Testing Lorentz and CPT Symmetries with Neutrons*

Lorentz and CPT symmetries are foundational symmetries of our current best theories describing nature. The two symmetries state that the laws of physics are invariant under Lorentz transformation or combined transformations of charge conjugation (C), parity inversion (P), and time reversal (T). However, tiny violations of these symmetries could occur in a more fundamental theory. This project investigated possible signals for Lorentz and CPT violation arising from experiments searching for a nonzero electric dipole moment for neutrons (nEDM). We started with the free Dirac equation and obtained the free-particle solutions. We then extracted operators for Lorentz and CPT violation from the Standard-Model Extension framework and applied perturbation theory to derive the energy modifications for spin-up and spin-down neutrons due to Lorentz and CPT violation. The contributions to the spin precession frequency of a neutron were then obtained by taking the energy differences between different spin states. To transform the results from the laboratory frame to the Sun-centered frame, we applied a general rotation matrix that involves the Earth's sidereal frequency and the colatitude of the laboratory. We found that any Lorentz- and CPT-violating signals would oscillate with the Earth's sidereal frequency. Finally, we used existing bounds of nEDMs reported by experiments and constrained the relevant coefficients for Lorentz and CPT violation.