A Problem in Particle Physics and Its Bayesian Analysis

TL;DR

This paper introduces a Bayesian method with MCMC for estimating infinite parameters in Lattice QCD problems, reducing complexity and enabling new insights into particle physics and related fields.

Contribution

It presents a novel Bayesian approach with a telescoping series reduction and MCMC implementation for complex parameter estimation in Lattice QCD problems.

Findings

Successfully validated on simulated data and physics code data

Enables answering previously intractable questions in particle physics

Applicable to other fields with similar mathematical structures

Abstract

There is a class of statistical problems that arises in several contexts, the Lattice QCD problem of particle physics being one that has attracted the most attention. In essence, the problem boils down to the estimation of an infinite number of parameters from a finite number of equations, each equation being an infinite sum of exponential functions. By introducing a latent parameter into the QCD system, we are able to identify a pattern which tantamounts to reducing the system to a telescopic series. A statistical model is then endowed on the series, and inference about the unknown parameters done via a Bayesian approach. A computationally intensive Markov Chain Monte Carlo (MCMC) algorithm is invoked to implement the approach. The algorithm shares some parallels with that used in the particle Kalman filter. The approach is validated against simulated as well as data generated by a physics code pertaining to the quark masses of protons. The value of our approach is that we are now able to answer questions that could not be readily answered using some standard approaches in particle physics. The structure of the Lattice QCD equations is not unique to physics. Such architectures also appear in mathematical biology, nuclear magnetic imaging, network analysis, ultracentrifuge, and a host of other relaxation and time decay phenomena. Thus, the methodology of this paper should have an appeal that transcends the Lattice QCD scenario which motivated us.