arXiv subjects

Zeno Capatti

Publications and source records attributed to Zeno Capatti.

15 recordsLinked to original sources

arXiv2026

A Task Force on Strong Coupling Determinations from Event Shapes

The strong coupling constant $\alpha_s$ is a fundamental parameter of the Standard Model. Its precise determination is essential for accurately predicting, studying, and understanding processes at the Large Hadron Collider and future experiments such as the Future Circular Collider. Event shape and correlator observables measured at electron-positron colliders provide one of the cleanest environments for extracting $\alpha_s$, thanks to their sensitivity to $\alpha_s$ and the availability of high-precision data from the Large Electron-Positron Collider. More broadly, such observables provide an ideal setting to develop and test our understanding of the perturbative and non-perturbative elements of Quantum Chromodynamics, which will underpin the field's precision and discovery frontiers for decades to come. Despite these advances, significant discrepancies persist between different determinations of $\alpha_s$ from event shapes, both in the extracted central values and estimated uncertainties. This document motivates the establishment of a dedicated Task Force to coordinate a community-wide effort addressing these open questions. We report on the first two-day meeting held at CERN in November 2025, summarizing the scientific discussion and documenting the experimental analyses identified as priorities during the meeting, as well as the concrete list of tasks to be carried out by the theory community in preparation for future meetings.

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arXiv2025

NNLO QCD corrections to $\gamma \gamma \rightarrow Q\bar{Q}$ 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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arXiv2025

Multi-partonic interactions, iterated discontinuities and the virtuality expansion in deep inelastic scattering

We introduce a perturbative model that accounts for the contribution of multi-partonic interactions to collider observables. A key feature of this multi-parton model is that cross sections are organised in terms of building blocks that are separately infrared-finite in virtue of the KLN theorem. We find compact expressions for these building blocks in terms of double discontinuities of Feynman-type integrals obtained by endowing a vacuum graph with additional topological information. The framework is applied to the computation of next-to-leading order structure functions in deep inelastic scattering. We comment on the scale dependence of these structure functions and discuss the possibility of relating them by a scheme change to those computed in the parton model. Finally we lay down next steps for analogous computations for deep inelastic scattering at NNLO and Drell-Yan at NLO.

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arXiv2025

Universal corrections to the superfluid gap in a cold Fermi gas

A framework for computing the superfluid gap in an effective field theory (EFT) of fermions interacting via momentum-independent contact forces is developed. The leading universal corrections in the EFT are one-loop in-medium effects at the Fermi surface, and reproduce the well-known Gor'kov-Melik-Barkhudarov result. The complete subleading universal corrections are presented here, and include one-loop effects away from the Fermi surface, two-loop in-medium effects, as well as modifications to the fermion propagator. Together, these effects are found to reduce the gap at low densities. Applications to neutron superfluidity in neutron stars are also discussed.

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arXiv2024

Classical worldlines from scattering amplitudes

We present a systematic diagrammatic investigation of the classical limit of observables computed from scattering amplitudes in quantum field theory through the Kosower-Maybee-O'Connell (KMOC) formalism, motivated by the study of gravitational waves from black hole binaries. We achieve the manifest cancellation of divergences in the $\hbar \to 0$ limit at the integrand level beyond one loop by employing the Schwinger parametrisation to rewrite both cut and uncut propagators in a worldline-like representation before they are combined. The resulting finite classical integrand takes the same form as the counterpart in the worldline formalisms such as post-Minkowskian effective field theory (PMEFT) and worldline quantum field theory (WQFT), and in fact exactly coincides with the latter in various examples, showing explicitly the equivalence between scattering amplitude and worldline formalisms. The classical causality flow, as expressed by the retarded propagator prescription, appears as an emergent feature. Examples are presented for impulse observables in electrodynamics and a scalar model at two loops, as well as certain subclasses of diagrams to higher orders and all orders.

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arXiv2023

Derivation of the Cross-Free Family representation for the box diagram

I work out in full detail the derivation of the Cross-Free Family (CFF) representation for the box diagram, and highlight the differences with its Time Ordered Perturbation Theory (TOPT) representation. I briefly discuss implications for the threshold singularity structure of the diagram.

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arXiv2023

Flow Oriented Perturbation Theory

Flow Oriented Perturbation Theory (FOPT) is a novel approach to Feynman diagrams based on the coordinate (position) space description of Quantum Field Theories (QFT). FOPT offers interesting features regarding the computation of higher-loop Feynman amplitudes such as combinatorial and canonical Feynman rules, explicit infrared singularity factorization on a per-diagram level and the potential to have manifest cancellation of real and virtual singularities. In these proceedings we briefly summarize the derivation of FOPT and present its Feynman rules for covariant diagrams, S-matrix elements and cut diagrams in massless scalar QFT, supported by examples. We then discuss the extension of FOPT to massless fermion fields and indicate steps towards the treatment of massive lines in arbitrary dimensions.

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arXiv2023

Flow-oriented perturbation theory

We introduce a new diagrammatic approach to perturbative quantum field theory, which we call flow-oriented perturbation theory (FOPT). Within it, Feynman graphs are replaced by strongly connected directed graphs (digraphs). FOPT is a coordinate space analogue of time-ordered perturbation theory and loop-tree duality, but it has the advantage of having combinatorial and canonical Feynman rules, combined with a simplified $i\varepsilon$ dependence of the resulting integrals. Moreover, we introduce a novel digraph-based representation for the S-matrix. The associated integrals involve the Fourier transform of the flow polytope. Due to this polytope's properties, our S-matrix representation exhibits manifest infrared singularity factorization on a per-diagram level. Our findings reveal an interesting interplay between spurious singularities and Fourier transforms of polytopes.

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arXiv2022

Exposing the threshold structure of loop integrals

The understanding of the physical laws determining the infrared behaviour of amplitudes is a longstanding and topical problem. In this paper, we show that energy conservation alone implies strong constraints on the threshold singularity structure of Feynman diagrams. In particular, we show that it implies a representation of loop integrals in terms of Fourier transforms of non-simplicial convex cones. We then engineer a triangulation that has a direct diagrammatic interpretation in terms of a straightforward edge-contraction operation. We use it to develop an algorithmic procedure that performs the Fourier integrations in closed form, yielding the novel Cross-Free Family three-dimensional representation of loop integrals. Contrary to the TOPT and LTD representations, its singularity structure is entirely and elegantly expressed in terms of the graph-theoretic notions of connectedness and crossing. These results can be used to classify infrared-finite scattering theories, numerically evaluate loop integrals and to simplify threshold regularisation procedures.

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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

Within the Local Unitarity formalism, any physical cross-section is re-written in such a way that cancellations of infrared singularities between real and virtual contributions are realised locally. Consequently, phase-space and loop integrals are regulated locally without the need of any counter-terms or dimensional regularisation aside from those strictly needed to achieve ultraviolet regularisation. This Local Unitarity representation is especially suitable to direct Monte Carlo integration. As such, it offers a clear and direct path to automate the computation of fixed-order differential observables in Quantum Field Theories.

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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

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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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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