- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Application of Laplace filters to the analysis of lattice time correlators

Antonin Portelli

Justus Tobias Tsang

  • CERN, Department of Theoretical Physics and Theoretical Physics Division, Department of Mathematical Sciences, University of Liverpool, Liverpool L69 3BX, United Kingdom

PDF

Phys. Rev. D 112, 094512 – Published 21 November, 2025

DOI: https://doi.org/10.1103/3v93-9s9t

Abstract

The analysis of lattice simulation correlation function data is notoriously hindered by the ill conditioning of the Euclidean time covariance matrix. Additionally, the isolation of a single physical state in such functions is generally affected by systematic contamination from unwanted states. In this paper, we present a new methodology based on regulated Laplace filters and demonstrate that it can be used to address both issues using state-of-the-art simulation data. Regulated Laplace filters are invertible high-pass filters that suppress local correlations in the data, and we show that they can reduce the condition number of covariance matrices by several orders of magnitude. Furthermore, Laplace filters can annihilate functions that decay exponentially with time, which can be used to alter the spectrum of a lattice correlation function. We show that this property can be exploited to significantly reduce excited-state contamination in the determination of matrix elements. The same property can also be used to constrain the spectral content of a correlation function and has the potential to form the basis of new methods to extract physical information from lattice data.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (35)

  1. Y. Aoki et al. (Flavour Lattice Averaging Group (FLAG) Collaboration), FLAG review 2024, Phys. Rev. D (to be published), 10.1103/nfzp-p5dn.
  2. R. Aliberti et al., The anomalous magnetic moment of the muon in the standard model: An update, Phys. Rep. 1143, 1 (2025).
  3. C. Michael, Fitting correlated data, Phys. Rev. D 49, 2616 (1994).
  4. C. Michael and A. McKerrell, Fitting correlated hadron mass spectrum data, Phys. Rev. D 51, 3745 (1995).
  5. O. Ledoit and M. Wolf, A well-conditioned estimator for large-dimensional covariance matrices, J. Multivariate Anal. 88, 365 (2004).
  6. J. Green, N. Hasan, S. Meinel, M. Engelhardt, S. Krieg, J. Laeuchli, J. Negele, K. Orginos, A. Pochinsky, and S. Syritsyn, Up, down, and strange nucleon axial form factors from lattice QCD, Phys. Rev. D 95, 114502 (2017).
  7. O. Ledoit and M. Wolf, Nonlinear shrinkage estimation of large-dimensional covariance matrices, Ann. Stat. 40, 1024 (2012).
  8. O. Ledoit and M. Wolf, Analytical nonlinear shrinkage of large-dimensional covariance matrices, Ann. Stat. 48, 3043 (2020).
  9. M. Bruno and R. Sommer, On fits to correlated and auto-correlated data, Comput. Phys. Commun. 285, 108643 (2023).
  10. R. J. Dowdall, C. T. H. Davies, R. R. Horgan, G. P. Lepage, C. J. Monahan, J. Shigemitsu, and M. Wingate, Neutral B-meson mixing from full lattice QCD at the physical point, Phys. Rev. D 100, 094508 (2019).
  11. C. R. Allton et al. (UKQCD Collaboration), Gauge invariant smearing and matrix correlators using Wilson fermions at Beta=6.2, Phys. Rev. D 47, 5128 (1993).
  12. F. Knechtli, T. Korzec, M. Peardon, and J. A. Urrea-Niño, Optimizing creation operators for charmonium spectroscopy on the lattice, Phys. Rev. D 106, 034501 (2022).
  13. G. de Prony, Essai expérimental et analytique: Sur les lois de la dilatabilité des fluides élastiques et sur celles de la force expansive de la vapeur de l’eau et de la vapeur de l’alcool, à différentes températures, J. l’École Polytech. 1, 24 (1795).
  14. G. T. Fleming, What can lattice QCD theorists learn from NMR spectroscopists?, in 3rd International Workshop on Numerical Analysis and Lattice QCD (2004), pp. 143–152, arXiv:hep-lat/0403023.
  15. S. R. Beane, W. Detmold, T. C. Luu, K. Orginos, A. Parreno, M. J. Savage, A. Torok, and A. Walker-Loud, High statistics analysis using anisotropic clover lattices: (I) Single hadron correlation functions, Phys. Rev. D 79, 114502 (2009).
  16. M. L. Wagman, Lanczos algorithm, the transfer matrix, and the signal-to-noise problem, Phys. Rev. Lett. 134, 241901 (2025).
  17. J. Ostmeyer, A. Sen, and C. Urbach, On the equivalence of Prony and Lanczos methods for Euclidean correlation functions, Eur. Phys. J. A 61, 26 (2025).
  18. R. Abbott, D. C. Hackett, G. T. Fleming, D. A. Pefkou, and M. L. Wagman, Filtered Rayleigh-Ritz is all you need, arXiv:2503.17357.
  19. B. Blossier, M. Della Morte, G. von Hippel, T. Mendes, and R. Sommer, On the generalized eigenvalue method for energies and matrix elements in lattice field theory, J. High Energy Phys. 04 (2009) 094.
  20. D. Chakraborty, D. Sood, A. Radhakrishnan, and N. Mathur, Estimating energy levels from lattice QCD correlation functions using a transfer matrix formalism, Phys. Rev. D 112, 074506 (2025).
  21. S. Borsanyi et al. (BMW Collaboration), Ab initio calculation of the neutron-proton mass difference, Science 347, 1452 (2015).
  22. W. I. Jay and E. T. Neil, Bayesian model averaging for analysis of lattice field theory results, Phys. Rev. D 103, 114502 (2021).
  23. T. Blum et al. (RBC, UKQCD Collaborations), Domain wall QCD with physical quark masses, Phys. Rev. D 93, 074505 (2016).
  24. P. A. Boyle, L. Del Debbio, N. Garron, A. Jüttner, A. Soni, J. T. Tsang, and O. Witzel (RBC/UKQCD Collaborations), SU(3)-breaking ratios for D(s) and B(s) mesons, arXiv:1812.08791.
  25. P. A. Boyle, F. Erben, J. M. Flynn, N. Garron, J. Kettle, R. Mukherjee, and J. T. Tsang (RBC, UKQCD Collaborations), Kaon mixing beyond the standard model with physical masses, Phys. Rev. D 110, 034501 (2024).
  26. Y.-G. Cho, S. Hashimoto, A. Jüttner, T. Kaneko, M. Marinkovic, J.-I. Noaki, and J. T. Tsang, Improved lattice fermion action for heavy quarks, J. High Energy Phys. 05 (2015) 072.
  27. J. M. Flynn, R. C. Hill, A. Jüttner, A. Soni, J. T. Tsang, and O. Witzel (RBC/UKQCD Collaborations), Exclusive semileptonic Bs→Kℓν decays on the lattice, Phys. Rev. D 107, 114512 (2023).
  28. S. S. Wilks, The large-sample distribution of the likelihood ratio for testing composite hypotheses, Ann. Math. Stat. 9, 60 (1938).
  29. S. Holm, A simple sequentially rejective multiple test procedure, Scand. J. Stat. Theory Appl. 6, 65 (1979), https://www.jstor.org/stable/4615733.
  30. N. Christ, R. Eranki, and C. Kelly (RBCUKQCD Collaborations), Bootstrap-determined p values in lattice QCD, Phys. Rev. D 111, 074514 (2025).
  31. Bär, Oliver, and Colic, Haris, Nπ-state contamination in lattice calculations of the nucleon electromagnetic form factors, Phys. Rev. D 103, 114514 (2021).
  32. Bär and Oliver, Nπ-state contamination in lattice calculations of the nucleon axial form factors, Phys. Rev. D 99, 054506 (2019).
  33. Bär, Oliver, and Broll, Alexander and Sommer, Rainer, Bπ excited-state contamination in lattice calculations of B-meson correlation functions, Eur. Phys. J. C 83, 757 (2023).
  34. www.dirac.ac.uk.
  35. A. Portelli and J. T. Tsang, Application of laplace filters to the analysis of lattice time correlators, 10.5281/zenodo.16921526 (2025).

Outline

Information

Phys. Rev. D 112, 094512– Published 21 November, 2025
  • Received 22 August 2025
  • Accepted 23 October 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation