An, HaipengIn a class of other beyond-standard-model theories, CP-odd observables, such as the neutron electric dipole moment, receive significant contributions from flavorneutral P-odd and CP-odd four-quark operators. However, considerable uncertainties exist in the hadronic matrix elements of these operators strongly affecting the experimental constraints on CP-violating parameters in the theories. Here we study their hadronic matrix elements in combined chiral perturbation theory and nucleon models. We first classify the operators in chiral representations and present the leading-order QCD evolutions. We then match the four-quark operators to the corresponding ones in chiral hadronic theory, finding symmetry relations among the matrix elements. Although this makes lattice QCD calculations feasible, we choose to estimate the non-perturbative matching coefficients in simple quark models. We finally compare the results for the neutron electric dipole moment and P-odd and CP-odd pion-nucleon couplings with the previous studies using naive factorization and QCD sum rules. Our study shall provide valuable insights on the present hadronic physics uncertainties in these observables. Using an effective theory approach, the neutron electric dipole moment in the minimal left-right symmetric model with both explicit and spontaneous CP violations is recalculated systematically. Using the state-of-the-art hadronic matrix elements, nEDM as a function of right-handed W-boson mass and CP-violating parameters is obtained. The most stringent constraint yet on the left-right symmetric scale in the minimal version of left-right symmetric model is obtained to be M_WR > (10 ± 3) TeV. Light WIMP (weakly interacting massive particle)-like signals were reported by dark matter direct detection experiments. WIMP candidates in this energy range can be constrained by various collider experiments. We show that colliders can impose strong constraints on models of low mass dark matter, in particular in the case that the direct detection interaction depends on the momentum of dark matter. We also find in the case of low mass dark matter, there are tensions between the observed relic abundance and collider constraints. Putting the constraints from collider physics, relic abundance and direct detection experiments, a large part of parameter space in different models can be ruled out.DissertationPhysicsCollider PhysicsCP violationDark MatterNeutron Electric Dipole MomentParity violationSpontaneous Symmetry Breaking