Status of R-parity conserving supersymmetry after the LHC Run 2 and other experiments

Supersymmetry, if it describes our universe, may provide an explanation for some of the most vexing puzzles in particle physics and cosmology. Despite arguments that support supersymmetry (SUSY) as a general hypothesis, direct evidence for SUSY is yet to be observed. Decades of searches for SUSY at the energy frontier, including 12 years of searches performed at the LHC, have failed to turn up a positive signal. However, it is an open question to what extent the general hypothesis has been constrained by all of the data collected so far, and it is an open possibility that SUSY has manifested in these analyses but was not identified, either because its signal strength is small or because its signatures are challenging or spread out rather than confined to a single analysis strategy. This thesis presents a study of the viability of the Minimal Supersymmetric Standard Model (MSSM) given a wide variety of experimental results. It makes use of the phenomenological MSSM (pMSSM) as a proxy model for the MSSM. The pMSSM is sampled by means of Markov chain Monte Carlo (McMC), steered by measurements of the Higgs mass, constraints from LEP on the mass of the charginos and on the branching ratio BR(Z → invisible), and a suite of measurements from the flavor sector. The resulting pMSSM scan is a discrete representation of the posterior density with respect to the measurements included in the McMC, consisting of 27 million pMSSM models. The ensemble of model scenarios procured from this McMC are confronted with Run 2 data from ATLAS and CMS searches at the CERN LHC, as well as with data from dark matter measurements and searches interpreted within the standard model of cosmology, and with considerations from naturalness and fine tuning. The LHC impact is evaluated on the basis of five direct SUSY searches, covering the 0-lepton P${}_T^{miss}$ +jets final state, the di-lepton final state, the soft-di-lepton final state, the multi-lepton final state, and the final state featuring disappearing tracks. Within the considered parameter space, approximately 47% of the pMSSM scan is excluded by the LHC, with the largest impact coming from the P${}_T^{miss}$ +jets search, followed by the search for disappearing tracks. The LHC is directly sensitive to the mass of the lightest supersymmetric particle (LSP) of m(${\tilde{\chi }}_1^0$) $\simeq$ 700 GeV, with m(${\tilde{\chi }}_1^0$) $\leqq$ 500 GeV significantly disfavored by the data, particularly for wino-like LSPs. All LSP masses remain viable in some parts of the pMSSM. A small excess in the data seen by the multi-lepton search is well fit by the pMSSM at ∆m(${\tilde{\chi }}_1^{\pm }$, ${\tilde{\chi }}_1^0$) $\simeq$ 100 GeV. Left-chiral selectrons and smuons with masses below 600 GeV are severely disfavored, with masses below 400 GeV almost entirely excluded. Sensitivity to right-chiral sleptons is significantly smaller, with surviving models featuring slepton masses as small as 100 GeV. Mass-compressed slepton-LSP scenarios remain particularly viable even for very small slepton masses of order 100 GeV. Colored superpartners with masses below 1 TeV are strongly disfavored, but not completely excluded. Significant suppression is evident up to m($\tilde{g}$) $\simeq$ 2 TeV, and to a lesser degree for m(${\tilde{u}}_R$, ${\tilde{c}}_R$), m(${\tilde{u}}_L$. ${\tilde{c}}_L$), and m(${\tilde{d}}_L$, ${\tilde{s}}_L$) $\simeq$ 2 TeV. A significant population of models with light stop survive in the compressed model space, namely where the LSP mass is only a few hundred GeV or less below the stop mass. Direct detection constraints are found to exclude approximately 15% of both the LHC prior and posterior densities. They are most constraining on models with a higgsino-like LSP or a wino-like LSP, especially mixed wino-higgsino scenarios. A fraction of models are excluded in the whole range of scanned LSP masses, including large LSP masses that are currently out of reach for the LHC. Constraints from indirect dark matter detection exclude a very small fraction of the LHC prior, and no part of the LHC posterior density. Higher-order corrections not included in this study may lead to a significant strengthening of the constraint. Constraints in the form of upper bounds on the dark matter relic density Ωh${}^2$ exclude most bino-like LSP, most higgsino-like LSP with m(${\tilde{\chi }}_1^0$) $\gtrsim$ 1.2 TeV, and wino-like LSP with m(${\tilde{\chi }}_1^0$) $\gtrsim$ 1.8 TeV, complementing the LHC well. Lower bounds on Ωh${}^2$ progressively exclude models with larger m(${\tilde{\chi }}_1^0$) for wino-like and higgsino-like LSP, with Ωh${}^2$> 0.1 Ωh${}_{Planck}^2$ excluding m(${\tilde{\chi }}_1^0$) $\lesssim$ 600 GeV, and m(${\tilde{\chi }}_1^0$) $\lesssim$ 300 GeV for wino-like and higgsino-like LSP, respectively. These mass ranges are within the reach of LHC sensitivity. For Ωh${}^2$ ∈ [0.9, 1.1] Ωh${}_{Planck}^2$, surviving models include higgsino-like LSPs at m(${\tilde{\chi }}_1^0$) $\simeq$ 1.1 TeV, wino-like LSPs at m(${\tilde{\chi }}_1^0$) $\simeq$ 1.7 TeV, and wino- higgsino mixed LSPs in between. Some models with mixed-bino LSP, or pure bino LSP inside the A-funnel region, survive. Constraints from direct detection complement these constraints, particularly for models with wino-higgsino mixed LSPs. Low fine tuning is largely incompatible with LHC data if additionally requiring that the LSP account for all dark matter. However, so-called natural models with low fine tuning remain viable in regions of the pMSSM with lower Ωh${}^2$ saturation, and a small sliver of models with m(${\tilde{\chi }}_1^0$) $\simeq$ 350 GeV and ∆m(${\tilde{\chi }}_1^{\pm }$) $\simeq$ 1 GeV survives all constraints. Interpretations and limits within simplified model limits are compared with conclusions drawn from the MSSM study. It is found that, with a small number of exceptions, the intuition garnered rom simplified models is in stark contrast with the full model analysis, and are thus potentially misleading. The only subsets of the pMSSM for which conclusions coincide with simplified model limits are subsets with a bino-like LSP for which colored superpartner cross sections dominate over electroweak cross sections.