I describe the first continuous space nuclear path integral quantum Monte Carlo method, and calculate the ground state properties of light nuclei including Deuteron, Triton, Helium-3 and Helium-4, using both local chiral interaction up to next-to-next-to-leading-order and the Argonne $v_6'$ interaction. Compared with diffusion based quantum Monte Carlo methods such as Green's function Monte Carlo and auxiliary field diffusion Monte Carlo, path integral quantum Monte Carlo has the advantage that it can directly calculate the expectation value of operators without tradeoff, whether they commute with the Hamiltonian or not. For operators that commute with the Hamiltonian, e.g., the Hamiltonian itself, the path integral quantum Monte Carlo light-nuclei results agree with Green's function Monte Carlo and auxiliary field diffusion Monte Carlo results. For other operator expectations which are important to understand nuclear measurements but do not commute with the Hamiltonian and therefore cannot be accurately calculated by diffusion based quantum Monte Carlo methods without tradeoff, the path integral quantum Monte Carlo method gives reliable results. I show root-mean-square radii, one-particle number density distributions, and Euclidean response functions for single-nucleon couplings. I also systematically describe all the sampling algorithms used in this work, the strategies to make the computation efficient, the error estimations, and the details of the implementation of the code to perform calculations. This work can serve as a benchmark test for future calculations of larger nuclei or finite temperature nuclear matter using path integral quantum Monte Carlo.

This work presents analysis and results for the NPDGamma experiment, measuring

the spin-correlated photon directional asymmetry in the $\vec{n}p\rightarrow

d\gamma$ radiative capture of polarized, cold neutrons on a parahydrogen

target. The parity-violating (PV) component of this asymmetry

$A_{\gamma,PV}$ is unambiguously related to the $\Delta I = 1$ component of

the hadronic weak interaction due to pion exchange. Measurements in the second

phase of NPDGamma were taken at the Oak Ridge National Laboratory (ORNL)

Spallation Neutron Source (SNS) from late 2012 to early 2014, and then again in

the first half of 2016 for an unprecedented level of statistics in order to

obtain a measurement that is precise with respect to theoretical predictions of

$A_{\gamma,PV}=O(10^{-8})$. Theoretical and experimental background,

description of the experimental apparatus, analysis methods, and results for

the high-statistics measurements are given.

A search for Klong to pi0 nu nubar was performed on the initial Physics data taken by the KOTO collaboration by the 30-GeV proton synchrotron at JPARC, located in Tokai, Japan. The detector used in the experiment is an upgraded version of the E391 detector, KOTO's predecessor experiment performed at KEK. The analysis was performed on 2.49 E+11 ± (0.91%)stat ± (2.50%)syst kaon decays. The analysis uses Klong to 3pi0, Klong to 2pi0, and Klong to 2 gamma; for normalization and Monte Carlo validation. Based on my independent analysis, the single event sensitivity was determined to be 1.31 E-8 ± (1.22%)stat ± (7.12%)syst, comparable with the E391 result. An upper limit of 5.12 E-8 was measured for the Klong to pi0 nu nubar branching ratio at a 90% confidence level.