The Energy Spectrum of the Pion from Lattice QCD

TL;DR

This paper uses lattice QCD simulations to compute the pion's energy spectrum across various momenta, validating the computational approach by comparing the dispersion relation with theoretical predictions.

Contribution

It introduces a systematic method for extracting pion energy eigenvalues from lattice QCD data and compares the resulting dispersion relation with theoretical models.

Findings

Good agreement with theoretical dispersion relations

Reliable energy eigenvalues obtained across multiple momenta

Insights into the validity range of lattice QCD simulations

Abstract

In this report, computational techniques are employed to extract the energy eigenvalues of the pion from two-point correlation function data that has been simulated using the lattice formulation of Quantum Chromodynamics (QCD) across various momentum values for the particle. The analysis focuses on systematically obtaining these eigenvalues to understand better the behavior of the pion under different kinematic conditions. Once extracted, these energy eigenvalues obtained through plateau fitting of the Energy vs Time graph, are utilized to plot the dispersion relation of the pion. This resulting dispersion relation is then compared with theoretical predictions to assess the accuracy and validity of the computational approach. The comparison provides insights into how well the lattice QCD simulations align with established theoretical expectations, and what range of kinematic variables are reliable.