Phenomenology of dark matter at present and future experiments

In this thesis we present a study of two different dark matter candidates. We focus on the neutralino in split supersymmetric models and in models of Dirac gauginos, and on the QCD axion. In the first part of the thesis we discuss supersymmetric searches at future hadron colliders and dark matter direct detection experiments. We obtain mass reach for several simplified models in split supersymmetry with neutralino or gravitino lightest supersymmetric particle at 14, 33 and 100 TeV collider. In particular, a supersymmetric simplified model of anomaly mediation with long lived Winos has crucial importance in the hunt for dark matter since a Wino lightest supersymmetric particle is expected to thermally saturate the relic density for $m_{\tilde{W}}\sim 3$ TeV. In addition, we consider the discovery reach of a future 100 TeV collider for strongly coupled states in supersymmetric theories with Majorana gluinos, and extend this to the cases with Dirac gluinos. Furthermore, we discuss the current bounds and future reach from dark matter direct detection experiments for split SUSY models with universal gaugino masses and models of anomaly mediation. We then study the interplay between the collider and dark matter searches for the models considered. Also, we consider the dark matter candidate in Dirac gaugino models and the relation between collider searches and dark matter direct detection experiments. In the second part of this thesis, we study the properties of the QCD axion at zero and finite temperature. The computation of the relic abundance for QCD axion from the misalignment mechanism dramatically depends on the behaviour of the axion potential at finite temperature. Consequently, we compute the axion potential, and therefore its mass, at temperatures below the crossover ($T_c\sim170$ MeV) exploiting chiral Lagrangians. Around the critical temperature $T_c$ there is no known reliable perturbative expansion under control and non-perturbative methods, such as lattice QCD, are required. At higher temperatures, when QCD becomes perturbative, the dilute instanton gas approximation is available, which is expected to be reliable at temperatures large enough. We point out however that the bad convergence of the perturbative QCD expansion at finite temperatures makes the instanton result unreliable for temperatures below $10^{6}$ GeV. Therefore, we study the impact of the uncertainty in the computation of the axion relic abundance, providing updated plots for the allowed axion parameter space. Finally, motivated by the fact that zero temperature properties of the QCD axion are fundamental in case of axion discovery in order to infer its possible UV completion, we perform a NLO computation using chiral Lagrangians. We extract zero temperature axion properties, such as the mass, the potential, the self-coupling, the coupling to photon and the tension of domain walls, at the percent level. Moreover, we show a new strategy to extract couplings to nucleons directly from first principle QCD at the 10\% level. Such result can be improved as more lattice QCD simulations become available.