The Energy Spectrum of the Pion from Lattice QCD

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.