arXiv subjects

Valentin Hirschi

Publications and source records attributed to Valentin Hirschi.

At least 19 recordsLinked to original sources

arXiv2026

pyAmpliCol: fast tree-level matrix elements

Tree-level matrix elements sit at the heart of collider event generation, but their cost rises rapidly just where additional resolved radiation becomes most important. We present pyAmpliCol, a public generator aimed at extending the practical reach of colour-resolved matrix elements to higher multiplicities. It builds on the colour-ordered, off-shell-current strategy of AmpliCol, providing fast access to individual leading-colour flows while retaining the option of next-to-leading or exact full colour. The latter introduces its own high-multiplicity bottleneck: the dense interference of factorially many colour orderings. pyAmpliCol addresses this contraction with a fast Fourier transform on the symmetric group, preserving the exact colour result while avoiding the direct pairwise sum. Representative full-colour benchmarks demonstrate substantial speedups over the reference calculations considered here. It supports Standard Model processes and a broad class of UFO models, selected or summed helicities, vectorised evaluation and controllable numerical precision. It further provides colour- and spin-correlated Born quantities and tree-level colour connections at arbitrary perturbative order, opening the same framework to local subtraction and other higher-order applications. Together, these capabilities connect high-multiplicity matrix elements to their use in event generation, merging, parton showers and precision calculations within a single generator.

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arXiv2026

Exact color sums for multi-gluon amplitudes: direct, multiplet and symmetric-group Fourier methods

We compare three approaches for computing color-summed tree-level all-gluon squared matrix elements: evaluation using direct contraction in the trace and adjoint decompositions, orthonormal multiplet bases, and fast Fourier transforms (FFT) based on the irreducible representations of the symmetric group for the trace and adjoint decompositions. The multiplet method reduces the color sum to a sum of absolute squares and utilizes an amplitude recursion labeled by SU(3) representations. The FFT exploits the relative-permutation dependence of color overlaps to replace the direct double sum with smaller independent contractions, using standard color-ordered partial amplitudes. This invokes the symmetric group at the level of gluon labels, and therefore makes maximal use of the permutation symmetry. We compare CPU time and memory use for four through eleven gluons. At eleven gluons, the direct adjoint contraction evaluates a fixed-helicity color-summed matrix element in an estimated 1.7 10${}^3$ s after initialization, compared with 19.8 s for the multiplet recursion and 0.814 s for the FFT adjoint method. The adjoint FFT is fastest from six through eleven gluons, despite its factorial scaling compared with the exponential scaling of the multiplet recursion.

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arXiv2026

NNLO QCD corrections to $γγ\rightarrow Q\bar{Q}$ from Local Unitarity combined with Coulomb resummation and NLO EW effects

The Local Unitarity (LU) formalism provides a constructive, integrand-level realisation of the Kinoshita-Lee-Nauenberg (KLN) theorem, by combining loop and phase-space integrals appearing in scattering cross-sections in such a way that their final-state infrared singularities cancel before integration. Supplemented with localised ultraviolet renormalisation, it enables the direct Monte Carlo integration of cross sections at arbitrary perturbative order in four-dimensional spacetime. In this paper, we present its application to the next-to-next-to-leading order (NNLO) QCD total cross sections for heavy-quark pair production in direct photon fusion, involving the contribution from 138 distinct forward-scattering diagrams where external photons couple only to heavy quarks. By combining NNLO QCD with next-to-leading order (NLO) electroweak (EW) corrections and next-to-leading power (NLP) Coulomb resummation, we obtain state-of-the-art predictions for top-, bottom-, and charm-quark production in ultraperipheral hadron collisions and at $e^+ e^-$ colliders.

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arXiv2024

Light-by-Light Scattering at Next-to-Leading Order in QCD and QED

The recent experimental observation of Light-by-Light (LbL) scattering at the Large Hadron Collider has revived interest in this fundamental process, and especially of the accurate prediction of its cross-section, which we present here for the first time at Next-to-Leading Order (NLO) in both QCD and QED. We compare two radically different computational approaches, both exact in the fermion mass dependence, thus offering a strong cross-check of our results. The first approach is a fully analytic method to calculate compact and well-organized two-loop helicity amplitudes. The second one is entirely numerical and leverages the Local Unitarity construction. Our two calculations agree with each other and conclude that including the exact fermion mass contribution typically increases the size of the NLO corrections. Moreover, we find that the exact result converges slowly to the massless limit of the high-energy regime, thus emphasizing the importance of including the full mass dependence at NLO. We also compare our results with the ATLAS measurement of LbL in ultra-peripheral lead-lead collisions, and find that the inclusion of exact NLO corrections reduces, but does not eliminate, the existing tension with theoretical predictions.

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arXiv2023

UFO 2.0 -- The Universal Feynman Output format

We present an update of the Universal FeynRules Output model format, commonly known as the UFO format, that is used by several automated matrix-element generators and high-energy physics software. We detail different features that have been proposed as extensions of the initial format during the last ten years, and collect them in the current second version of the model format that we coin the Universal Feynman Output format. Following the initial philosophy of the UFO, they consist of flexible and modular additions to address particle decays, custom propagators, form factors, the renormalisation group running of parameters and masses, and higher-order quantum corrections.

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arXiv2022

Local Unitarity: cutting raised propagators and localising renormalisation

The Local Unitarity (LU) representation of differential cross-sections locally realises the cancellations of infrared singularities predicted by the Kinoshita-Lee-Nauenberg theorem. In this work we solve the two remaining challenges to enable practical higher-loop computations within the LU formalism. The first concerns the generalisation of the LU representation to graphs with raised propagators. The solution to this problem results in a generalisation of distributional Cutkosky rules. The second concerns the regularisation of ultraviolet and spurious soft singularities, solved using a fully automated and local renormalisation procedure based on Bogoliubov's R-operation. We detail an all-order construction for the hybrid $\overline{\text{MS}}$ and On-Shell scheme whose only analytic input is single-scale vacuum diagrams. Using this novel technology, we provide (semi-)inclusive results for two multi-leg processes at NLO, study limits of individual supergraphs up to N3LO and present the first physical NNLO cross-sections computed fully numerically in momentum-space, namely for the processes $γ^* \rightarrow j j$ and $γ^* \rightarrow t \bar{t}$.

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arXiv2021

Local Unitarity: a representation of differential cross-sections that is locally free of infrared singularities at any order

We propose a novel representation of differential scattering cross-sections that locally realises the direct cancellation of infrared singularities exhibited by its so-called real-emission and virtual degrees of freedom. We take advantage of the Loop-Tree Duality representation of each individual forward-scattering diagram and we prove that the ensuing expression is locally free of infrared divergences, applies at any perturbative order and for any process without initial-state collinear singularities. Divergences for loop momenta with large magnitudes are regulated using local ultraviolet counterterms that reproduce the usual Lagrangian renormalisation procedure of quantum field theories. Our representation is especially suited for a numerical implementation and we demonstrate its practical potential by computing fully numerically and without any IR counterterm the next-to-leading order accurate differential cross-section for the process $e^+ e^- \rightarrow d \bar{d}$. We also show first results beyond next-to-leading order by computing interference terms part of the N4LO-accurate inclusive cross-section of a $1\rightarrow 2+X$ scalar scattering process.

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arXiv2020

Numerical Loop-Tree Duality: contour deformation and subtraction

We introduce a novel construction of a contour deformation within the framework of Loop-Tree Duality for the numerical computation of loop integrals featuring threshold singularities in momentum space. The functional form of our contour deformation automatically satisfies all constraints without the need for fine-tuning. We demonstrate that our construction is systematic and efficient by applying it to more than 100 examples of finite scalar integrals featuring up to six loops. We also showcase a first step towards handling non-integrable singularities by applying our work to one-loop infrared divergent scalar integrals and to the one-loop amplitude for the ordered production of two and three photons. This requires the combination of our contour deformation with local counterterms that regulate soft, collinear and ultraviolet divergences. This work is an important step towards computing higher-order corrections to relevant scattering cross-sections in a fully numerical fashion.

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arXiv2020

NLO Corrections to Light-Quark Mixed QCD-EW Contributions to Higgs Production

We present for the first time the exact NLO QCD corrections to the light-quark part of the mixed QCD-EW contributions to Higgs production via gluon fusion at LHC13, with exact EW-boson mass dependence. The relevant two-loop real-emission matrix element is computed using a dynamic one-dimensional series expansion strategy whose stability and speed allows for a numerical phase-space integration using local IR subtraction counterterms. For $μ_R=μ_F=M_H$, we find: \begin{equation}σ^{(α_s^2α^2+α_s^3α^2)}_{g g\rightarrow H+X} = 1.467(2)^{\;+18.7\%}_{\;-14.6\%}\;(μ_R\;\text{var.})\;\pm 2\%\;(\text{PDF}) \ \textrm{pb},\end{equation} which we use to provide the best result including an estimate of suppressed contributions: \begin{equation}σ^{(\text{EW},\textrm{best})}_{p p\rightarrow H+X} = 2.11 \pm 0.28 \ (\textrm{theory}) \ \mathrm{pb}.\end{equation}

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arXiv2020

Manifestly Causal Loop-Tree Duality

Loop-Tree Duality (LTD) is a framework in which the energy components of all loop momenta of a Feynman integral are integrated out using residue theorem, resulting in a sum over tree-like structures. Originally, the LTD expression exhibits cancellations of non-causal thresholds between summands, also known as dual cancellations. As a result, the expression exhibits numerical instabilities in the vicinity of non-causal thresholds and for large loop momenta. In this work we derive a novel, generically applicable, Manifestly Causal LTD (cLTD) representation whose only thresholds are causal thresholds, i.e. it manifestly realizes dual cancellations. Consequently, this result also serves as a general proof for dual cancellations. We show that LTD, cLTD, and the expression stemming from Time Ordered Perturbation Theory (TOPT) are locally equivalent. TOPT and cLTD both feature only causal threshold singularities, however LTD features better scaling with the number of propagators. On top of the new theoretical perspectives offered by our representation, it has the useful property that the ultraviolet (UV) behaviour of the original 4D integrand is maintained for every summand. We show that the resulting LTD integrand expression is completely stable in the UV region which is key for practical applications of LTD to the computation of amplitudes and cross sections. We present explicit examples of the LTD expression for a variety of up to four-loop integrals and show that its increased computational complexity can be efficiently mitigated by optimising its numerical implementation. Finally, we provide computer code that automatically generates the LTD expression for an arbitrary topology.

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arXiv2020

Higgs production in bottom quark fusion: Matching the 4- and 5-flavour schemes to third order in the strong coupling

We present analytic results for the partonic cross sections for the production of a Higgs boson via the fusion of two bottom quarks at N$^3$LO in QCD perturbation theory in the five-flavour scheme. We combine this perturbative result with NLO accurate predictions in the four-flavour scheme that include the full bottom quark mass dependence by appropriately removing any double-counting stemming from contributions included in both predictions. We thereby obtain state-of-the-art predictions for the inclusive production probability of a Higgs boson via bottom quark fusion at hadron colliders.

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arXiv2019

Automated simulations beyond the Standard Model: supersymmetry

The MadGraph5 aMC@NLO framework aims to automate all types of leading- and next-to-leading-order-accurate simulations for any user-defined model that stems from a renormalisable Lagrangian. In this paper, we present all of the key ingredients of such models in the context of supersymmetric theories. In order to do so, we extend the FeynRules package by giving it the possibility of dealing with different renormalisation options that are relevant to supersymmetric models. We also show how to deal with the problem posed by the presence of narrow resonances, thus generalising the so-called on-shell subtraction approaches. We extensively compare our total rate results with those of both Prospino2 and Resummino, and present illustrative applications relevant to the 13 TeV LHC, both at the total-rate and differential levels. The computer programs that we have used to obtain the predictions presented here are all publicly available.

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arXiv2019

Proposal for the validation of Monte Carlo implementations of the standard model effective field theory

We propose a procedure to cross-validate Monte Carlo implementations of the standard model effective field theory. It is based on the numerical comparison of squared amplitudes computed at specific phase-space and parameter points in pairs of implementations. Interactions are fully linearised in the effective field theory expansion. The squares of linear effective field theory amplitudes and their interference with standard-model contributions are compared separately. Such pairwise comparisons are primarily performed at tree level and a possible extension to the one-loop level is also briefly considered. We list the current standard model effective field theory implementations and the comparisons performed to date.

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arXiv2019

Loop Tree Duality for multi-loop numerical integration

Loop Tree Duality (LTD) offers a promising avenue to numerically integrate multi-loop integrals directly in momentum space. It is well-established at one loop, but there have been only sparse numerical results at two loops. We provide a formal derivation for a novel multi-loop LTD expression and study its threshold singularity structure. We apply our findings numerically to a diverse set of up to four-loop finite topologies with kinematics for which no contour deformation is needed. We also lay down the ground work for constructing such a deformation. Our results serve as an important stepping stone towards a generalised and efficient numerical implementation of LTD, applicable to the computation of virtual corrections.

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arXiv2019

One-loop weak corrections to Higgs production

We compute mixed QCD-weak corrections to inclusive Higgs production at the LHC from the partonic process $g g \rightarrow H q \bar{q}$. We start from the UV- and IR-finite one-loop weak amplitude and consider its interference with the corresponding one-loop QCD amplitude. This contribution is a $\mathcal{O}(α_sα)$ correction to the leading-order gluon-fusion cross section, and was not numerically assessed in previous works. We also compute the cross section from the square of this weak amplitude, suppressed by $\mathcal{O}(α^2)$. Finally, we consider contributions from the partonic process $g q \rightarrow H q$, which are one order lower in $α_s$, as a reference for the size of terms which are not enhanced by the large gluon luminosity. We find that, given the magnitude of the uncertainties on current state-of-the-art predictions for Higgs production, all contributions computed in this work can be safely ignored, both fully inclusively and in the boosted Higgs regime. This result supports the approximate factorisation of QCD and weak corrections to that process.

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arXiv2017

Spin Polarisation of $t\bar{t}γγ$ production at NLO+PS with GoSam interfaced to MadGraph5_aMC@NLO

We present an interface between the multipurpose NLO Monte Carlo tool MadGraph5_aMC@NLO and the automated one-loop amplitude generator GoSam. As a first application of this novel framework, we compute the NLO corrections to $pp \to t\bar{t}H$ and $pp \to t\bar{t}γγ$ matched to a parton shower. In the phenomenological analyses of these processes, we focus our attention on observables which are sensitive to the polarisation of the top quarks.

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arXiv2017

Accurate predictions for charged Higgs production: closing the $m_{H^{\pm}}\sim m_t$ window

We present predictions for the total cross section for the production of a charged Higgs boson in the intermediate-mass range ($m_{H^{\pm}}\sim m_t$) at the LHC, focusing on a type-II two-Higgs-doublet model. Results are obtained at next-to-leading order (NLO) accuracy in QCD perturbation theory, by studying the full process $pp\to H^\pm W^\mp b \bar b$ in the complex-(top)-mass scheme with massive bottom quarks. Compared to lowest-order predictions, NLO corrections have a sizeable impact: they increase the cross section by roughly 50\% and reduce uncertainties due to scale variations by more than a factor of two. Our computation reliably interpolates between the low- and high-mass regime. Our results provide the first NLO prediction for charged Higgs production in the intermediate-mass range and therefore allow to have NLO accurate predictions in the full $m_{H^{\pm}}$ range. The extension of our results to different realisations of the two-Higgs-doublet model or to the supersymmetric case is also discussed.

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arXiv2017

NLO predictions for the production of a spin-two particle at the LHC

We obtain predictions accurate at the next-to-leading order in QCD for the production of a generic spin-two particle in the most relevant channels at the LHC: production in association with coloured particles (inclusive, one jet, two jets and $t\bar t$), with vector bosons ($Z,W^\pm,γ$) and with the Higgs boson. We present total and differential cross sections as well as branching ratios as a function of the mass and the collision energy also considering the case of non-universal couplings to standard model particles. We find that the next-to-leading order corrections give rise to sizeable $K$ factors for many channels, in some cases exposing the unitarity-violating behaviour of non-universal couplings scenarios, and in general greatly reduce the theoretical uncertainties. Our predictions are publicly available in the MadGraph5\_aMC@NLO framework and can, therefore, be directly used in experimental simulations of spin-two particle production for arbitrary values of the mass and couplings.

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