arXiv subjects

Claude Duhr

Publications and source records attributed to Claude Duhr.

At least 19 recordsLinked to original sources

arXiv2026

Three-Reggeon exchange in $\mathcal{N}=4$ SYM to leading logarithmic accuracy

We study eight-point amplitudes in the planar $\mathcal{N}=4$ Super Yang-Mills theory in multi-Regge kinematics in the Mandelstam region that receives contributions from both two- and three-Reggeon exchange. We use an effective field theory approach to compute the leading contribution from three-Reggeon exchange, and we explicitly evaluate the relevant diagrams up to four loops. We also propose a compact Fourier-Mellin representation for the contribution from two-Reggeon exchange in this region which involves the same ingredients as in other Mandelstam regions and can in principle be evaluated to any desired order in perturbation theory. To validate our proposal, we show that we can reproduce the multi-Regge limit of the known results for octagons up to three loops. We then combine the contributions from two- and three-Reggeon exchange to obtain novel results for octagons in MRK up to next-to-leading-logarithmic accuracy at four loops for the maximally helicity violating (MHV) configuration, and up to three loops for non-MHV contributions. We also discuss how our result can be extended to more particles, and we present the contribution from three-Reggeon exchange for three-loop MHV amplitudes with an arbitrary number of legs.

hep-th↗

arXiv2026

IterInt: Evaluating iterated integrals via differential equations

We introduce IterInt, a novel package implemented in both Mathematica and C++ for the numerical evaluation of iterated integrals involving arbitrary integration kernels. After the user has defined the integration kernels, IterInt transforms the iterated integrals into a system of first-order linear differential equations which can be solved efficiently and with high precision using well established libraries. IterInt is also able to automatically perform shuffle-regularisation. This makes it possible to evaluate also integrals where the integrand has a pole at the starting point of the integration path. As an illustration of our code, and also to validate it and gauge its performance, we compare the output of IterInt to the results obtained by GiNaC for ordinary and elliptic multiple polylogarithms, and also to existing results for the first few orders for banana integrals with up to four loops.

hep-ph↗

arXiv2026

Discrete symmetries of Feynman integrals

We perform a comprehensive study of a certain class of discrete symmetries of families of Feynman integrals, defined as affine changes of variables that map different sectors of the family into each other. We show that these transformations are always encoded into permutations of the Feynman parameters that relate the Lee-Pomeransky polynomials of the two sectors, irrespective of the integral representation used to define the Feynman integrals. We then construct an affine map in loop-momentum space that encodes such a permutation. We also show that these symmetries can be naturally embedded into the framework of twisted cohomology theories, and the period and intersection parings are invariant under the symmetry transformations. If we focus on symmetries within a fixed sector, we obtain a group acting on the twisted cohomology group, and we study the decomposition of this action into irreducible representations. One of our main mathematical results is that the character of this representation is proportional to the Euler characteristic of the corresponding fixed-point set. We then study the implications for Feynman integrals, in particular for the intersection matrix in a canonical basis. We also present a formula for the number of master integrals in a given sector in the presence of a non-trivial symmetry group in terms of the Euler characteristics of fixed-point sets. As an application, we obtain the numbers of master integrals for banana integrals with up to four loops for arbitrary configurations of non-zero masses. In order to achieve our results, we had to combine tools from various different areas of mathematics, including graph theory, group theory and algebraic topology.

hep-th↗

arXiv2026

NNLOCAL: Fully Local Subtractions for Precision Predictions in Hadron Collisions

This work extends the CoLoRFulNNLO subtraction method to address soft and collinear divergences in the computation of higher-order corrections for hadronic collisions. By utilizing universal local counterterms which can be integrated analytically over the unresolved phase space, we achieve numerically stable, fully-differential predictions. Our publicly available NNLOCAL code serves as a proof-of-concept implementation, validated by calculating the NNLO cross-section for Higgs boson production in gluon-gluon fusion with no light quarks.

hep-ph↗

arXiv2026

Elliptic Multiple Polylogarithms with Arbitrary Arguments in \textsc{GiNaC}

We present an algorithm for the numerical evaluation of elliptic multiple polylogarithms for arbitrary arguments and to arbitrary precision. The cornerstone of our approach is a procedure to obtain a convergent $q$-series representation of elliptic multiple polylogarithms. Its coefficients are expressed in terms of ordinary multiple polylogarithms, which can be evaluated efficiently using existing libraries. In a series of preparation steps the elliptic polylogarithms are mapped into a region where the $q$-series converges rapidly. We also present an implementation of our algorithm into the \texttt{GiNaC} framework. This release constitutes the first public package capable of evaluating elliptic multiple polylogarithms to high precision and for arbitrary values of the arguments.

hep-ph↗

arXiv2026

Canonical differential equations beyond polylogs

Feynman integrals whose associated geometries extend beyond the Riemann sphere, such as elliptic curves and Calabi-Yau varieties, are increasingly relevant in modern precision calculations. They arise not only in collider cross-section calculations, but also in the post-Minkowskian expansion of gravitational-wave scattering. A powerful approach to compute integrals of this type is via differential equations, particularly when cast in a canonical form, which simplifies their $\varepsilon$-expansion and makes analytic properties manifest. In these proceedings, we will present a method to systematically construct canonical differential equations even for integrals that evaluate beyond multiple polylogarithms. The discussion is kept as light as possible, focusing on the two-loop sunrise integral, deferring the technical details to the original publications.

hep-th↗

arXiv2026

Intersection theory and canonical differential equations

In these proceedings we will review recent progress in applying ideas from the mathematical framework of twisted cohomology to the study of canonical differential equations for Feynman integrals. Firstly, we will show how the intersection matrix can shed some light on the nature of the canonical basis of a Feynman integral family, a concept still not fully understood in the general case. In particular we will show how the intersection matrix can detect hidden linear dependencies of the iterated integrals resulting from an $\eps$-factorized differential equation, which are difficult to find otherwise. Furthermore, we will explain how the intersection matrix can help in deriving (polynomial) relations between the transcendental functions occurring in the rotation to the canonical basis. This allows us to simplify the rotation, and furthermore leads to simplifications in the final result. The discussion we be kept as light as possible, focusing on a simple running example and deferring the technical details to the original publications.

hep-th↗

arXiv2026

Two-loop renormalisation of the quark fields in the presence of four-fermion SMEFT operators

We compute the contributions of the dimension-6 SMEFT operators involving four third-generation quarks to the two-loop renormalisation of the quark fields and masses. We perform the computations in both the Naive Dimensional Regularisation (NDR) and the Breitenlohner-Maison-`t Hooft-Veltman (BMHV) schemes, and we present results for all relevant field and mass renormalisation constants in the on-shell and MS-bar schemes. We carefully discuss all scheme choices which affect the final results. This completes the computation of field and mass renormalisation constants relevant for two-loop computations in QCD involving dimension-six SMEFT operators.

hep-ph↗

arXiv2026

NNLOCAL: Completely Local Subtractions

The computation of higher-order corrections to cross sections relevant at LHC involves the evaluation of phase-space integrals that exhibit soft and collinear divergences. The subtraction of these divergences is a key ingredient to obtain fully-differential predictions for physical observables. We discuss a subtraction method to handle these divergences based on the construction of universal local counterterms. The integration of the counterterms is carried out analytically, giving a strong control on the numerical stability of our predictions. We implement our method in a numerical program, that we dub NNLOCAL, and validate it by computing the fully-differential NNLO cross-section for Higgs boson production in gluon-gluon fusion.

hep-ph↗

arXiv2025

Analytic results for one-loop integrals in dimensional regularisation

We present a method to obtain analytic results in terms of multiple polylogarithms for one-loop triangle, box and pentagon integrals depending on an arbitrary number of scales and to any desired order in the Laurent expansion in the dimensional regulator $\varepsilon$. Our method leverages the fact that for $\varepsilon=0$ one-loop integrals compute volumes of simplices in hyperbolic spaces, which can always be evaluated in terms of polylogarithms using an algorithm recently introduced in pure mathematics. The higher orders in $\varepsilon$ can then be expressed as a one-fold integral involving the result for $\varepsilon=0$. Remarkably, we find that for up to five external legs, all integrals can be evaluated algorithmically in terms of polylogarithms using direct integration techniques, which, in particular, requires us to rationalise all appearing square roots. We also discuss how we can use the connection to hyperbolic geometry to perform the analytic continuation from the Euclidean region to other kinematic regions.

hep-ph↗

arXiv2025

Three-loop banana integrals with three equal masses

We obtain and solve the canonical differential equations for the three-loop banana integrals in dimensional regularisation when three of the four masses are equal. The K3 surface associated with the maximal cuts factorises into a product of two elliptic curves. This allows us to express the differential forms in the canonical differential equations in terms of meromorphic modular forms. We present a rigorous proof that these differential forms only have simple poles and that they define independent cohomology classes. We also present explicit results for all master integrals in terms of iterated integrals of meromorphic modular forms (and integrals thereof). This is the first time that it was possible to express the results of a Feynman integral associated with a K3 geometry and depending on two dimensionless ratios in terms of functions that have previously been studied in the literature.

hep-th↗

arXiv2025

Canonical differential equations and intersection matrices

Differential equations are one of the main approaches to evaluate multi-loop Feynman integrals. The construction of a canonical or $\varepsilon$-factorised basis for multi-loop integrals remains a key bottleneck for this approach, especially when the differential equation involves non dlog-forms. Recently, several methods have been proposed to find $\varepsilon$-factorised differential equations. Many of them introduce new functions that are themselves defined as iterated integrals. If and when these iterated integrals can be explicitly evaluated in terms of other classes of functions remains an open problem. In this paper we elaborate on the recent proposal that one can use the fact that the intersection matrix computed in a canonical basis can be used to derive polynomial relations between these iterated integrals. On the one hand, we discuss properties of the canonical intersection matrix, in particular methods to determine the intersection matrix in a canonical basis. On the other hand we show how one can reduce the non-linear constraints on the iterated integrals to linear ones. We illustrate these ideas on examples involving Calabi-Yau varieties and higher-genus Riemann surfaces.

hep-th↗

arXiv2025

ANATAR: AN Automated Tool for higher-order Amplitude geneRation

We present a new Mathematica package that provides a platform to perform multi-loop computations. ANATAR integrates several existing tools designed for higher-order computations. In particular, it uses QGRAF to generate Feynman diagrams and relies on FORM to perform the Dirac and colour algebras. This makes it very efficient without compromising user-friendliness and flexibility. In addition, ANATAR is equipped with functionalities to manipulate the generated amplitudes and to extract scalar form factors. The resulting expressions can be mapped to integral families that can subsequently be reduced to master integrals via dedicated interfaces to codes for integration-by-parts reduction. Support for large classes of BSM models with the same gauge group as the SM is provided, and in particular, ANATAR is optimised for computations in effective field theories. We review and introduce the main functionalities of ANATAR and illustrate its use for phenomenological applications.

hep-ph↗

arXiv2025

A comprehensive analysis of Drell-Yan production uncertainties and mass effects at moderate and low dilepton masses

We present a thorough investigation of the sources of uncertainties to the Drell-Yan production using state-of-the-art predictions for both neutral and charged current channels, focusing on the low invariant mass region. Differential predictions for the invariant mass spectrum are provided at N$^3$LO supplemented with exact charm and bottom quark mass effects calculated at $\mathcal{O}(\alpha_s^2)$. The impact of PDF choices (including approximate N$^3$LO), scale variations, the variation of the strong coupling constant, and impact heavy quark mass effects on the distributions is studied in detail. We also comment on the correlation of high-energy astrophysical processes with the low-mass DY region.

hep-ph↗

arXiv2025

Two-loop renormalisation of quark and gluon fields in the SMEFT in the on-shell scheme

We compute the contributions of CP-conserving dimension-six SMEFT operators to the two-loop renormalisation constants of quark and gluon fields in the on-shell scheme. Specifically, we consider the top-quark chromomagnetic operator and the triple gluon operator. We also compute the contribution of four-quark operators to the gluon renormalisation constant and discuss the implications for the running of the strong coupling constant.

hep-ph↗

arXiv2025

Three-loop banana integrals with four unequal masses

We present a system of canonical differential equations satisfied by the three-loop banana integrals with four distinct non-zero masses in $D = 2-2\eps$ dimensions. Together with the initial condition in the small-mass limit, this provides all the ingredients to find analytic results for three-loop banana integrals in terms of iterated integrals to any desired order in the dimensional regulator. To obtain this result, we rely on recent advances in understanding the K3 geometry underlying these integrals and in how to construct rotations to an $\eps$-factorized basis. This rotation typically involves the introduction of objects defined as integrals of (derivatives of) K3 periods and rational functions. We apply and extend a method based on results from twisted cohomology to identify relations among these functions, which allows us to reduce their number considerably. We expect that the methods that we have applied here will prove useful to compute further multiloop multiscale Feynman integrals attached to non-trivial geometries.

hep-th↗

arXiv2025

Infrared singularities and the collinear limits of multi-leg scattering amplitudes

Scattering amplitudes are expected to admit a factorised structure in special kinematic limits, such as the Regge, soft and collinear limits. However, less is known about the precise mechanisms through which factorisation of $n$-particle scattering amplitudes is realised at high perturbative orders, where more complex structures arise. Starting with the soft anomalous dimension, in this work we investigate the multi-particle collinear limits of massless amplitudes at three- and four-loop orders. Using colour conservation and rescaling symmetry, we show how strict collinear factorisation of multiple massless final-state coloured particles is realised, and provide results for the corresponding splitting amplitude soft anomalous dimensions. In particular, we demonstrate through four loops that the conditions on the structure of the soft anomalous dimension that are required by strict collinear factorisation in all two-particle collinear limits, are sufficient to guarantee such factorisation also in any multiple collinear limit. Then, assuming that strict collinear factorisation of massless partons holds also for amplitudes containing massive coloured particles, we derive new constraints on the soft anomalous dimension from multi-collinear limits.

hep-ph↗

arXiv2025

A critical appraisal of tests of locality and of entanglement versus non-entanglement at colliders

It has been argued more than 30 years ago that it is not possible to test locality at colliders, due to the inability to directly measure non-commutating observables such as spin components in current collider experiments. Recently, there has been a lot of phenomenological and experimental activity around testing locality via Bell-type experiments or entanglement versus non-entanglement in a collider environment. These results seem to evade the earlier no-go theorem by indirectly measuring spin correlations via their relation to angular correlations between momenta. We perform a careful study of the feasibility of such an approach. We scrutinize the relationship between spin and angular correlations in both quantum mechanics and local hidden variable theories. Our conclusion is that it is currently not possible to perform a logically coherent set of experimental measurements at colliders that would allow one to test locality or entanglement versus non-entanglement. This reaffirms the earlier no-go theorem. We stress that the no-go theorem does not apply to measurements of observables inspired from entanglement and Quantum Information Theory to test the Standard Model of particle physics.

hep-ph↗