2013/10/15 by David Dudal, Orlando Oliveira, Paulo J. Silva · 103 citations
Mathematics · Physics and Astronomy · #Euclidean geometry #Geometry #High-Energy Particle Collisions Research #Inverse problem #Mathematical analysis #Mathematical physics #Mathematics #Particle physics theoretical and experimental studies #Physics #Propagator #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Regularization (linguistics) #Tikhonov regularization #hep-lat #hep-ph #hep-th
paper · pdf · doi:10.1103/physrevd.89.014010
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 89(1) (American Physical Society) · 5 pages, 7 .pdf figures
arxiv created 2013/10/15 · openalex publication_date 2014/01/09 · arxiv updated 2014/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider the problem of ``measuring'' the K"all'en-Lehmann spectral density of a particle (be it elementary or bound state) propagator by means of 4D lattice data. As the latter are obtained from operations at (Euclidean momentum squared) p2\ensuremath≥0, we are facing the generically ill-posed problem of converting a limited data set over the positive real axis to an integral representation, extending over the whole complex p2 plane. We employ a linear regularization strategy, commonly known as the Tikhonov method with the Morozov discrepancy principle, with suitable adaptations to realistic data, e.g. with an unknown threshold. An important virtue over the (standard) maximum entropy method is the possibility to also probe unphysical spectral densities, for example, of a confined gluon. We apply our proposal here to ``physical'' mock spectral data as a litmus test and then to the lattice SU(3) Landau gauge gluon at zero temperature.