We find that all Feynman integrals (FIs), having any number of loops, can be completely determined once linear relations between FIs are provided. Therefore, FI computation is conceptually changed to a linear algebraic problem. Examples up to five loops are given to verify this observation. As a by-product, we obtain a powerful method to calculate perturbative corrections in quantum field theory. 

/pdf/determining-feynman-integrals-with-only-input-from-linear-29qs06j8.pdf

Determining Feynman Integrals with Only Input from Linear Algebra

We present the first calculation of the complete set of NNLO QED corrections for muon-electron scattering. This includes leptonic, non-perturbative hadronic, and photonic contributions. All fermionic corrections as well as the photonic subset that only corrects the electron or the muon line are included with full mass dependence. The genuine four-point two-loop topologies are computed as an expansion in the small electron mass, taking into account both, logarithmically enhanced as well as constant mass effects using massification. A fast and stable implementation of the numerically delicate real-virtual contribution is achieved by combining OpenLoops with next-to-soft stabilisation. All matrix elements are implemented in the McMule framework, which allows for the fully-differential calculation of any infrared-safe observable. This calculation is to be viewed in the context of the MUonE experiment requiring a background prediction at the level of 10 ppm. Our results thus represent a major milestone towards this ambitious precision goal. 

/pdf/muon-electron-scattering-at-nnlo-25ddy3pe.pdf

Muon-electron scattering at NNLO

Evaluating Feynman integrals at higher orders in coupling constants in quantum field theories remains a complicated task. In this paper, the authors complete another step in the ongoing program of calculating Feynman integrals using the auxiliary mass flow method, namely they show how to include linear propagators up to four loops. 

/pdf/automatic-computation-of-feynman-integrals-containing-linear-2hausaz8.pdf

Automatic computation of Feynman integrals containing linear propagators via auxiliary mass flow

We find that all Feynman integrals (FIs), having any number of loops, can be completely determined once linear relations between FIs are provided. Therefore, FI computation is conceptually changed to a linear algebraic problem. Examples up to five loops are given to verify this observation. As a by-product, we obtain a powerful method to calculate perturbative corrections in quantum field theory.

Determining Feynman Integrals with Only Input from Linear Algebra.

We present a major update of the program pySecDec, a toolbox for the evaluation of dimensionally regulated parameter integrals. The new version enables the evaluation of multi-loop integrals as well as amplitudes in a highly distributed and flexible way, optionally on GPUs. The program has been optimised and runs up to an order of magnitude faster than the previous release. A new integration procedure that utilises construction-free median Quasi-Monte Carlo rules is implemented. The median lattice rules can outperform our previous component-by-component rules by a factor of 5 and remove the limitation on the maximum number of sampling points. The expansion by regions procedures have been extended to support Feynman integrals with numerators, and functions for automatically determining when and how analytic regulators should be introduced are now available. The new features and performance are illustrated with several examples. Program Title: pySecDec CPC Library link to program files: https://doi.org/10.17632/dnrkf5jxzh.4 Developer's repository link: https://github.com/gudrunhe/secdec, https://secdec.readthedocs.io (Online documentation) Licensing provisions: GNU Public License v3 Programming language: Python, Form, C++, Cuda External routines/libraries: GSL [1], NumPy [2], SymPy [3], Nauty [4], Cuba [5], Form [6], GiNaC and CLN [7], Normaliz [8], GMP [9]. Journal reference of previous version: Comput. Phys. Commun. 273 (2022) 108267 [1]. Does the new version supersede the previous version?: Yes. Nature of problem: Scattering amplitudes at higher orders in perturbation theory are typically represented as a linear combination of coefficients — containing the kinematic invariants and the space-time dimension — multiplied with loop integrals which contain singularities and whose analytic representation might be unknown. Solution method: Extraction of singularities in the dimensional regularization parameter as well as in analytic regulators for potential spurious singularities is done using sector decomposition. The combined evaluation of the integrals with their coefficients is performed in an efficient way. Restrictions: Depending on the complexity of the problem, limited by memory and CPU/GPU time. M. Galassi et al., GNU Scientific Library Reference Manual. ISBN: 0954612078, http://www.gnu.org/software/gsl/. C.R. Harris, K.J. Millman, S.J. van der Walt, et al., Array programming with NumPy, Nature 585 (2020) 357–362. https://doi.org/10.1038/s41586-020-2649-2, http://www.numpy.org/. A. Meurer, et al., SymPy: symbolic computing in Python, PeerJ Comp. Sci. 3 (2017) e103. https://doi.org/10.7717/peerj-cs.103, http://www.sympy.org/. B.D. McKay, A. Piperno, Practical graph isomorphism, II, J. Symb. Comput. 60 (2014) 94–112. https://doi.org/10.1016/j.jsc.2013.09.003, http://pallini.di.uniroma1.it. T. Hahn, CUBA: a library for multidimensional numerical integration, Comput. Phys. Commun. 168 (2005) 78. arXiv:hep-ph/0404043, http://www.feynarts.de/cuba/. J. Kuipers, T. Ueda, J.A.M. Vermaseren, Code optimization in FORM, Comput. Phys. Commun. 189 (2015) 1. arXiv:1310.7007, http://www.nikhef.nl/~form/. C.W. Bauer, A. Frink, R.B. Kreckel, Introduction to the GiNaC framework for symbolic computation within the C++ programming language, J. Symb. Comput. 33 (2002) 1–12. arXiv:cs/0004015, https://www.ginac.de/. W. Bruns, B. Ichim, B.T. Römer, C. Söger, Normaliz, Algorithms for rational cones and affine monoids. http://www.math.uos.de/normaliz/. T. Granlund et al., GMP: The GNU Multiple Precision Arithmetic Library. https://gmplib.org/. 

Numerical scattering amplitudes with pySecDec

https://doi.org/10.1016/j.cpc.2022.108565

AMFlow: A Mathematica package for Feynman integrals computation via auxiliary mass flow

In this study, an aerospace thermosetting composite was co-curing joined by Polyether-ether-ketone (PEEK) and Polyethylenimine (PEI) films, with an aim of developing advanced composite joints. The semi-crystalline PEEK films were surface activated upon a UV-irradiation technique to obtain a strong film–composite interface, while the amorphous PEI films could be directly used. The fracture behaviour of the composite joints was evaluated and compared with benchmark aerospace adhesive joints. The experimental results proved remarkable mode-I and mode-II fracture resistance of the PEEK co-cured joints at 22 °C and 130 °C, while the PEI co-cured joints exhibited excellent mode-I fracture resistance at 22 °C and mode-II fracture resistance in both testing temperature cases. Extensive elongation, tearing and fracture of the PEEK/PEI plastics were proved to be the main mechanisms for toughness enhancement. Overall, this work had successfully demonstrated the effectiveness of developing advanced composite joints via a co-curing process using high-performance thermoplastic films. 

On the application of strong thermoplastic–thermoset interactions for developing advanced aerospace-composite joints

/pdf/on-the-mix-mode-fracture-of-carbon-fibre-epoxy-composites-brwj2nz5.pdf

On the mix-mode fracture of carbon fibre/epoxy composites interleaved with various thermoplastic veils

The mix-mode fracture behaviour of aerospace composite joints co-cured by different forms of advanced thermoplastics

In this study, a novel high‐power UV irradiation technique was used to activate the bonding surfaces of carbon fiber reinforced low‐melt polyaryl‐ether‐ketone (CF/LM‐PAEK) laminates, followed by bonding with an aerospace adhesive. The effects of hygrothermal aging and aerospace‐solution immersion treatment on the mechanical properties and failure behavior of the CF/LM‐PAEK adhesive joints were investigated. The results indicated that the UV‐irradiation technique efficiently promoted the surface activity of the CF/LM‐PAEK surface. Accordingly, high‐performance CF/LM‐PAEK adhesive joints with a lap‐shear strength of 33.4 MPa were obtained. However, the lap‐shear strength of the joints decreased to 21.2 MPa after a hygrothermal aging treatment. The failure surface analysis revealed that the joint strength reduction was due to the strength degradation at the matrix/carbon fiber interface in the CF/LM‐PAEK composite and the adhesive/composite bonding interface. In contrast, immersing the adhesive joints into aviation kerosene, antifreeze, and hydraulic oil solutions had negligible effects on the lap‐shear strength of the joints. The main failure mechanism was the stripping of the resin matrix at the top surface of the composite substrate, which is identical to the pre‐aging condition. Overall, these findings highlight the importance of surface treatment and environmental factors on the mechanical performance of the CF/LM‐PAEK adhesive joints.

The development of advanced low‐melt polyaryl‐ether‐ketone (LM‐PAEK) composite adhesive joints with good hygrothermal and chemical resistance

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