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Extraction of spectral densities from lattice correlators: Decoupling signal from noise

Alessandro Lupo*

Nazario Tantalo†

  • *Contact author: alessandro.lupo@cpt.univ-mrs.fr
  • †Contact author: nazario.tantalo@roma2.infn.it
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Phys. Rev. D 114, 074511 – Published 20 October, 2026

DOI: https://doi.org/10.1103/g99j-k1fj

Abstract

We expand the treatment of the problem of the extraction of smeared spectral densities from Euclidean correlators, introduced in [Extraction of spectral densities from lattice correlators, Phys. Rev. D 99, 094508 (2019).], providing an alternative which does not rely on the Backus-Gilbert regularization. This is possible due to the observation that the solution can be decomposed into a sum of terms, in the spirit of the singular value decomposition, where those with the largest contribution to the statistical noise happen to contribute the least to the central value of the smeared spectral density. The analysis of the systematics of the inverse problem is then shifted to finding the optimal truncation of such summation, so that the signal is saturated before the noise explodes. We scrutinize the performance and systematics of this approach either as a stand-alone procedure, or to complement the stability analysis required to extrapolate the unbiased result in the Backus-Gilbert regulated version of the solution.

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Phys. Rev. D 114, 074511– Published 20 October, 2026
  • Received 5 June 2026
  • Accepted 28 September 2026
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