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PreprintCC BY 4.0arXiv

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

  • Alessandro Lupo
  • Nazario Tantalo
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Abstract

We expand the treatment of the problem of the extraction of smeared spectral densities from Euclidean correlators introduced in [Phys. Rev. D 99, 094508], 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 scrutinise the performance and systematics of this approach either as a standalone 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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Cite

BibTeXRIS
BibTeX
@misc{lupo2026extraction,
  title = {{Extraction of spectral densities from lattice correlators: decoupling signal from noise}},
  author = {Alessandro Lupo and Nazario Tantalo},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2605.14652},
  eprint = {2605.14652},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.14652},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Extraction of spectral densities from lattice correlators: decoupling signal from noise
AU  - Alessandro Lupo
AU  - Nazario Tantalo
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2605.14652
UR  - https://arxiv.org/abs/2605.14652
AB  - We expand the treatment of the problem of the extraction of smeared spectral densities from Euclidean correlators introduced in [Phys. Rev. D 99, 094508], 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 scrutinise the performance and systematics of this approach either as a standalone procedure, or to complement the stability analysis required to extrapolate the unbiased result in the Backus-Gilbert regulated version of the solution.
ER  -