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In this paper we extend the study initiated in arXiv:2302.04709v2 [hep-th] to the computation of one-loop elastic amplitudes. We consider 1+1 dimensional massive bosonic Lagrangians with polynomial-like potentials and absence of inelastic…

High Energy Physics - Theory · Physics 2024-03-08 Matheus Fabri , Davide Polvara

We derive a general formula for two-loop counterterms in Effective Field Theories (EFTs) using a geometric approach. This formula allows the two-loop results of our previous paper to be applied to a wide range of theories. The two-loop…

High Energy Physics - Phenomenology · Physics 2023-11-13 Elizabeth E. Jenkins , Aneesh V. Manohar , Luca Naterop , Julie Pagès

We numerically integrate finite two- and three-loop scalar integrals using the threshold subtraction method. This represents a first step towards extending our calculation of the $N_f$-part to the full NNLO virtual corrections for the…

High Energy Physics - Phenomenology · Physics 2024-08-01 Dario Kermanschah , Matilde Vicini

We review recent progress in D-dimensional integrand reduction algorithms for two loop amplitudes and give examples of their application to non-planar maximal cuts of the five-point all-plus helicity amplitude in QCD.

High Energy Physics - Phenomenology · Physics 2014-07-14 Simon Badger , Hjalte Frellesvig , Yang Zhang

We study the applicability of the Z-Sum approach to multi-loop calculations with massive particles in perturbative quantum field theory. We systematically analyze the case of one-loop scalar integrals, which represent the building blocks of…

High Energy Physics - Phenomenology · Physics 2015-05-28 Paulo A. Rottmann , Laura Reina

In this paper, we generalize the unitarity method to two-loop diagrams and use it to discuss the integral bases of reduction. To test out method, we focus on the four-point double-box diagram as well as its related daughter diagrams, i.e.,…

High Energy Physics - Theory · Physics 2015-06-18 Bo Feng , Jun Zhen , Rijun Huang , Kang Zhou

We extend the maximal-unitarity formalism at two loops to double-box integrals with four massive external legs. These are relevant for higher-point processes, as well as for heavy vector rescattering, VV -> VV. In this formalism, the…

High Energy Physics - Theory · Physics 2025-05-08 Henrik Johansson , David A. Kosower , Kasper J. Larsen

We present a diagrammatic decomposition of the transition pair correlation function for the uniform electron gas. We demonstrate explicitly that ring and ladder diagrams are dual counterparts that capture significant long- and short-ranged…

Materials Science · Physics 2019-10-16 Andreas Irmler , Felix Hummel , Andreas Grüneis

Generalized-unitarity calculations of two-loop amplitudes are performed by expanding the amplitude in a basis of master integrals and then determining the coefficients by taking a number of generalized cuts. In this paper, we present a…

High Energy Physics - Phenomenology · Physics 2025-05-08 Simon Caron-Huot , Kasper J. Larsen

We introduce a two-level trust-region method (TLTR) for solving unconstrained nonlinear optimization problems. Our method uses a composite iteration step, which is based on two distinct search directions. The first search direction is…

Numerical Analysis · Mathematics 2024-09-10 Andrea Angino , Alena Kopaničáková , Rolf Krause

Modern particle physics is increasingly becoming a precision science that relies on advanced theoretical predictions for the analysis and interpretation of experimental results. The planned physics program at the LHC and future colliders…

High Energy Physics - Phenomenology · Physics 2023-01-04 Ievgen Dubovyk , Ayres Freitas , Janusz Gluza , Krzysztof Grzanka , Martijn Hidding , Johann Usovitsch

Numerical integration is a classical problem emerging in many fields of science. Multivariate integration cannot be approached with classical methods due to the exponential growth of the number of quadrature nodes. We propose a method to…

Numerical Analysis · Mathematics 2021-08-23 Lev I. Vysotsky , Alexander V. Smirnov , Eugene E. Tyrtyshnikov

This paper presents a canonical duality approach for solving a general topology optimization problem of nonlinear elastic structures. By using finite element method, this most challenging problem can be formulated as a mixed integer…

Discrete Mathematics · Computer Science 2017-06-29 David Yang Gao

The computation of the correlation numbers in Minimal Liouville Gravity involves an integration over moduli spaces of complex curves. There are two independent approaches to the calculation: the direct one, based on the CFT methods and…

High Energy Physics - Theory · Physics 2016-12-21 Konstantin Aleshkin , Vladimir Belavin

We compute the average Lund multiplicity of high-energy QCD jets. This extends an earlier calculation, done for event-wide multiplicity in $e^+e^-$ collisions [arxiv:2205.02861], to the large energy range available at the LHC. Our…

High Energy Physics - Phenomenology · Physics 2023-05-10 Rok Medves , Alba Soto-Ontoso , Gregory Soyez

We study loop corrections in boundary string field theory (BSFT). After commenting on problems with quantizing the tree level BSFT as an ordinary field theory, we discuss the tree level coupling to closed strings and define the loop…

High Energy Physics - Theory · Physics 2009-11-07 Ben Craps , Per Kraus , Finn Larsen

A tree decomposition of the coordinates of a code is a mapping from the coordinate set to the set of vertices of a tree. A tree decomposition can be extended to a tree realization, i.e., a cycle-free realization of the code on the…

Information Theory · Computer Science 2016-11-17 Navin Kashyap

We show that, by viewing a 4D effective-field theory as the infrared (IR) limit of the compactified version in 5D, we can compute two-loop anomalous dimensions without gauge-breaking counter-terms, IR re-arrangement or geometric methods.…

High Energy Physics - Phenomenology · Physics 2025-12-04 Mikael Chala , Javier López Miras

Four-dimensional renormalized (FDR) integrals play an increasingly important role in perturbative loop calculations. Thanks to them, loop computations can be performed directly in four dimensions and with no ultraviolet (UV) counterterms.…

High Energy Physics - Theory · Physics 2015-09-07 Roberto Pittau

The reformulation-linearization technique (RLT) is a prominent approach to constructing tight linear relaxations of non-convex continuous and mixed-integer optimization problems. The goal of this paper is to extend the applicability and…

Optimization and Control · Mathematics 2024-07-22 Ksenia Bestuzheva , Ambros Gleixner , Tobias Achterberg