Stochastic reconstructions of spectral functions: Application to lattice QCD

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 o...

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Bibliographic Details
Published in:Physical review. D 2018-05, Vol.97 (9), Article 094503
Main Authors: Ding, H.-T., Kaczmarek, O., Mukherjee, Swagato, Ohno, H., Shu, H.-T.
Format: Article
Language:English
Subjects:
Bayesian analysis
Clover
Correlation analysis
Fermions
Lattices
Mathematical analysis
Maximum entropy method
NUCLEAR PHYSICS AND RADIATION PHYSICS
Quantum chromodynamics
Regression analysis
Statistical inference
Transition temperature
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Summary: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 1.5Tc, Tc 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.
ISSN:2470-0010
2470-0029
DOI:10.1103/PhysRevD.97.094503