Advances in High Energy Physics

Volume 2018, Article ID 5340935, 12 pages

https://doi.org/10.1155/2018/5340935

## Portal Dark Matter in the Minimal Model

Graduate School of Science and Engineering, Yamagata University, Yamagata 990-8560, Japan

Correspondence should be addressed to Satomi Okada; moc.liamg@taerg.eht.imotas

Received 5 March 2018; Accepted 2 May 2018; Published 15 July 2018

Academic Editor: Farinaldo Queiroz

Copyright © 2018 Satomi Okada. 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

We consider a dark matter scenario in the context of the minimal extension of the Standard Model (SM) with a (baryon number minus lepton number) gauge symmetry, where three right-handed neutrinos with a charge and a Higgs field with a charge are introduced to make the model anomaly-free and to break the gauge symmetry, respectively. The gauge symmetry breaking generates Majorana masses for the right-handed neutrinos. We introduce a symmetry to the model and assign an odd parity only for one right-handed neutrino, and hence the -odd right-handed neutrino is stable and the unique dark matter candidate in the model. The so-called minimal seesaw works with the other two right-handed neutrinos and reproduces the current neutrino oscillation data. We consider the case that the dark matter particle communicates with the SM particles through the gauge boson ( boson) and obtain a lower bound on the gauge coupling () as a function of the boson mass () from the observed dark matter relic density. On the other hand, we interpret the recent LHC Run-2 results on the search for a boson resonance to an upper bound on as a function of . These two constraints are complementary for narrowing down an allowed parameter region for this “ portal” dark matter scenario, leading to a lower mass bound of TeV.

#### 1. Introduction

In 2012, the Higgs boson, which is the last piece of the Standard Model (SM), was finally discovered by the A Toroidal LHC ApparatuS (ATLAS) and Compact Muon Solenoid (CMS) experiments at the Cern Large Hadron Collider (LHC) [1, 2]. The SM is the best theory to describe elementary particles and fundamental interactions among them (strong, weak, and electromagnetic interactions) and agrees with a number of experimental results in a high accuracy. For example, properties of the weak gauge bosons ( and ) in the SM, such as their masses and couplings with the quarks and leptons, were measured at the Large Electron-Positron (LEP) collider with a very high degree of precision [3, 4]. Properties of the Higgs boson have also been measured to be consistent with the SM predictions at the LHC [5].

Despite its great success, there are some observational problems that the SM cannot account for. One of the major missing pieces of the SM is the neutrino mass matrix. Since, in contrast to the other fermions, right-handed partners of the SM left-handed neutrinos are missing in the SM particle content, the SM neutrinos cannot acquire their masses at the renormalizable level, even after the electroweak symmetry is broken. However, neutrino oscillation phenomena among three neutrino flavors have been confirmed by the Super-Kamiokande experiments in 1998 [6] and the Sudbury Neutrino Observatory (SNO) in 2001 [7]. Neutrino oscillation phenomena require neutrino masses and flavor mixings, and therefore we need a framework beyond the SM to incorporate them. The so-called type I seesaw mechanism [8–12] is a natural way for this purpose, where heavy Majorana right-handed neutrinos are introduced.

Another major missing piece of the SM is a candidate for the dark matter particle in the present universe. Based on the recent results of the precision measurements of the cosmic microwave background (CMB) anisotropy by the Wilkinson Microwave Anisotropy Probe (WMAP) [13] and the Planck satellite [14, 15], the energy budget of the present universe is determined to be composed of 73% dark energy, 23% cold dark matter, and only 4% from baryonic matter. Since the SM has no suitable candidate for the (cold) dark matter particle, we need to extend the SM to incorporate it. The weakly interacting massive particle (WIMP) [16] has long been studied as one of the most promising candidates for the dark matter. Through its interaction with the SM particles, the WIMP was in thermal equilibrium in the early universe and the WIMP dark matter is a thermal relic from the early universe. Note that the relic density of the WIMP dark matter is independent of the history of the universe before it has been gotten in thermal equilibrium.

Among many possibilities, the minimal gauged extension of the SM [17–21] is a very simple way to incorporate neutrino masses and flavor mixings via the seesaw mechanism. In this extension, the accidental global (baryon number minus lepton number) symmetry in the SM is gauged. Associated with this gauging, three right-handed neutrinos with a charge are introduced to cancel all the gauge and mixed-gravitational anomalies of the model. In other words, the right-handed neutrinos which play the essential role in the type I seesaw mechanism must be present for the theoretical consistency. SM gauge singlet Higgs boson with a charge is also contained in the model and its vacuum expectation value (VEV) breaks the gauge symmetry. The Higgs VEV generates the gauge boson mass as well as Majorana masses of the right-handed neutrinos. After the electroweak symmetry breaking, the SM neutrino Majorana masses are generated through the seesaw mechanism. The mass spectrum of new particles introduced in the minimal model, the gauge boson ( boson), the right-handed Majorana neutrinos, and the Higgs boson, is controlled by the symmetry breaking scale. If the breaking scale lies around the TeV scale the minimal model can be tested at the LHC in the future.

Although the minimal model supplements the SM with the neutrino masses and mixings, a cold dark matter candidate is still missing. Towards a more complete scenario, we need to consider a further extension of the model. Ref. [22] has proposed a concise way to introduce a dark matter candidate to the minimal model, where instead of introducing a new particle as a dark matter candidate, a Z_{2} symmetry is introduced and an odd parity is assigned only for one right-handed neutrino. Thanks to the Z_{2} symmetry, the Z_{2}-odd right-handed neutrino becomes stable and hence plays the role of dark matter. On the other hand, the other two right-handed neutrinos are involved in the seesaw mechanism. It is known that the type I seesaw with two right-handed neutrinos is a minimal system to reproduce the observed neutrino oscillation data. This so-called minimal seesaw [23, 24] predicts one massless neutrino. Dark matter phenomenology in this model context has been investigated in [22, 25, 26]. The right-handed neutrino dark matter can communicate with the SM particles through (i) the boson and (ii) two Higgs bosons which are realized as linear combinations of the SM Higgs and the Higgs bosons. The cases (i) and (ii) are, respectively, called “ portal” and “Higgs portal” dark matter scenarios. In the following, we focus on the “ portal” dark matter scenario. See [22, 25, 26] for extensive studies on the Higgs portal dark matter scenario.

In recent years, the portal dark matter has attracted a lot of attention [27–64], where a dark matter candidate along with a new gauge symmetry is introduced and the dark matter particle communicates with the SM particles through the gauge boson ( boson). Through this boson interaction, we can investigate a variety of dark matter physics, such as the dark matter relic density and the direct/indirect dark matter search. Very interestingly, the search for a boson production by the LHC experiments can provide the information which is complementary to the information obtained by dark matter physics.

Note that the minimal model with the right-handed neutrino dark matter introduced above is a simple example of the portal dark matter scenario. In this article, we consider this portal dark matter scenario. Since the model is very simple, dark matter physics is controlled by only three free parameters, namely, the gauge coupling (), the boson mass (), and the dark matter mass (). We first identify allowed parameter regions of the model by considering the cosmological bound on the dark matter relic density. We then consider the results from the search for a boson resonance with dilepton final states to identify allowed parameter regions. Combining the cosmological and the LHC constraints, we find a narrow allowed region. This complementarity between the cosmological and the LHC constraints has been investigated in [46, 54]. The purpose of this article is to update the results in the references by employing the latest LHC results, along with a review of the minimal model with the right-handed neutrino dark matter.

The plan of this article is as follows: In the next section, we give a review of the minimal model. In Section 3, we introduce the minimal model with symmetry, where one right-handed neutrino, which is a unique -odd particle in the model, is identified with the dark matter particle. In Section 4, the cosmological constraints on the right-handed neutrino dark matter are considered and an allowed parameter region is identified. In Section 5, we consider the LHC Run-2 constraints from the search for a narrow resonance with dilepton final states and find the constraints on our model parameters. Combining the results obtained in Section 3, we find an allowed region. The cosmological constraint and the LHC constraints are complementary for narrowing down the allowed parameter regions. Section 6 is devoted to conclusions.

#### 2. The Minimal Model

The SM Lagrangian at the tree-level is invariant under the global and transformations:where and are constant phases associated with the and transformations, and and are charges identified as a baryon number () and a lepton number () of the fermion , respectively. The baryon number is a quantum number to characterize fermions. A quark (antiquark) has a baryon number , while SM lepton has 0. The lepton number is a quantum number similar to baryon number. A lepton (antilepton) has a lepton number 1 , while a quark has 0. Although these symmetries are anomalous under the SM gauge group, the combination of is anomaly-free. The symmetry means that the SM Lagrangian is invariant under the global transformation:where is a constant phase associated with the transformation.

In the minimal model [17–21], this global symmetry in the SM is gauged, and hence this model is based on the gauge group . Three right-handed neutrinos (, , is a generation index) and an SM singlet scalar field () are introduced to make the theory anomaly-free and to break the gauge symmetry, respectively. The particle content of the minimal model is listed in Table 1.