Search for charge nonconservation and Pauli exclusion principle violation with the Majorana Demonstrator

Charge conservation and the Pauli exclusion principle (PEP) result from fundamental symmetries in the Standard Model, and are typically taken as axiomatic. High-precision tests for small violations of these symmetries could point to new physics. In this work we consider three models for violation of these processes which would produce detectable ionization in the high-purity germanium detectors of the Majorana Demonstrator. Using a 37.5 kg-yr exposure, we report a new lower limit on the electron mean lifetime of $\tau_e>3.2 \times 10^{25}$ yr (90\% CL), the best result for this decay channel ($e \rightarrow \nu_e \overline{\nu_e} \nu_e$ or more generally $e \rightarrow \mathrm{invisibles}$) in more than two decades. We also present searches for two types of violation of the PEP, setting new limits on the probability of two electrons forming a symmetric quantum state. Using our $^{228}$Th calibration data set, which introduces electrons new to the system through electron-positron pair production, we obtain a world-leading model-independent limit for a terrestrial experiment of $\beta^2/2<1.0 \times 10^{-3}$ (99.7\% CL). Our 37.5 kg-yr exposure is also used to search for a process where an electron in an atomic system spontaneously violates the PEP, resulting in a model-dependent upper limit of $\beta^2/2<1.0 \times 10^{-48}$ (90\% CL).