Impact of LHC results on dark matter searches
Dark matter (DM) is required to form the observed large-scale structures of the universe and is one of the most serious challenge for the particle physics SM. The five requirements for a particle to be a dark matter candidate x can be spelled out as   
- (4) not baryonic;
- (5) giving at most the right thermal relic density as measured by CMB experiments, Qh = 0.120 ± 0.003, where h is the Hubble constant.
The second condition excludes all SM particles apart from the neutrinos and the fermions e, u, and d. The third condition rejects the neutrinos and the fourth the remaining fermions. So SM does not provide any viable DM candidate, while “natural” BSM theories do, as shown in Fig. 8.21(a). Assuming that dark matter is explained by only one particle with mass mDM and relevant gauge coupling constant gDM, then Qx ж mDM/sDM. With this in mind, three categories can be formed: (i) the WIMP sector where mDM « Ле-w and gDM = gEW = 2(%/2GF)1/2mW = 2mW/v « 0.65,
(ii) the hidden sector, gathering SuperWIMP and axions, where mDM < ЛEw and gDM ^ gEW, and (iii) the undetectable sector with fuzzy dark matter, where the interaction is purely gravitational. Among all the candidates, WIMP particles are still the most popular, since they are motivated by the resolution of the hierarchy problem, a completely uncorrelated reason (the so-called “WIMP miracle”).
Since a lot of information is already available in chapter 9 by Silk in the present volume and in the excellent reviews by Bertone et al. (2005); Feng (2010), I shall only discuss the LHC input to the DM search. By analogy with the weak interaction described by Fermi theory, DM could be produced at LHC via qq, qg, gg ^ X ^ xX and could be observed in a monojet analysis (the jet is an initial-state radiation) (see Fig. 8.18(a)). The mediator X of mass M could be scalar, vector, or axial vector, and interact with quarks and WIMPs with coupling factors gq,g and gx. The contact interaction scale is then defined as Л = M/x/gq,ggx. This approach allows the conversion into DM-nucleon cross-section limits for a given x mass, directly comparable with dedicated DM searches (Bai et al., 2010; Goodman et al., 2011). For a vectorlike mediator, Fig. 8.21(b) shows that the LHC could exclude low-mass WIMPs, for which direct searches have no sensitivity because of the undetectable energy recoil of the nucleon. For an axial-vector mediator or DM-gluon coupling with scalar or vector mediators, LHC results exceed all present limits (CMS Coll., 2012c).
The leading WIMP candidate is (still) X0, but it cannot be probed by monojet analysis because of the too low cross-section, а = O(1) fb for m,^o = 100 GeV. In direct SUSY searches, m,^o is generally not directly accessible, but many models predicting mxo ~ 500-600 GeV are currently excluded (Section 8.3.1). It is therefore interesting to scan a subset of MSSM models, satisfying the present experimental LHC constraints from direct SUSY searches and Higgs mass, and see what flavor and mass range of X1 survives (Cahill-Rowley et al., 2013). Constraints from direct and indirect DM non- LHC searches can also be included, as mentioned above, and the complementarity of the different approaches appears clearly in Fig. 8.22(a). The surviving models are shown in Fig. 8.22(b). Interestingly, a huge number of models are still alive today and the only models that saturate the thermal relic density have a bino-like LSP. Note also that almost all surviving models will be reachable by experiments in the near future. To conclude, it is worth mentioning that the ZH(^ xx) searches, not included in this
Fig. 8.21 (a) DM candidate particles shown in the plane of x-nucleon cross-section (pb) versus X mass (Park, 2007). (b) Exclusion curves obtained in the same plane by LHC and direct DM search experiments, assuming a vector-like mediator for the x-nucleon interaction.
Fig. 8.22 (a) MSSM models and experimental constraints in the plane of x-nucleon crosssection versus m^o. (b) LSP composition of surviving pMSSM models in the plane of thermal relic density versus m^o. For the figure in color, please see the online version of the lectures.
study, are also excellent probes for mDM < mH/2, and cover ax- Nucl ~10-7-10-11 pb, depending on the mediator properties (Djouadi et al., 2013).