## Honors Scholar Theses

#### Date of Completion

Fall 12-15-2022

Luchang Jin, Peter Schweitzer

Physics

#### Disciplines

Elementary Particles and Fields and String Theory | Quantum Physics

#### Abstract

The linear sigma model is a low energy effective model of Quantum Chromodynamics. This model mimics the breaking of chiral symmetry both spontaneously and explicitly through the quark condensate and pion mass matrix respectively. Fourier acceleration is a method that can be implemented in the Hybrid Monte-Carlo algorithm which decreases autocorrelations due to critical slowing down through tuning the mass parameters in the HMC algorithm. Fourier acceleration is applied to the linear sigma model with a novel mass estimation procedure, by assuming the modes behave approximately like simple harmonic oscillators. The masses are chosen by sampling the expectation values of $\langle\dot{\Pi}\rangle$ and $\langle | \phi_i(p) - \nu\delta_{i,0}\delta_{p,0}|\rangle$ (auxiliary momentum, and vacuum expectation of the fields) generated by the HMC algorithm. Additional findings in the linear sigma model during exploration of the symmetry breaking point are also discussed.

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