Related papers: New ideas for handling of loop and angular integra…
Higher order calculations in perturbative Quantum Field Theories often produce coupled linear systems of differential equations which factorize to first order. Here we present an algorithm to solve such systems in terms of iterated…
An efficient numerical algorithm to evaluate one-loop amplitudes using tensor integrals is presented. In particular, it is shown by explicit calculations that for ordered QCD amplitudes with a number of external legs up to 10, its…
Perturbation expansions appear to be divergent series in many physically interesting situations, including in quantum field theories like quantum electrodynamics (QED) and quantum chromodynamics (QCD), where the perturbative coefficients…
We give a new method for the reduction of tensor integrals to finite integral representations and UV divergent analytic expressions. This includes a new method for the handling of the gamma-algebra. TYPO IN EQUATION (5) CORRECTED, MACROS…
We present a new procedure using on-shell recursion to determine coefficients of integral functions appearing in one-loop scattering amplitudes of gauge theories, including QCD. With this procedure, coefficients of integrals, including…
We present the details of a recently discovered representation of conformal four-point ladder integrals as thermal one-point functions in scalar field theories. We show that the conformal ladder integrals can be constructed from the…
We briefly describe a new general algorithm for carrying out QCD calculations to next-to-leading order in perturbation theory. The algorithm can be used for computing arbitrary jet cross sections in arbitrary processes and can be…
We construct the generalized version of covariant Z_3-graded differential calculus introduced by one of us (R.K.), and then extended to the case of arbitrary Z_N grading. Here our main purpose is to establish the recurrence formulae for the…
A recursion formula is derived which allows to evaluate invariant integrals over the orthogonal group O(N), where the integrand is an arbitrary finite monomial in the matrix elements of the group. The value of such an integral is…
The advent of efficient numerical algorithms for the construction of one-loop amplitudes has played a crucial role in the automation of NLO calculations, and the development of similar algorithms at two loops is a natural strategy for NNLO…
The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and "tensor" formulation of Q-units with their possible representations are discussed and groups…
We introduce a prescription to define form factor integrands at loop level in planar $\mathcal{N}=4$ supersymmetric Yang-Mills theory. This relies on a periodic kinematic configuration that has been instrumental to describe form factors at…
We present a simplification of the recursive algorithm for the evaluation of intersection numbers for differential $n$-forms, by combining the advantages emerging from the choice of delta-forms as generators of relative twisted cohomology…
The method introduced in a previous paper to simplify the tensorial reduction in multi-leg loop calculations is extended to generic one-loop integrals, with arbitrary internal masses and external momenta.
We present a new formula for the coaction of a large class of integrals. When applied to one-loop (cut) Feynman integrals, it can be given a diagrammatic representation purely in terms of pinches and cuts of the edges of the graph. The…
We consider one-loop scalar and tensor integrals with an arbitrary number of external legs relevant for multi-parton processes in massless theories. We present a procedure to reduce N-point scalar functions with generic 4-dimensional…
Multi-loop scattering amplitudes constitute a serious bottleneck in current high-energy physics computations. Obtaining new integrand level representations with smooth behaviour is crucial for solving this issue, and surpassing the…
In this paper, we present a new algorithm for computing the linear recurrence relations of multi-dimensional sequences. Existing algorithms for computing these relations arise in computational algebra and include constructing structured…
We prove the decomposition of arbitrary diagonal operators into tensor and matrix products of smaller matrices, focusing on the analytic structure of the resulting formulas and their inherent symmetries. Diagrammatic representations are…
The S-matrix for planar N = 4 super Yang-Mills theory can be computed as the correlation function for a holomorphic polygonal Wilson loop in twistor space. In an axial gauge, this leads to the construction of the all-loop integrand via MHV…