Stochastic reconstructions of spectral functions: Application to lattice QCD

Abstract

We present a detailed study of the applications of two stochastic approaches, stochastic optimization method (SOM) and stochastic analytical inference (SAI), to extract spectral functions from Euclidean correlation functions. SOM has the advantage that it does not require prior information. On the other hand, SAI is a more generalized method based on Bayesian inference. Under mean field approximation SAI reduces to the often-used maximum entropy method (MEM), and for a specific choice of the prior SAI becomes equivalent to SOM. To test the applicability of these two stochastic methods to lattice QCD, firstly, we apply these methods to various reasonably chosen model correlation functions, and present detailed comparisons of the reconstructed spectral functions obtained from SOM, SAI and MEM. Next, we present similar studies for charmonia correlation functions obtained from lattice QCD computations using clover-improved Wilson fermions on large, fine, isotropic lattices at $0.75$ and $1.5T_c$, $T_c$ being the deconfinement transition temperature of a pure gluon plasma. We find that SAI and SOM give consistent results to MEM at these two temperatures.

24 pages, 18 figures

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• Quarkonium in-medium properties from realistic lattice NRQCD
• Thermal properties of light mesons from holography
• ACFlow: An open source toolkit for analytical continuation of quantum Monte Carlo data
• Bayesian inference of real-time dynamics from lattice QCD
• Spectral and transport properties from lattice QCD
• Bryan's Maximum Entropy Method -- diagnosis of a flawed argument and its remedy
• Charmonium and bottomonium spectral functions in the vector channel
• Machine learning spectral functions in lattice QCD
• Charm and beauty in the deconfined plasma from quenched lattice QCD
• Reconstructing lattice QCD spectral functions with stochastic pole expansion and Nevanlinna analytic continuation
• Open-charm Euclidean correlators within heavy-meson EFT interactions
• Insight into thermal modifications of quarkonia from a comparison of continuum-extrapolated lattice results to perturbative QCD${}^{†}$
• Källén-Lehmann Spectral Representation of the Scalar SU(2) Glueball
• Flavor dependence of the thermal dissociations of vector and axial-vector mesons
• In-medium bottomonium properties from lattice NRQCD calculations with extended meson operators
• Study of quarkonium in QGP from unquenched lattice QCD
• Shear and bulk viscosities of the gluon plasma across the transition temperature from lattice QCD
• Sparse modeling study of extracting charmonium spectral functions from lattice QCD at finite temperature