as our understanding of perturbation theory at the quantum level. We present…
We describe the application of a novel approach for the reduction of scattering amplitudes, based on multivariate polynomial division, which we have recently presented. This technique yields the complete integrand decomposition for…
We show how generalised unitarity cuts in D = 4 - 2 epsilon dimensions can be used to calculate efficiently complete one-loop scattering amplitudes in non-supersymmetric Yang-Mills theory. This approach naturally generates the rational…
We present a method for the computation of hepta-cuts of two loop scattering amplitudes. Four dimensional unitarity cuts are used to factorise the integrand onto the product of six tree-level amplitudes evaluated at complex momentum values.…
We present the building blocks that can be combined to produce tree-level S-matrix elements of a variety of theories with various spins mixed in arbitrary dimensions. The new formulas for the scattering of $n$ massless particles are given…
We present a new formulation for Yang-Mills scattering amplitudes in any number of dimensions and at any loop order, based on the same combinatorial and binary-geometric ideas in kinematic space recently used to give an all-order…
Scattering amplitudes in Yang-Mills theory can be represented in the formalism of Cachazo, He and Yuan (CHY) as integrals over an auxiliary projective space---fully localized on the support of the scattering equations. Because solving the…
We give an explicit recursive formula for the all L-loop integrand for scattering amplitudes in N=4 SYM in the planar limit, manifesting the full Yangian symmetry of the theory. This generalizes the BCFW recursion relation for tree…
Several problems in computer algebra can be efficiently solved by reducing them to calculations over finite fields. In this paper, we describe an algorithm for the reconstruction of multivariate polynomials and rational functions from their…
Pure Yang-Mills amplitudes with all external gluons carrying positive helicity, known as all-plus amplitudes, have an especially simple structure. The tree amplitudes vanish and, up to at least two loops, the loop-level amplitudes are…
Scattering amplitudes in planar super-Yang-Mills theory satisfy several basic physical and mathematical constraints, including physical constraints on their branch cut structure and various empirically discovered connections to the…
We review the computation of scattering amplitudes of planar maximally super-symmetric Yang-Mills at strong coupling. By using the AdS/CFT duality the problem boils down to the computation of the area of certain minimal surfaces on AdS. The…
After reduction techniques, two-loop amplitudes in N=4 super Yang-Mills theory can be written in a basis of integrals containing scalar double-box integrals with rational coefficients, though the complete basis is unknown. Generically, at…
I study constraints on fundamental physics emerging from consistency of a unitary, local and perturbative $S$-matrix in $4d$. For massless particles, some new constraints arising from consistent complex factorisation of $2\rightarrow 2$…
Following Alday and Maldacena, we describe a string theory method to compute the strong coupling behavior of the scattering amplitudes of quarks and gluons in planar N=2 super Yang-Mills theory in the probe approximation. Explicit…
We compute the integrand of the full-colour, two-loop, five-gluon scattering amplitude in pure Yang-Mills theory with all helicities positive, using generalized unitarity cuts. Tree-level BCJ relations, satisfied by amplitudes appearing in…
This thesis aims at providing better understanding of the perturbative expansion of gauge theories with and without supersymmetry. At tree level, the BCFW recursion relations are analyzed with respect to their validity for general off-shell…
One-loop amplitudes of gluons in supersymmetric Yang-Mills are four-dimensional cut-constructible. This means that they can be determined from their unitarity cuts. We present a new systematic procedure to explicitly carry out any finite…
We calculate one-loop scattering amplitudes in N=4 super Yang-Mills theory away from the origin of the moduli space and demonstrate that the results are extremely simple, in much the same way as in the conformally invariant theory.…