Related papers: Optimizing the Reduction of One-Loop Amplitudes
This paper investigates constructive interference (CI)-based waveform design for phase shift keying and quadrature amplitude modulation symbols under relaxed block-level power constraints in multi-user multiple-input single-output (MU-MIMO)…
The calculation of hard scattering amplitudes up to NLO is automated in numerical tools, such as OpenLoops. The LHC and future experiments, however, demand high-precision predictions at NNLO and beyond for a wide range of particle…
We present the analytic and compact two-loop helicity amplitudes for QCD and QED corrections to the light-by-light scattering process with massive internal fermions. We express the master integrals either in terms of multiple polylogarithms…
A method to separate pentagon contributions from the evaluation of the cut constructible part of primitive amplitudes within the framework of D-dimensional unitarity is proposed. The cut constructible part is thus reconstructed with…
We propose to resum exactly any number of one-loop vacuum polarization insertions into the scale of the coupling of lowest order radiative corrections. This makes maximal use of the information contained in one-loop perturbative corrections…
The inverse amplitude method is used to unitarize the two loop $\pi\pi$ scattering amplitudes of SU(2) Chiral Perturbation Theory in the $I=0,J=0$, $I=1,J=1$ and $I=2,J=0$ channels. An error analysis in terms of the low energy one-loop…
We briefly sketch the methods for a numerically stable evaluation of tensor one-loop integrals that have been used in the calculation of the complete electroweak one-loop corrections to $\Pep\Pem\to4 $fermions. In particular, the…
We calculate field theory loop amplitudes by string methods, applied to half-maximal 4-point one-loop graviton amplitudes. Infrared divergences are regulated similarly to soft-collinear effective field theory (SCET): new mass scales are…
We present an algorithm for the optimization of a class of finite element integration loop nests. This algorithm, which exploits fundamental mathematical properties of finite element operators, is proven to achieve a locally optimal…
An improved method is presented for the numerical evaluation of multi-loop integrals in dimensional regularization. The technique is based on Mellin-Barnes representations, which have been used earlier to develop algorithms for the…
Numerical tools, such as OpenLoops, provide NLO scattering amplitudes for a very wide range of hard scattering amplitudes in a fully automated way. In order to match the numerical precision of current and future experiments, however, the…
Analog circuit design can be formulated as a non-linear constrained optimisation problem that can be solved using any suitable optimisation algorithms. Different optimisation techniques have been reported to reduce the design time of analog…
We present a method for the direct extraction of rational contributions to one-loop scattering amplitudes, missed by standard four-dimensional unitarity techniques. We use generalised unitarity in $D=4-2\e$ dimensions to write the loop…
We present a method to numerically evaluate infrared-finite one- and two-loop integrals within the Four-Dimensional Regularization/Renormalization approach, in which a small mass serves as regulator. Typical integrals exhibit a logarithmic…
An adaptive algorithm for spectral proper orthogonal decomposition (SPOD) of mixed broadband-tonal turbulent flows is developed. Sharp peak resolution at tonal frequencies is achieved by locally minimizing the bias of the spectrum. Smooth…
This work aims to introduce the framework of polynomial optimization theory to solve fractional polynomial problems (FPPs). Unlike other widely used optimization frameworks, the proposed one applies to a larger class of FPPs, not…
We consider a property of positive polynomials on a compact set with a small perturbation. When applied to a Polynomial Optimization Problem (POP), the property implies that the optimal value of the corresponding SemiDefinite Programming…
A formalism for the numerical integration of one- and two-loop integrals is presented. It is based on subtraction terms which remove the soft, collinear and some of the ultraviolet divergences from the integrand. The numerical integral is…
We develop an algorithm of polynomial complexity for evaluating one-loop amplitudes with an arbitrary number of external particles. The algorithm is implemented in the Rocket program. Starting from particle vertices given by Feynman rules,…
Systematic optimization over a wide power range is often achieved through the combination of modules of different power levels. This paper addresses the issue of enhancing the efficiency of a multiple module system connected in parallel…