Related papers: Optimizing the Reduction of One-Loop Amplitudes
We present the first numerical results for the two-loop helicity amplitudes for the scattering of four partons and a W-boson in QCD. We use a finite field sampling method to reduce directly from Feynman diagrams to the coefficients of a set…
We show that the evaluation of scattering amplitudes can be formulated as a problem of multivariate polynomial division, with the components of the integration-momenta as indeterminates. We present a recurrence relation which, independently…
We compute the two-loop master integrals for leading-color QCD scattering amplitudes including a closed light-quark loop in $t\bar{t}H$ production at hadron colliders. Exploiting numerical evaluations in modular arithmetic, we construct a…
The numerical unitarity approach has been important for obtaining reliable QCD predictions for the LHC. Here I discuss the extension of the approach beyond the leading quantum corrections for computing multi-loop amplitudes. The numerical…
The four-loop QCD corrections to the electroweak $\rho$-parameter arising from top and bottom quark loops are computed. Specifically we evaluate the missing ``non-singlet'' piece. Using algebraic methods the amplitude is reduced to a set of…
We recompute the functions describing the collinear factorization of one-loop amplitudes using the unitarity-based method. We present the results in a form suitable for use as an ingredient in two-loop calculations. We also present a…
I describe a method for determining the coefficients of scalar integrals for one-loop amplitudes in quantum field theory. The method is based upon generalized unitarity and the behavior of amplitudes when the free parameters of the cut…
We apply the recently proposed amplitude reduction at the integrand level method, to the computation of the scattering process 2 photons -> 4 photons, including the case of a massive fermion loop. We also present several improvements of the…
We present formulas for the coefficients of 2-, 3-, 4- and 5-point master integrals for one-loop massive amplitudes. The coefficients are derived from unitarity cuts in D dimensions. The input parameters can be read off from any…
Loop amplitudes are conveniently expressed in terms of master integrals whose coefficients carry the process dependent information. Similarly before integration, the loop integrands may be expressed as a linear combination of propagator…
We propose an alternative approach based on series representation to directly reduce multi-loop multi-scale scattering amplitude into set of freely chosen master integrals. And this approach avoid complicated calculations of inverse matrix…
We present a semi-numerical algorithm to calculate one-loop virtual corrections to scattering amplitudes. The divergences of the loop amplitudes are regulated using dimensional regularization. We treat in detail the case of amplitudes with…
An optimisation algorithm is proposed for designing PID controllers, which minimises the asymptotic open-loop gain of a system, subject to appropriate robust- stability and performance QFT constraints. The algorithm is simple and can be…
Two program packages are presented for evaluating one-loop amplitudes. They can work either in dimensional regularization or in constrained differential renormalization. The latter method is found at the one-loop level to be equivalent to…
Some of the tools and techniques that have recently been used to compute Higgs boson pair production at NLO in QCD are discussed. The calculation relies on the use of integral reduction, to reduce the number of integrals which must be…
NLO scattering amplitudes are provided by fully automated numerical tools, such as OpenLoops, for a very wide range of processes. In order to match the numerical precision of current and future collider experiments, the higher precision of…
This article reviews on-shell methods for analytic computation of loop amplitudes, emphasizing techniques based on unitarity cuts. Unitarity techniques are formulated generally but have been especially useful for calculating one-loop…
Optimal pulse patterns (OPPs) are a modulation technique in which a switching signal is computed offline through an optimization process that accounts for selected performance criteria, such as current harmonic distortion. The optimization…
We discuss recent progress in multi-loop integrand reduction methods. Motivated by the possibility of an automated construction of multi-loop amplitudes via generalized unitarity cuts we describe a procedure to obtain a general…
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. Particularly useful are the constraints imposed by…