Exploring Supersymmetry and Naturalness in Light of New Experimental Data

This thesis investigates extensions of the Standard Model (SM) that are based on either supersymmetry or the Twin Higgs model. New experimental data, primarily collected at the Large Hadron Collider (LHC), play an important role in these investigations. Specifically, we examine the following five cases.We first consider Mini-Split models of supersymmetry. These types of models can be generated by both anomaly and gauge mediation and we examine both cases. LHC searches are used to constrain the relevant parameter spaces, and future prospects at LHC 14 and a 100 TeV proton proton collider are investigated.Next, we study a scenario where Higgsino neutralinos and charginos are pair produced at the LHC and promptly decay due to the baryonic R-parity violating superpotential operator λ′′UcDcDc. More precisely, we examine this phenomenology in the case of a single non-zero λ′′3jkcoupling. By recasting an experimental search, we derive novel constraints on this scenario.We then introduce an R-symmetric model of supersymmetry where the R-symmetry can be identified with baryon number. This allows the operator λ′′UcDcDcin the superpotential without breaking baryon number. However, the R-symmetry will be broken by at least anomaly mediation and this reintroduces baryon number violation. Under these conditions, we investigate baryon number violating processes and flavour physics, as well as the collider phenomenology of both stops and the first two generations of squarks assuming they decay due to a single non-zero λ′′3jkcoupling.There have been several experimental anomalies related to the quark level transition b→sℓℓ. We investigate these anomalies with the R-parity violating superpotential operator λ′LQDc. By examining diagrams featuring winos we find new parameter space capable of explaining these anomalies while at the same time avoiding other experimental bounds.Finally, a variation of the Twin Higgs model is presented. These models stabilize the electroweak scale with particles uncharged under the SM colour group. This is accomplished by introducing a mirror sector to the SM and requiring an approximate Z2symmetry between the two sectors. It is shown that it is beneficial to break the Z2symmetry spontaneously rather than explicitly.