Bayesian approach to spectral function reconstruction for Euclidean quantum field theories

Area of Science:

• Theoretical Physics
• Computational Physics
• Bayesian Inference

Background:

• Spectral functions are crucial for understanding particle physics.
• Extracting spectral functions from Euclidean time correlators is challenging.
• Existing methods like the Maximum Entropy Method (MEM) have limitations.

Purpose of the Study:

• To introduce a novel Bayesian approach for spectral function inference.
• To overcome limitations of the Maximum Entropy Method (MEM).
• To accurately determine the heavy quark potential from lattice QCD data.

Main Methods:

• Postulating new axioms for prior probability.
• Explicitly integrating out hyperparameters, avoiding Gaussian approximations.
• Applying the method to nonperturbative extraction of the heavy quark potential.

Main Results:

• Developed an improved spectral function inference method.
• Established data requirements for successful heavy quark potential extraction.
• Provided an improved potential estimation for quenched lattice QCD.

Conclusions:

• The novel Bayesian method offers an improvement over MEM for spectral function inference.
• The method is effective for nonperturbative calculations in lattice QCD.
• Accurate potential estimation is achievable with sufficient data quality and quantity.