Aspects of Particle Physics Beyond the Standard Model

This dissertation describes a few aspects of particles beyond the Standard Model, with a focus on the remaining questions after the discovery of a Standard Model-like Higgs boson. In specific, three topics are discussed in sequence: neutrino mass and baryon asymmetry, naturalness problem of Higgs mass, and placing constraints on theoretical models from precision measurements.\\\\First, the consequence of the neutrino mass anarchy on cosmology is studied. Attentions are paid in particular to the total mass of neutrinos and baryon asymmetry through leptogenesis. With the assumption of independence among mass matrix entries in addition to the basis independence, Gaussian measure is the only choice. On top of Gaussian measure, a simple approximate $U(1)$ flavor symmetry makes leptogenesis highly successful. Correlations between the baryon asymmetry and the light-neutrino quantities are investigated. Also discussed are possible implications of recently suggested large total mass of neutrinos by the SDSS/BOSS data.\\\\Second, the Higgs mass implies fine-tuning for minimal theories of weak-scale supersymmetry (SUSY). Non-decoupling effects can boost the Higgs mass when new states interact with the Higgs, but new sources of SUSY breaking that accompany such extensions threaten naturalness. I will show that two singlets with a Dirac mass can increase the Higgs mass while maintaining naturalness in the presence of large SUSY breaking in the singlet sector. The modified Higgs phenomenology of this scenario, termed ``Dirac NMSSM'', is also studied.\\\\Finally, the sensitivities of future precision measurements in probing physics beyond the Standard Model are studied. A practical three-step procedure is presented for using the Standard Model effective field theory (SM EFT) to connect ultraviolet (UV) models of new physics with weak scale precision observables. With this procedure, one can interpret precision measurements as constraints on the UV model concerned. A detailed explanation is given for calculating the effective action up to one-loop order in a manifestly gauge covariant fashion. This covariant derivative expansion method dramatically simplifies the process of matching a UV model with the SM EFT, and also makes available a universal formalism that is easy to use for a variety of UV models. A few general aspects of RG running effects and choosing operator bases are discussed. Mapping results are provided between the bosonic sector of the SM EFT and a complete set of precision electroweak and Higgs observables to which present and near future experiments are sensitive. Many results and tools which should prove useful to those wishing to use the SM EFT are detailed in several appendices.