arXiv subjects

Matteo Saccardi

Publications and source records attributed to Matteo Saccardi.

8 recordsLinked to original sources

arXiv2026

Spectral densities from Euclidean correlators via integral transforms: theoretical framework

Spectral densities link experimental measurements to dynamical properties of a quantum field theory which, in turn, can be resolved non-perturbatively from the Euclidean time-dependence of correlation functions. By making extensive use of integral transforms, we present analytic formulae to carry out the inverse Laplace transform so as to extract spectral densities from either the continuum or the discrete sampling of correlation functions in the Euclidean time. Formulae extend to regulated and/or smeared spectral densities as well. We explicitly show that the proposed lattice solution tends to its continuum counterpart up to $O(a^2)$ effects in the lattice spacing $a$ if the lattice correlator is $O(a)$-improved. In practical computations, lattices have necessarily a finite Euclidean temporal extent, a lack of knowledge which suggests to introduce incomplete integral transforms and the corresponding incomplete smeared spectral densities. The contribution from the unknowns to a smeared spectral density can then be rigorously bound and kept under control if the integral transform of the smearing function decays fast enough with the conjugate variable. Conversely, the bound can be used to plan lattices so as to achieve a given target precision on the reconstructed spectral density of interest. The formulae presented here in the context of lattice field theory can be easily applied or extended to other areas of research.

hep-lat↗

arXiv2026

Kernel transformations and bounds for smeared spectral functions

This work develops a framework for transforming between smeared spectral functions computed using different smearing kernels. The kernel-transformation problem naturally arises when information is available for one family of energy-smeared observables, while phenomenology or comparison with other calculations require a different smearing. For exact transformations, analytic conditions are established for the maps to exist and converge without arbitrary regularization. Explicit expressions are provided for several kernel classes of interest, including Cauchy-to-Gaussian transformations and Gaussian-to-Cauchy width mixtures. When exact transformations are unavailable, the inverse problem is tackled through regulated maps paired with bounds on the associated systematic error, directly computable from the given input data. Errors on the input smeared spectral functions, either statistical or in the form of pointwise rigorous bounds, are then propagated to the target observables. Enforcing spectral positivity can be used to tighten the bounds.

hep-lat↗

arXiv2026

The Causal Bootstrap: Bounding Smeared Spectral Functions from Non-Perturbative Euclidean Data

This work introduces the causal bootstrap, a framework for bounding smeared spectral observables from finite non-perturbative Euclidean data. The method optimizes over the convex set of positive spectral densities compatible with the data to compute rigorous upper and lower bounds on the target observable. Statistical uncertainties, including correlations, are incorporated through compatibility regions using the covariance matrix. The bounds are equivalent, via Lagrange duality, to certified bounds on the target smearing kernel. For polynomial, rational, and piecewise rational kernels, the resulting dual problems can be reduced to finite-dimensional semidefinite programs using techniques familiar, e.g., in the numerical conformal bootstrap. The present formulation clarifies the relation to moment problems, Nevanlinna--Pick interpolation, and linear kernel-reconstruction methods. Numerical examples demonstrate the method.

hep-lat↗

arXiv2025

Spectral densities from Euclidean-time lattice correlation functions

In quantum field theories, spectral densities are directly related to relevant physical observables. In Lattice QCD, their non-perturbative extraction from first principles requires the Inverse Laplace transform of Euclidean-time correlation functions, a notorious ill-posed problem. Here we review our recent proposal [1,2] for a new strategy to perform this inversion both in the continuum and on the lattice, also suitable for smeared spectral densities, both in the continuum and in the discrete cases.

hep-lat↗

arXiv2024

Spectral densities from Euclidean lattice correlators via the Mellin transform

Spectral densities connect correlation functions computed in quantum field theory to observables measured in experiments. For strongly-interacting theories, their non-perturbative determinations from lattice simulations are therefore of primary importance. They entail the inverse Laplace transform of correlation functions calculated in Euclidean time. By making use of the Mellin transform, we derive explicit analytic formulae to define spectral densities from the time dependence of correlation functions, both in the continuum and on the lattice. The generalization to smeared spectral densities turns out to be straightforward. The formulae obtained here within the context of lattice field theory can be easily applied or extended to other areas of research.

hep-lat↗

arXiv2023

On the prediction of spectral densities from Lattice QCD

Hadronic spectral densities play a pivotal role in particle physics, a prime example being the R-ratio defined from electron-positron scattering into hadrons. To predict them from first principles using Lattice QCD, we face a numerically ill-posed inverse problem, due to the Euclidean signature adopted in practical simulations. Here we present a recent numerical analysis of the vector isovector spectral density extracted using the multi-level algorithm (recently extended also to the case of dynamical fermions) and discuss its implications.

hep-lat↗

arXiv2022

Four-dimensional domain decomposition for the factorization of the fermion determinant

The non-local dependence of the fermion determinant on the gauge field limits our ability of simulating Quantum Chromodynamics on the lattice. Here we present a factorization of the gauge field dependence of the fermion determinant based on an overlapping four-dimensional domain decomposition of the lattice. The resulting action is block-local in the gauge and in the auxiliary bosonic fields. Possible applications are multi-level integration, master field simulations, and more efficient parallelizations of Monte Carlo algorithms and codes.

hep-lat↗

arXiv2022

Four-dimensional factorization of the fermion determinant in lattice QCD

In the last few years it has been proposed a one-dimensional factorization of the fermion determinant in lattice QCD with Wilson-type fermions that leads to a block-local action of the auxiliary bosonic fields. Here we propose a four-dimensional generalization of this factorization. Possible applications are more efficient parallelizations of Monte Carlo algorithms and codes, master field simulations, and multi-level integration.

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