arXiv subjects

German F. R. Sborlini

Publications and source records attributed to German F. R. Sborlini.

At least 19 recordsLinked to original sources

arXiv2026

A quantum representation of $π$ fragmentation functions through variational quantum circuits

We present a variational quantum-circuit model for fragmentation functions (FFs). Isospin and charge-conjugation symmetries are imposed to construct an independent six-flavor basis describing charged and neutral pion production, while physics-inspired Ansätze, including logarithmic feature maps and mass thresholds, encode the relevant kinematics. This quantum architecture substantially reduces the quantum circuit redundancies and improve optimization convergence. Using the DSS14 pion FF set as a benchmark, we first develop a one-dimensional variational representation (FF-VQR) in the momentum fraction at fixed energy scale, and show how entanglement between quark and gluon FFs yields a significant improvement, with accurate results already obtained using just two variational layers. A spectral analysis further demonstrates that the quantum model achieves high expressivity with a limited number of Fourier modes, supporting its use as a compact non-perturbative parametrization suitable for DGLAP evolution. We then extend the FF-VQR to two dimensions by incorporating the energy-scale dependence. By encoding all flavor channels within a single entangled quantum circuit, the quantum model provides a unified representation with higher accuracy than an independent encoding for each partonic species.

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arXiv2026

On the analytic continuation and matching of threshold singularities from Vacuum Amplitudes

We provide a detailed discussion for all kinematical configurations of the analytic continuation to negative values of initial-state on-shell energies used to generate interferences of scattering amplitudes from vacuum amplitudes in the Loop-Tree Duality. We also extend previous discussions on the matching of threshold singularities and introduce angular averaging as an efficient strategy to achieve a local cancellation when the matching of threshold singularities from vacuum amplitudes is constrained by flavour.

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arXiv2026

Understanding IR singularities in the Loop-Tree Duality

One of the main advantages of the Loop-Tree Duality representation of scattering amplitudes is that it makes the origin of infrared and threshold singularities particularly transparent. This talk reviews recent progress in describing how singularities emerge and cancel at the level of scattering and vacuum amplitudes, discusses a novel strategy to efficiently construct finite integrals, and presents a complementary perspective based on encoding the underlying causal and singular structure in terms of qubits and quantum circuits.

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arXiv2026

A Systematic Approach to Finite Multiloop Feynman Integrals

Finite Feynman integrals have been advocated as the optimal components for constructing a basis of master integrals in multiloop calculations, due to their improved analytic and numerical properties. In this paper, we show how the Loop-Tree Duality (LTD) is particularly well suited for systematically identifying finite integrals, as it makes the origin of infrared and threshold singularities fully transparent at the integrand level. This clear separation of singular and non-singular contributions enables a more efficient strategy for isolating and promoting finite integrals, thereby streamlining both reduction and numerical evaluation. We present a new strategy based on numerator and raised propagator Ansätze that provides results similar to other methods, although in a clearer and compact way. While this construction and other approaches establish a robust foundation, they often produce integrands that exhibit a rapid growth in the ultraviolet (UV) regime. To mitigate this bad UV behaviour, we introduce a generalized set of integrands fully defined within LTD. This new set is inherently infrared-finite and frequently free of threshold singularities, offering a more versatile framework for high-order calculations.

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arXiv2024

Vacuum amplitudes and time-like causal unitary in the loop-tree duality

We present the first proof-of-concept application to decay processes at higher perturbative orders of LTD causal unitary, a novel methodology that exploits the causal properties of vacuum amplitudes in the loop-tree duality (LTD) and is directly well-defined in the four physical dimensions of the space-time. The generation of loop- and tree-level contributions to the differential decay rates from a kernel multiloop vacuum amplitude is shown in detail, and explicit expressions are presented for selected processes that are suitable for a lightweight understanding of the method. Specifically, we provide a clear physical interpretation of the local cancellation of soft, collinear and threshold singularities, and of the local renormalisation of ultraviolet singularities. The presentation is illustrated with numerical results that showcase the advantages of the method.

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arXiv2024

Rewording Theoretical Predictions at Colliders with Vacuum Amplitudes

We propose multiloop vacuum amplitudes as the optimal building blocks for efficiently assembling theoretical predictions at high-energy colliders. This hypothesis is strongly supported by the manifestly causal properties of the loop-tree duality (LTD) representation of a vacuum amplitude. The vacuum amplitude, acting as a kernel, encodes all the final states contributing to a given scattering or decay process through residues in the on-shell energies of the internal propagators. It also naturally implements gauge invariance and the wave function renormalisation of the external legs. This methodological approach, dubbed LTD causal unitary, leads to a novel representation of differential cross sections and decay rates that is locally free of ultraviolet and infrared singularities at all orders in perturbation theory. Threshold singularities also match between different phase-space residues. Most notably, it allows us to conjecture for the first time the local functional form of initial-state collinear singularities. The fulfillment of all these properties provides a theoretical description of differential observables at colliders that is well defined in the four physical dimensions of the space-time.

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arXiv2024

Using analytic models to describe effective PDFs

Parton distribution functions play a pivotal role in hadron collider phenomenology. They are non-perturbative quantities extracted from fits to available data, and their scale dependence is dictated by the DGLAP evolution equations. In this article, we discuss machine-assisted strategies to efficiently compute PDFs directly incorporating the scale evolution without the need of separately solving DGLAP equations. Analytical approximations to the PDFs as a function of $x$ and $Q^2$, including up to next-to-leading order effects in Quantum Chromodynamics, are obtained. The methodology is tested by reproducing the $\texttt{HERAPDF2.0}$ set and implementing the analytical expressions in benchmarking codes. It is found that the computational cost is reduced while the precision of the simulations stays well under control.

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arXiv2023

Triple-collinear splittings with massive particles

We analyze in detail the most singular behaviour of processes involving triple-collinear splittings with massive particles in the quasi-collinear limit, and present compact expressions for the splitting amplitudes and the corresponding splitting kernels at the squared-amplitude level. Our expressions fully agree with well-known triple-collinear splittings in the massless limit, which are used as a guide to achieve the final expressions. These results are important to quantify dominant mass effects in many observables, and constitute an essential ingredient of current high-precision computational frameworks for collider phenomenology.

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arXiv2023

Variational quantum eigensolver for causal loop Feynman diagrams and directed acyclic graphs

We present a variational quantum eigensolver (VQE) algorithm for the efficient bootstrapping of the causal representation of multiloop Feynman diagrams in the Loop-Tree Duality (LTD) or, equivalently, the selection of acyclic configurations in directed graphs. A loop Hamiltonian based on the adjacency matrix describing a multiloop topology, and whose different energy levels correspond to the number of cycles, is minimized by VQE to identify the causal or acyclic configurations. The algorithm has been adapted to select multiple degenerated minima and thus achieves higher detection rates. A performance comparison with a Grover's based algorithm is discussed in detail. The VQE approach requires, in general, fewer qubits and shorter circuits for its implementation, albeit with lesser success rates.

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arXiv2023

Towards higher-order collinear splittings with massive partons

The singularities associated with QCD factorization in the collinear limit are key ingredients for high-precision theoretical predictions in particle physics. They govern the collinear behaviour of scattering amplitudes, as well as the perturbative energy evolution of parton densities (PDFs) and fragmentation functions (FFs). In this talk, we present the computation of multiple collinear and higher-order QCD splittings with massive partons. Our results are highly-relevant for the consistent introduction of mass effects in the subtraction formalism and PDF/FF evolution.

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arXiv2023

Tackling Feynman integrals with quantum minimization algorithms

One of the most severe bottlenecks to reach high-precision predictions in QFT is the calculation of multiloop multileg Feynman integrals. Several new strategies have been proposed in the last years, allowing impressive results with deep implications in particle physics. Still, the efficiency of such techniques starts to drastically decrease when including many loops and legs. In this talk, we explore the implementation of quantum algorithms to optimize the integrands of scattering amplitudes. We rely on the manifestly causal loop-tree duality, which translates the loop into phase-space integrals and avoids the spurious singularities due to non-causal effects. Then, we built a Hamiltonian codifying causal-compatible contributions and minimize it using a Variational Quantum Eigensolver. Our very promising results point towards a potential speed-up for achieving a more numerically-stable representation of Feynman integrals by using quantum computers.

hep-th↗

arXiv2023

Using photon-hadron production to impose restrictions on heavy-hadrons fragmentation functions

Fragmentation Functions (FF) are universal non-perturbative objects that model hadronization in some general kind of processes. They are mainly extracted from experimental data, hence constraining the parameters of the corresponding fits is crucial for achieving reliable results. As expected, the production of lighter hadrons is favoured w.r.t. heavy ones, thus we would like to exploit the precise knowledge of pion FFs to constraint the shape of kaon (or heavier) FFs. In this talk, we show how imposing specific cuts on photon-hadron production leads to relations between the $u$-started FFs. For doing so, we exploit the reconstruction of momentum fractions in terms of experimentally-accessible quantities and introduce NLO QCD + LO QED corrections to reduce the theoretical uncertainties.

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arXiv2023

Geometrical causality: casting Feynman integrals into quantum algorithms

The calculation of higher-order corrections in Quantum Field Theories is a challenging task. In particular, dealing with multiloop and multileg Feynman amplitudes leads to severe bottlenecks and a very fast scaling of the computational resources required to perform the calculation. With the purpose of overcoming these limitations, we discuss efficient strategies based on the Loop-Tree Duality, its manifestly causal representation and the underlying geometrical interpretation. In concrete, we exploit the geometrical causal selection rules to define a Hamiltonian whose ground-state is directly related to the terms contributing to the causal representation. In this way, the problem can be translated into a minimization one and implemented in a quantum computer to search for a potential speed-up.

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arXiv2023

Constraining fragmentation functions through hadron-photon production at higher-orders

In certain situations, such as one-particle inclusive processes, it is possible to model the hadronization through Fragmentation Functions (FFs), which are universal non-perturbative functions extracted from experimental data through advanced fitting techniques. Constraining the parameters of such fits is crucial to reduce the uncertainties, and provide reliable and accurate FFs. In this article, we explore strategies to relate pion and FFs for other hadrons (in particular, kaons), comparing cross-section ratios imposing proper kinematical cuts. We exploit the phenomenology of photon-hadron production at colliders, including up to NLO QCD and LO QED corrections, and make use of accurate formulae to reconstruct the partonic momentum fractions. By studying different cuts, we manage to isolate the contribution of $u$-started FFs. Then, we relate the ratios of the $z$-spectrum for pion and kaon production, with the corresponding FFs ratios. The methodology described in this article can be used to relate FFs for any pair of hadrons, and could be further explored to keep track of the flavour of the partons undergoing the hadronization.

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arXiv2023

Combining QED and QCD transverse-momentum resummation for W and Z boson production at hadron colliders

In this article, we consider the transverse momentum ($q_T$) distribution of $W$ and $Z$ bosons produced in hadronic collisions. We combine the $q_T$ resummation for QED and QCD radiation including the QED soft emissions from the $W$ boson in the final state. In particular, we perform the resummation of enhanced logarithmic contributions due to soft and collinear emissions at next-to-leading accuracy in QED, leading-order accuracy for mixed QED-QCD and next-to-next-to-leading accuracy in QCD. In the small-$q_T$ region we consistently include in our results the next-to-next-to-leading order (i.e.\ two loops) QCD corrections and the next-to-leading order (i.e.\ one loop) electroweak corrections. The matching with the fixed-order calculation at large $q_T$ has been performed at next-to-leading order in QCD (i.e.\ at $\mathcal{O}(α_S^2)$) and at leading order in QED. We show numerical results for $W$ and $Z$ production at the Tevatron and the LHC. Finally, we consider the effect of combined QCD and QED resummation for the ratio of $W$ and $Z$ $q_T$ distributions, and we study the impact of the QED corrections providing an estimate of the corresponding perturbative uncertainties.

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arXiv2022

From five-loop scattering amplitudes to open trees with the Loop-Tree Duality

Characterizing multiloop topologies is an important step towards developing novel methods at high perturbative orders in quantum field theory. In this article, we exploit the Loop-Tree Duality (LTD) formalism to analyse multiloop topologies that appear for the first time at five loops. Explicitly, we open the loops into connected trees and group them according to their topological properties. Then, we identify a kernel generator, the so-called N$^7$MLT universal topology, that allow us to describe any scattering amplitude of up to five loops. Furthermore, we provide factorization and recursion relations that enable us to write these multiloop topologies in terms of simpler subtopologies, including several subsets of Feynman diagrams with an arbitrary number of loops. Our approach takes advantage of many symmetries present in the graphical description of the original fundamental five-loop topologies. The results obtained in this article might shed light into a more efficient determination of higher-order corrections to the running couplings, which are crucial in the current and future precision physics program.

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arXiv2022

Reconstructing parton collisions with machine learning techniques

Having access to the parton-level kinematics is important for understanding the internal dynamics of particle collisions. Here, we present new results aiming to an efficient reconstruction of parton collisions using machine-learning techniques. By simulating the collider events, we related experimentally-accessible quantities with the momentum fractions of the involved partons. We used photon-hadron production to exploit the cleanliness of the photon signal, including up to NLO QCD-QED corrections. Neural networks led to an outstanding reconstruction efficiency, suggesting a powerful strategy for unveiling the behaviour of the fundamental bricks of matter in high-energy collisions.

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arXiv2022

Quantum algorithm for Feynman loop integrals

We present a novel benchmark application of a quantum algorithm to Feynman loop integrals. The two on-shell states of a Feynman propagator are identified with the two states of a qubit and a quantum algorithm is used to unfold the causal singular configurations of multiloop Feynman diagrams. To identify such configurations, we exploit Grover's algorithm for querying multiple solutions over unstructured datasets, which presents a quadratic speed-up over classical algorithms when the number of solutions is much smaller than the number of possible configurations. A suitable modification is introduced to deal with topologies in which the number of causal states to be identified is nearly half of the total number of states. The output of the quantum algorithm in \emph{IBM Quantum} and \emph{QUTE Testbed} simulators is used to bootstrap the causal representation in the loop-tree duality of representative multiloop topologies. The algorithm may also find application and interest in graph theory to solve problems involving directed acyclic graphs.

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