Applications of Lattice Qcd to Hadronic Cp Violation

Experimental tests of the Standard Model are reaching a precision in which they are probing beyond Standard Model parameter spaces. Increasingly precise experimental tests of the Standard Model (SM) require a concurrent theoretical push to provide ever more precise predictions to interpret experimental results. For example, future direct dark matter detection experiments, searches for Majorana neutrinos, and neutron electric dipole moment searches, all require a fundamental understanding of nuclear physics in the low-energy regime. Nuclear physics emerges from non-perturbative dynamics of the fundamental theory of the strong interaction, QCD, at low energies. Lattice QCD is currently our only systematically controllable solution to QCD in the low-energy regime, and coupled with effective field theory, can be used to provide precise physical predictions from QCD. in this thesis, we focused on lattice calculations which have implications for precision tests of the Standard Model. After a brief introduction to lattice QCD and EFT, we present a lattice computation of the strong isospin breaking contribution to the neutron-proton and cascade mass splitting. We observe non-analytic behavior in the neutron-proton and cascade mass splittings, which is uniquely indicative of chiral dynamics. The neutron-proton mass splitting is related via chiral symmetry to the CP-violating pion-nucleon interactions induced by the QCD θ-term, and we provide an estimate of the induced pion-nucleon coupling arising from the θ-term. in the next section, we present the first calculation of the renormalization factors for bilinear operators, and the four quark operator basis induced by new physics, which were computed on the Möbius Domain Wall fermion on gradient flowed HISQ ensembles. We use momentum sources and the RI-SMOM method, using two projection schemes, and use the step scaling procedure to calculate the running of our operators up to a scale of 3 GeV. in chapter 5, we presented progress in the first lattice QCD calculation of the CP-violating pion-nucleon couplings induced by the quark chromo-electric dipole operators. These long-range pion-nucleon interactions lead to an enhanced nuclear Schiff moment in diamagnetic atoms, and thus play an important role in the interpretation of nuclear EDM experiments. in this work, we use chiral perturbation theory, as well as an unconventional method of calculating nucleon matrix elements on the lattice, to calculate the bare couplings in terms of spectroscopic shifts of the nucleon mass induced by the CP-conserving quark chromo-magnetic dipole operators. We then detail the renormalization procedure to be used to renormalize the chromo-magnetic operator, including subtraction of the power divergent mixing with the scalar operator