Advances in High Energy Physics

Volume 2018, Article ID 5012043, 13 pages

https://doi.org/10.1155/2018/5012043

## Simplified Dark Matter Models

Deutsches Elektronen-Synchrotron DESY, Notkestraße 85, 22607 Hamburg, Germany

Correspondence should be addressed to Enrico Morgante; ed.ysed@etnagrom.ocirne

Received 30 March 2018; Accepted 16 May 2018; Published 17 December 2018

Academic Editor: Farinaldo Queiroz

Copyright © 2018 Enrico Morgante. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP^{3}.

#### Abstract

I review the construction of simplified models for dark matter searches. After discussing the philosophy and some simple examples, I turn the attention to the aspect of the theoretical consistency and to the implications of the necessary extensions of these models.

#### 1. Introduction

Producing and studying the properties of the dark matter (DM) particles at the LHC are an extremely exciting possibility that would open the door to a new understanding of the interplay between astrophysics, cosmology, and particle physics. Essentially all the naturalness-inspired scenarios can accommodate the presence of a good dark matter candidate: a neutral and very long-lived particle that was copiously produced in the early universe and then lost thermal contact with the SM (if it ever occurred) leaving a relic density of cold particles. The fact that such a stable weakly interacting massive particle with a mass around the weak scale has automatically a relic abundance close to the measured one is a remarkable property which is often dubbed* WIMP miracle*. The LHC is a perfectly suited machine to look for this kind of particles, and current bounds from ATLAS and CMS complement those from direct and indirect searches.

A key task in these studies is that of choosing a theoretical framework to compare with data and compare the results of different experiments. Given the plethora of particle physics models beyond the SM providing a WIMP candidate, it is highly desirable to study the signatures of this DM candidate in a model-independent way. In the early stages of the LHC, this was achieved by means of the effective field theory approach (EFT). In this framework, the Standard Model (SM) is complemented by a set of non-renormalizable operators that parametrize the interaction of the DM particle with SM fields in terms of one effective scale and of the DM mass [1]. The EFT approach has proven to be very useful in the analysis of LHC Run I data [1–15], because of the great advantage of giving bounds that are as model-independent as possible: for a given choice of the spin of the DM particle, the number of operators that can couple it to the SM and may give interesting signatures at the LHC is limited, for a fixed mass dimension. Since direct and indirect detection of WIMPs, as well as WIMP production at the LHC, all require an interaction of the WIMPs with the SM particles, and such an interaction may be generated by the same operator, the EFT approach has the additional advantage of facilitating the analysis of the correlations between the various kinds of experiments.

The important drawback of the EFT description is its intrinsic energy limitation. At energies larger than some cutoff , the contribution of higher dimension operators to the computation of scattering amplitudes becomes comparable to the lower ones, signalling the breakdown of perturbativity. More in particular, if the EFT is seen as the low energy limit of a theory with a mediator of mass which is above the energy scale probed by the experiment, the cutoff is obtained as , where is some combination of the coupling constants, and the theory is valid up to a momentum exchange , where we have assumed . In direct and indirect detection this constraint is typically satisfied thanks to the low velocity of the incoming particle. On the other hand, the momentum exchanged in the partonic interactions at the LHC is of order few TeV, larger than the values of that can be excluded within the EFT framework, making the naïve EFT bounds unreliable except for values of the couplings close to the perturbative bound [16–18]. In principle this does not mean that the EFT approach is not useful. Recasting procedures can be adopted to rederive bounds considering only a fraction of the events in the simulation that correspond to those which fulfil the requirement on the momentum [17, 19]. Clearly, the new bounds would be much weaker, but their simplicity still suggests that they should not be disregarded.

Partly in response to the problems of EFTs, and partly inspired by their rich phenomenological implications, in more recent years the LHC community has turned its attention to the tool-kit of simplified models. Such models are characterized by the most important state mediating the interaction of the DM particle with the SM, as well as the DM particle itself (see, for example, [14, 20–24] for early proposals). Including the effect of the mediator's propagator allows avoiding the energy limitation of the EFT, and simplified models are able to describe correctly the full kinematics of DM production at the LHC, at the price of a moderately increased number of parameters. As we are going to discuss below, the introduction of simplified models opens a new set of possibilities compared to the simpler EFT approach, while opening at the same time a set of new questions.

This paper is structured as follows. In Section 2, we are first going to describe the construction of DM simplified models from a bottom-up approach, providing some examples in Section 3. Then, in Section 4, we will point out the theoretical issues of such a construction, introducing a second generation of simplified models that have gained a lot of attention in recent times. Section 5 will contain our conclusions.

Thorough discussions about simplified DM models may be found in [25–30]. The second-generation models of Section 4 are discussed in [31, 32]. The discussion in this paper will be partly based on [33].

#### 2. Philosophy of Simplified DM Models

As in the case of the EFT, the idea behind simplified models is to provide a good representation of possibly all realistic WIMP scenarios within the energy reach of the LHC, restricting to the smallest possible set of benchmark models, each with the minimal number of free parameters. Simplified models should be complete enough to give an accurate description of the physics at the scale probed by colliders, but at the same time they must have a limited number of new states and parameters.

The starting point is always the SM Lagrangian, complemented with a DM particle and a mediator that couples to it, through renormalizable operators, to quarks and gluons, which is necessary for the production of these states at a hadron collider. A coupling to other SM particles can be included as well and will add interesting experimental signatures to the model. In general, some simplifying assumptions can be made: for example, one can take all couplings to be equal, or the couplings to third generation's quarks to be dominant. Interactions that violate the accidental global symmetries of the SM must be handled with great care. Indeed, constraints on processes that violate these symmetries are typically very strong and may overcome those coming from DM searches or even rule out all of the interesting parameter space of the simplified model. For this reason, CP, lepton number, and baryon number conservation is typically assumed, together with minimal flavour violation (MFV). (Constraints on BSM models from CP and flavour violating observables are very strong, and the energy scale at which new physics may show up must be larger than tens of TeV in the best case, if the flavour structure of the model is generic. Minimal Flavour Violation is a way to reconcile these constraints with possible new physics at the TeV scale [34]. The basic idea is that the structure of flavour changing interactions must reproduce that of the SM. The SM is invariant under the flavour group , except a small breaking associated with the Yukawa matrices and . The invariance is restored if these matrices are regarded as “spurions” with transformation law and . Imposing MFV amounts to requiring that new physics is invariant under .) Even with this assumption, there are cases in which constraints from flavour physics may be stronger than those coming from mono-X searches [35] (see also [36] for a discussion of a non-minimally flavour violating dark sector).

Most simplified models of interest may be understood as the limit of a more general new physics scenario, where all new states but a few are integrated out because they have a mass larger than the energy scale reachable at the LHC or because they have no role in DM interactions with the SM. Similarly, in the limit where the mass of the mediator is very large, the EFT framework may be recovered by integrating out the mediator. On the contrary, there are new physics models which cannot be recast in terms of vanilla simplified models, typically because more than just one operator is active at the same time, possibly interfering with each other. The situation is summarized in Figure 1.