arXiv subjects

Anton Olsson

Publications and source records attributed to Anton Olsson.

8 recordsLinked to original sources

arXiv2026

Accelerating Feynman Integral Evaluation by Avoiding Contour Deformation

We describe our method for rewriting dimensionally regulated Feynman parameter integrals in the Minkowski regime as a sum of real, positive integrands multiplied by complex prefactors. This representation eliminates the need for a contour deformation, which is one of the main computational bottlenecks in numerical integration. We demonstrate clearly how the method works on two examples, and benchmark the performance against contour deformation as implemented in pySecDec, where we observe performance gains of up to several orders of magnitude. We describe an improvement in the resolution procedure using the Generic Cylindrical Algebraic Decomposition algorithm, which generalises our method to any Feynman integral, including those with massive propagators.

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arXiv2026

Globally Optimal Contour Deformations with Neural Networks

In this article, we explore the use of contour deformation for the numerical evaluation of Feynman integrals after sector decomposition. In existing codes, the contour of integration is determined heuristically for each phase-space point by sampling the integrand. In this work, we introduce a method for choosing the contour deformation for an entire phase-space region using only an initial sampling or training step. We demonstrate that the resulting integrand has a lower variance than that obtained with heuristic methods and show that optimising a contour to reduce the estimated error of a Quasi-Monte Carlo sample is an ill-defined problem. The a priori knowledge of the integration path obtained in this work can be used to improve the speed of conventional integration methods or be leveraged for integration using neural networks, where, crucially, it removes the need to retrain the neural network for each phase-space point. The techniques described in this work can be adapted to other problems where a non-trivial integration path has to be chosen subject to a set of constraints.

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arXiv2025

Perturbative QCD

We give an introduction to perturbative Quantum Chromodynamics, focusing on a pedagogical description of concepts and methods to calculate cross sections measured at high energy colliders. After introducing basic concepts that allow for a perturbative expansion, such as factorisation and asymptotic freedom, we introduce loop integrals and the treatment of ultraviolet and infrared divergences in QCD. The definition of jets and event shape observables is also discussed. Finally, we give a brief overview of the current state of the art.

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arXiv2025

Positive Integrands from Feynman Integrals in the Minkowski Regime

We present a method for rewriting dimensionally regulated Feynman parameter integrals in the Minkowski regime as a sum of real, positive integrands multiplied by complex prefactors. This representation eliminates the need for contour deformation, allowing for direct numerical or analytic evaluation of the integrals. We develop an algorithm to construct such representations for a broad class of integrals and demonstrate its generalisation through selected examples. Our approach is applied to integrals up to three loops, including cases with internal masses and off-shell external legs. The resulting expressions are suitable for evaluation using existing techniques, such as sector decomposition, where we observe performance gains of up to four orders of magnitude in certain cases.

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arXiv2024

Interpolating amplitudes

The calculation of scattering amplitudes at higher orders in perturbation theory has reached a high degree of maturity. However, their usage to produce physical predictions within Monte Carlo programs is often precluded by the slow evaluation of two- and higher-loop virtual amplitudes, particularly those calculated numerically. As a remedy, interpolation frameworks have been successfully used for amplitudes depending on up to two kinematic invariants. For amplitude interpolation with more variables, such as the five dimensions of a 2 -> 3 phase space, efficient and reliable solutions are sparse. This work aims to pave the way for using amplitude interpolation in higher-dimensional phase spaces by reviewing state-of-the-art interpolation methods, and assessing their performance on a selection of 2 -> 3 scattering amplitudes. Specifically, we investigate interpolation methods based on polynomials, splines, spatially adaptive sparse grids, and neural networks (multilayer perceptron and Lorentz-Equivariant Geometric Algebra Transformer), all under the constraint of limited obtainable data. Our additional aim is to motivate further studies of the interpolation of scattering amplitudes among both physicists and mathematicians.

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arXiv2024

ftint: Calculating gradient-flow integrals with pySecDec

The program ftint is introduced which numerically evaluates dimensionally regulated integrals as they occur in the perturbative approach to the gradient-flow formalism in quantum field theory. It relies on sector decomposition in order to determine the coefficients of the individual orders in $\epsilon=(4-D)/2$, where $D$ is the space-time dimension. For that purpose, it implements an interface to the public library pySecDec. The current version works for massive and massless integrals up to three-loop level with vanishing external momenta, but the underlying method is extendable to more general cases.

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arXiv2024

Evaluating Parametric Integrals in the Minkowski Regime without Contour Deformation

We present selected examples demonstrating an alternative approach to contour deformation for numerically computing loop integrals in the Minkowski regime. This method focuses on identifying singular hypersurfaces (varieties of the $\mathscr{F}$ polynomial) and mapping them to known points which can then be resolved by employing blow-ups/sector decomposition techniques, thereby avoiding the need for contour deformation. Using this technique, we achieve improved convergence properties without the need for contour deformation, which is known to significantly increase the complexity of the integrand by introducing, for example, derivatives of the $\mathscr{F}$ polynomial and complicated Jacobians. We highlight that while we have only tested the approach on selected one-, two- and three-loop massless and one-loop massive examples, it shows promise for practical applications, offering potential benefits over the traditional approach. Evaluation times are compared with existing contour deformation implementations to illustrate the performance of this alternative method.

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arXiv2024

Two-loop amplitudes for ttH production: the quark-initiated Nf-part

We present numerical results for the two-loop virtual amplitude entering the NNLO corrections to Higgs boson production in association with a top quark pair at the LHC, focusing, as a proof of concept of our method, on the part of the quark-initiated channel containing loops of massless or massive quarks. Results for the UV renormalised and IR subtracted two-loop amplitude for each colour structure are given at selected phase-space points and visualised in terms of surfaces as a function of two-dimensional slices of the full phase space.

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