arXiv subjects

Luigi Del Debbio

Publications and source records attributed to Luigi Del Debbio.

At least 19 recordsLinked to original sources

arXiv2026

Symplectic lattice gauge theories in the Grid framework: domain wall fermions and continuum extrapolations

We report the results of the first numerical lattice study using domain-wall fermions in the Sp(4) gauge theory coupled to two flavours of (Dirac) fermions, transforming in the fundamental representation of the gauge group. This theory plays a prominent role in the literature on extensions of the Standard Model with composite dynamics. It provides a short-distance completion for a class of composite Higgs models, or, alternatively, of dark matter models based on the strongly interacting massive particle paradigm. We adopt the Möbius formulation of domain-wall fermions (MDWF), implemented within the Grid software environment. We report the results of extensive tests of the algorithm implementation, and of the optimisation of the choices of algorithmic parameters appearing in the MDWF action. We then measure masses and decay constants of the lightest flavoured mesons in ensembles with moderately large fermion masses and several choices of lattice coupling, and perform an extrapolation to the continuum. We compare our results for the physical observables to published measurements obtained in the same field theory, but derived on the lattice by employing Wilson fermions. We demonstrate that, with the deployment of moderate computational resources, the MDWF formulation can yield order-of-magnitude gains in the approach to the continuum limit, in regions of physical parameter space relevant to phenomenological applications of this theory.

hep-lat↗

arXiv2026

Quantitative Understanding of PDF Fits and their Uncertainties

Parton Distribution Functions (PDFs) play a central role in describing experimental data at colliders and provide insight into the structure of nucleons. As the LHC enters an era of high-precision measurements, a robust PDF determination with a reliable uncertainty quantification has become mandatory in order to match the experimental precision. The NNPDF collaboration has pioneered the use of Machine Learning (ML) techniques for PDF determinations, using Neural Networks (NNs) to parametrise the unknown PDFs in a flexible and unbiased way. The NNs are then trained on experimental data by means of stochastic gradient descent algorithms. The statistical robustness of the results is validated by extensive closure tests using synthetic data. In this work, we develop a theoretical framework based on the Neural Tangent Kernel (NTK) to analyse the training dynamics of neural networks. This approach allows us to derive, under precise assumptions, an analytical description of the neural network evolution during training, enabling a quantitative understanding of the training process. Having an analytical handle on the training dynamics allows us to clarify the role of the NN architecture and the impact of the experimental data in a transparent way. Similarly, we are able to describe the evolution of the covariance of the NN output during training, providing a quantitative description of how uncertainties are propagated from the data to the fitted function. While our results are not a substitute for PDF fitting, they do provide a powerful diagnostic tool to assess the robustness of current fitting methodologies. Beyond its relevance for particle physics phenomenology, our analysis of PDF determinations provides a testbed to apply theoretical ideas about the learning process developed in the ML community.

hep-ph↗

arXiv2026

Some Inverse Problems in Particle Physics

Inverse problems play a central role in current areas of research in particle phenomenology. In these lectures we focus on two examples, the extraction of Parton Distribution Functions (PDFs) from experimental data (or, equivalently, from pseudo- and quasi-PDFs computed in lattice QCD), and the extraction of spectral functions from lattice Euclidean time correlators. We investigate in detail three different approaches, namely Backus-Gilbert, Gaussian Processes and fits based on Neural Network parametrizations.

hep-lat↗

arXiv2026

Lattice studies of chimera baryons in Sp(4) gauge theory

We study chimera baryons, fermion bound states composed of two (hyper)quarks transforming in the fundamental and one in the antisymmetric representation of a non-Abelian gauge group. While in QCD they coincide with ordinary baryons, in composite Higgs models (CHMs) with top partial compositeness, spin-1/2 chimera baryons serve as partners of the top quark and are responsible for its large mass. We perform non-perturbative lattice calculations of the low-lying spectrum of the chimera baryons, in a specific realization of CHMs based on a Sp(4) gauge theory. In the quenched approximation, we present the numerical results in the continuum and massless limits. Then, for dynamical fermions, we measure the spectrum and matrix elements by employing a newly developed spectral density analysis for several choices of the lattice parameters.

hep-lat↗

arXiv2026

Circuit Harmonic Matrices: A Spectral Framework for Quantum Machine Learning

Parametrised quantum circuits are a central framework for near term quantum machine learning. However, it remains challenging to determine in advance how architectural choices, such as encoding strategies, gate placement, and entangling structure, influence both the expressive capacity of the model and its trainability during optimisation. We introduce a data-agnostic framework, one requiring no knowledge of a training dataset or optimisation trajectory, that maps a broad family of circuits into a single architecture matrix built over learnable features and parameters. We show that this framework provides an explicit link between circuit structure, the correlations among learnable features, and the geometry of training kernels through the factorisation of each of these objects as quadratic forms in terms of these matrices. We show how correlations between learnable features arise from shared parameter-induced harmonics generated by non-commuting gate-observable interactions during Heisenberg back-propagation, and how these correlations are encoded directly in the architecture matrix. From this perspective, kernel structure and coefficient statistics can be reconstructed analytically from circuit design alone, without reference to a dataset or optimisation trajectory. The resulting framework makes circuit-induced structure explicit, separating architectural effects from data-dependent ones, and provides a principled foundation for analysing and comparing parametrised quantum circuits based on intrinsic, design-level signatures.

quant-ph↗

arXiv2025

Chimera baryons and mesons on the lattice: a spectral density analysis

We develop and test a spectral-density analysis method, based on the introduction of smeared energy kernels, to extract physical information from two-point correlation functions computed numerically in lattice field theory. We apply it to a $Sp(4)$ gauge theory and fermion matter fields transforming in distinct representations, with $N_{\rm f}=2$ Dirac fermions in the fundamental and $N_{\rm as}=3$ in the 2-index antisymmetric representation. The corresponding continuum theory provides the minimal candidate model for a composite Higgs boson with partial top compositeness. We consider a broad class of composite operators, that source flavored mesons and (chimera) baryons, for several finite choices of lattice bare parameters. For the chimera baryons, which include candidate top-quark partners, we provide the first measurements, obtained with dynamical fermions, of the ground state and the lowest excited state masses, in all channels of spin, isospin, and parity. We also measure matrix elements and overlap factors, that are important to realize viable models of partial top compositeness, by implementing an innovative way of extracting this information from the spectral densities. For the mesons, among which the pseudoscalars can be reinterpreted to provide an extension of the Higgs sector of the Standard Model of particle physics, our measurements of the renormalized matrix elements and decay constants are new results. We complement them with an update of existing measurements of the meson masses, obtained with higher statistics and improved analysis. The analysis software is made publicly available, and can be used in other lattice studies, including application to quantum chromodynamics (QCD).

hep-lat↗

arXiv2025

Combination of aN$^3$LO PDFs and implications for Higgs production cross-sections at the LHC

We discuss how the two existing approximate N$^3$LO (aN$^3$LO) sets of parton distributions (PDFs) from the MSHT20 and NNPDF4.0 series can be combined for LHC phenomenology, both in the pure QCD case and for the QCD$\otimes$QED sets that include the photon PDF. Using the resulting combinations, we present predictions for the total inclusive cross-section for Higgs production in gluon fusion, vector boson fusion, and associated production at the LHC Run-3. For the gluon fusion and vector boson fusion channels, the corrections that arise when using correctly matched aN$^3$LO PDFs with N$^3$LO cross section calculations, compared to using NNLO PDFs, are significant, in many cases larger than the PDF uncertainty, and generally larger than the differences between the two aN$^3$LO PDF sets entering the combination. The combined aN$^3$LO PDF sets, MSHT20xNNPDF40_an3lo and MSHT20xNNPDF40_an3lo_qed, are made publicly available in the LHAPDF format and can be readily used for LHC phenomenology.

hep-ph↗

arXiv2024

Progress on the spectroscopy of lattice gauge theories using spectral densities

Spectral densities encode non-perturbative information crucial in computing physical observables in strongly coupled field theories. Using lattice gauge theory data, we perform a systematic study to demonstrate the potential of recent technological advances in the reconstruction of spectral densities. We develop, maintain and make publicly available dedicated analysis code that can be used for broad classes of lattice theories. As a test case, we analyse the Sp(4) gauge theory coupled to an admixture of fermions transforming in the fundamental and two-index antisymmetric representations. We measure the masses of mesons in energy-smeared spectral densities, after optimising the smearing parameters for available lattice ensembles. We present a summary of the mesons mass spectrum in all the twelve (flavored) channels available, including also several excited states.

hep-lat↗

arXiv2024

Approaches to the Inverse Problem

The analytical continuation of correlation functions from imaginary to real time is a crucial step in lattice gauge theories, and it challenges our ability to derive non-perturbative predictions from lattice simulations. We review aspects of this "inverse problem", which has driven both theoretical and algorithmic advancements in recent years, opening new promising avenues for non-perturbative studies of the Standard Model and beyond. The focus of this proceeding will be on variations of Backus-Gilbert and Bayesian methods.

hep-lat↗

arXiv2024

Meson spectroscopy from spectral densities in lattice gauge theories

Spectral densities encode non-perturbative information that enters the calculation of a plethora of physical observables in strongly coupled field theories. Phenomenological applications encompass aspects of standard-model hadronic physics, observable at current colliders, as well as correlation functions characterizing new physics proposals, testable in future experiments. By making use of numerical data produced in a Sp(4) lattice gauge theory with matter transforming in an admixture of fundamental and 2-index antisymmetric representations of the gauge group, we perform a systematic study to demonstrate the effectiveness of recent technological progress in the reconstruction of spectral densities. To this purpose, we write and test new software packages that use energy-smeared spectral densities to analyze the mass spectrum of mesons. We assess the effectiveness of different smearing kernels and optimize the smearing parameters to the characteristics of available lattice ensembles. We generate new ensembles for the theory in consideration, with lattices that have a longer extent in the time direction with respect to the spatial ones. We run our tests on these ensembles, obtaining new results about the spectrum of light mesons and their excitations. We make available our algorithm and software for the extraction of spectral densities, that can be applied to theories with other gauge groups, including the theory of strong interactions (QCD) governing hadronic physics in the standard model.

hep-lat↗

arXiv2024

Bayesian solution to the inverse problem and its relation to Backus-Gilbert methods

The problem of obtaining spectral densities from lattice data has been receiving great attention due to its importance in our understanding of scattering processes in Quantum Field Theory, with applications both in the Standard Model and beyond. The problem is notoriously difficult as it amounts to performing an inverse Laplace transform, starting from a finite set of noisy data. Several strategies are now available to tackle this inverse problem. In this work, we discuss how Backus-Gilbert methods, in particular the variation introduced by some of the authors, relate to the solution based on Gaussian Processes. Both methods allow computing spectral densities smearing with a kernel, whose features depend on the detail of the algorithm. We will discuss such kernel, and show how Backus-Gilbert methods can be understood in a Bayesian fashion. As a consequence of this correspondence, we are able to interpret the algorithmic parameters of Backus-Gilbert methods as hyperparameters in the Bayesian language, which can be chosen by maximising a likelihood function. By performing a comparative study on lattice data, we show that, when both frameworks are set to compute the same quantity, the results are generally in agreement. Finally, we adopt a strategy to systematically validate both methodologies against pseudo-data, using covariance matrices measured from lattice simulations. In our setup, we find that the determination of the algorithmic parameters based on a stability analysis provides results that are, on average, more conservative than those based on the maximisation of a likelihood function.

hep-lat↗

arXiv2024

Absorbing discretisation effects with a massive renormalization scheme: the charm-quark mass

We present the first numerical implementation of the massive SMOM (mSMOM) renormalization scheme and use it to calculate the charm quark mass. Based on ensembles with three flavours of dynamical domain wall fermions with lattice spacings in the range 0.11 -- 0.08 fm, we demonstrate that the mass scale which defines the mSMOM scheme can be chosen such that the extrapolation has significantly smaller discretisation effects than the SMOM scheme. Converting our results to the $\overline{\mathrm{MS}}$ scheme we obtain $\overline{m}_c(3\,\mathrm{GeV}) = 1.008(13)\,\mathrm{GeV}$ and $\overline{m}_c(\overline{m}_c) = 1.292(12)\,\mathrm{GeV}$.

hep-lat↗

arXiv2024

The Path to N$^3$LO Parton Distributions

We extend the existing leading (LO), next-to-leading (NLO), and next-to-next-to-leading order (NNLO) NNPDF4.0 sets of parton distribution functions (PDFs) to approximate next-to-next-to-next-to-leading order (aN$^3$LO). We construct an approximation to the N$^3$LO splitting functions that includes all available partial information from both fixed-order computations and from small and large $x$ resummation, and estimate the uncertainty on this approximation by varying the set of basis functions used to construct the approximation. We include known N$^3$LO corrections to deep-inelastic scattering structure functions and extend the FONLL general-mass scheme to $\mathcal{O}\left( α_s^3\right)$ accuracy. We determine a set of aN$^3$LO PDFs by accounting both for the uncertainty on splitting functions due to the incomplete knowledge of N$^3$LO terms, and to the uncertainty related to missing higher corrections (MHOU), estimated by scale variation, through a theory covariance matrix formalism. We assess the perturbative stability of the resulting PDFs, we study the impact of MHOUs on them, and we compare our results to the aN$^3$LO PDFs from the MSHT group. We examine the phenomenological impact of aN$^3$LO corrections on parton luminosities at the LHC, and give a first assessment of the impact of aN$^3$LO PDFs on the Higgs and Drell-Yan total production cross-sections. We find that the aN$^3$LO NNPDF4.0 PDFs are consistent within uncertainties with their NNLO counterparts, that they improve the description of the global dataset and the perturbative convergence of Higgs and Drell-Yan cross-sections, and that MHOUs on PDFs decrease substantially with the increase of perturbative order.

hep-ph↗

arXiv2024

Photons in the proton: implications for the LHC

We construct a set of parton distribution functions (PDFs), based on the recent NNPDF4.0 PDF set, that also include a photon PDF. The photon PDF is constructed using the LuxQED formalism, while QED evolution accounting for O(alpha), O(alpha alphas) and O(alpha^2) corrections is implemented and benchmarked by means of the EKO code. We investigate the impact of QED effects on NNPDF4.0, and compare our results both to our previous NNPDF3.1QED PDF set and to other recent PDF sets that include the photon. We assess the impact of photon-initiated processes and electroweak corrections on a variety of representative LHC processes, and find that they can reach the 5% level in vector boson pair production at large invariant mass.

hep-ph↗

arXiv2024

Determination of the theory uncertainties from missing higher orders on NNLO parton distributions with percent accuracy

We include uncertainties due to missing higher order corrections to QCD computations (MHOU) used in the determination of parton distributions (PDFs) in the recent NNPDF4.0 set of PDFs. We use our previously published methodology, based on the treatment of MHOUs and their full correlations through a theory covariance matrix determined by scale variation, now fully incorporated in the new NNPDF theory pipeline. We assess the impact of the inclusion of MHOUs on the NNPDF4.0 central values and uncertainties, and specifically show that they lead to improved consistency of the PDF determination with an ensuing moderate reduction of PDF uncertainties at NNLO.

hep-ph↗

arXiv2024

Bayesian Inference with Gaussian Processes for the Determination of Parton Distribution Functions

We discuss a Bayesian methodology for the solution of the inverse problem underlying the determination of parton distribution functions (PDFs). In our approach, Gaussian Processes (GPs) are used to model the PDF prior, while Bayes theorem is used in order to determine the posterior distribution of the PDFs given a set of data. We discuss the general formalism, the Bayesian inference at the level of both parameters and hyperparameters, and the simplifications which occur when the observable entering the analysis is linear in the PDF. We benchmark the new methodology in two simple examples for the determination of a single PDF flavor from a set of Deep Inelastic Scattering (DIS) data and from a set of equal-time correlators computed using lattice QCD. We discuss our results, showing how the proposed methodology allows for a well-defined statistical interpretation of the different sources of errors entering the PDF uncertainty, and how results can be validated a posteriori.

hep-ph↗

arXiv2024

Neural Networks Asymptotic Behaviours for the Resolution of Inverse Problems

This paper presents a study of the effectiveness of Neural Network (NN) techniques for deconvolution inverse problems relevant for applications in Quantum Field Theory, but also in more general contexts. We consider NN's asymptotic limits, corresponding to Gaussian Processes (GPs), where non-linearities in the parameters of the NN can be neglected. Using these resulting GPs, we address the deconvolution inverse problem in the case of a quantum harmonic oscillator simulated through Monte Carlo techniques on a lattice. In this simple toy model, the results of the inversion can be compared with the known analytical solution. Our findings indicate that solving the inverse problem with a NN yields less performing results than those obtained using the GPs derived from NN's asymptotic limits. Furthermore, we observe the trained NN's accuracy approaching that of GPs with increasing layer width. Notably, one of these GPs defies interpretation as a probabilistic model, offering a novel perspective compared to established methods in the literature. Our results suggest the need for detailed studies of the training dynamics in more realistic set-ups.

physics.comp-ph↗

arXiv2023

Charm quark mass using a massive nonperturbative renormalisation scheme

We present a first numerical implementation of a massive nonperturbative renormalisation scheme, RI/mSMOM, in the study of heavy quarks using the domain-wall fermion action. In particular, we calculate renormalisation constants for fermion bilinears at non-vanishing heavy-quark masses and compare the approach to the continuum of the renormalised charm-quark mass with that from a mass-independent scheme.

hep-lat↗