Advances in High Energy Physics

Volume 2018, Article ID 3905848, 11 pages

https://doi.org/10.1155/2018/3905848

## Anomalies in Transitions and Dark Matter

Instituto de Física Corpuscular (CSIC-Universitat de València), Apdo. 22085, E-46071 Valencia, Spain

Correspondence should be addressed to Avelino Vicente; se.vu.cifi@etneciv.onileva

Received 20 March 2018; Accepted 28 May 2018; Published 24 June 2018

Academic Editor: Farinaldo Queiroz

Copyright © 2018 Avelino Vicente. 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

Since 2013, the LHCb collaboration has reported on the measurement of several observables associated with transitions, finding various deviations from their predicted values in the Standard Model. These include a set of deviations in branching ratios and angular observables, as well as in the observables and , specially built to test the possible violation of Lepton Flavor Universality. Even though these tantalizing hints are not conclusive yet, the anomalies have gained considerable attention in the flavor community. Here we review new physics models that address these anomalies and explore their possible connection to the dark matter of the Universe. After discussing some of the ideas introduced in these works and classifying the proposed models, two selected examples are presented in detail in order to illustrate the potential interplay between these two areas of current particle physics.

#### 1. Introduction

The Standard Model (SM) of particle physics provides an excellent description for a vast amount of phenomena and can be regarded as one of the most successful scientific theories ever built. In fact, with the recent discovery of the last missing piece, the Higgs boson, the particle spectrum is finally complete and the SM looks stronger than ever. However, and despite its enormous success, there are several indications that clearly point towards the existence of a more complete theory, with neutrino masses and the baryon asymmetry of the Universe as the most prominent examples.

Another open question is the nature of the dark matter (DM) that accounts for of the energy density of the Universe [1]. Several ideas have been proposed to address this fundamental problem in current physics. Under the hypothesis that the DM is composed of particles, these cannot be identified with any of the states in the SM, hence demanding an extension of the model with new states and, possibly, new dynamics. Again, many directions exist. Interestingly, in scenarios involving New Physics (NP) at the TeV scale, the first signals from the new DM sector might be found in experiments not specially designed to look for them.

Rare decays stand among the most powerful tests of the SM. Since 2013, results obtained by the LHCb collaboration have led to an increasing interest in B physics, particularly in processes involving transitions. Deviations from the SM expectations have been reported in several observables, some of them hinting at the violation of Lepton Flavor Universality (LFU), a central feature in the SM. Even though these anomalies could be caused by a combination of unfortunate fluctuations and, perhaps, a poor theoretical understanding of some processes, it is tempting to speculate about their possible origin in terms of NP models, in particular models linking them to other open problems.

This* minireview* will pursue this goal, focusing on NP scenarios that relate the anomalies to DM. Several works [2–20] have already explored this connection, mostly by means of specific models that accommodate the observations in transitions with a new dark sector. We will review some of the ideas introduced in these works and highlight those that deserve further exploration. We will also classify the proposed models into two general categories: (i) models in which the NP contributions to transitions and DM production in the early Universe share a common mediator, and (ii) models with the DM particle running in loop diagrams that contribute to the solution of the anomalies. After a general discussion, a selected example of each class will be presented in detail.

The rest of the manuscript is organized as follows. First, we review the anomalies in transitions in Section 2 and interpret the experimental results in a model independent way in Section 3. In Section 4 we discuss and classify the proposed New Physics explanations to these anomalies that involve a link to the dark matter problem. Sections 5 and 6 present two simple example models that illustrate this connection. Finally, we summarize and draw our conclusions in Section 7.

#### 2. Experimental Situation

We begin by discussing the present experimental situation. The observed anomalies in transitions can be classified into two classes: (1) branching ratios and angular observables and (2) lepton flavor universality violating (LFUV) anomalies. Although they might be related (and caused by the same NP), they are conceptually different.

*Branching Ratios and Angular Observables*. using state-of-the-art computations of the hadronic form factors involved, one can compute branching ratios and angular observables for processes such as and look for deviations from the SM predictions. For the comparison to be meaningful, one must have a good knowledge of all possible Quantum ChromoDynamics (QCD) effects that might pollute the theoretical calculation and we currently have at our disposal several methods to minimize or at least estimate the uncertainties. (The size of the hadronic uncertainties in different calculations is a matter of hot debate nowadays. We will not discuss this issue here but just refer to the recent studies regarding form factors [21, 22] and nonlocal contributions [23–28] for extended discussions.) In particular, a basis of optimized observables for the decay , specially designed to reduce the hadronic uncertainties, was introduced in [29]. In 2013, the LHCb collaboration published results on these observables using their fb^{−1} dataset, finding a deviation between the measurement and the SM prediction for the angular observable in one dimuon invariant mass bin [30]. A systematic deficit with respect to the SM predictions in the branching ratios of several processes, mainly , was also reported by LHCb [31]. These discrepancies have been found later in other datasets. In 2015, LHCb confirmed these anomalies using their full Run 1 dataset with fb^{−1} [32, 33], whereas in 2016 the Belle collaboration presented an independent measurement of , compatible with the LHCb result [34, 35]. More recently, both ATLAS [36] and CMS [37] have also presented preliminary results on the angular observables, with relatively good agreement with LHCb.

*LFUV Anomalies*. One of the central features of the SM is that gauge bosons coupled with the same strength to all three families of leptons. This prediction can be tested by measuring observables such as the ratios, defined as [38]measured in specific dilepton invariant mass squared ranges . In the SM, these ratios should be very approximately equal to one. Furthermore, hadronic uncertainties are expected to cancel very good approximation in these ratios, which implies that, in contrast to the previous class of anomalies, deviations in these observables cannot be explained by uncontrolled QCD effects and would be a clear indication of NP at work. For this reason, they are sometimes referred to as* clean observables*. Interestingly, in 2014, the LHCb collaboration measured in the region GeV^{2} [39], finding a value significantly lower than one, while in 2017 similar measurements of the ratio in two bins [40] were also found to depart from their SM expected values:The comparison between these experimental results and the SM predictions [41, 42],shows deviations from the SM at the level in the case of , for in the low- region, and for in the central- region. Finally, Belle has recently measured the LFUV observable , with the observable defined for analogously to for [43]. The result, although statistically not very significant, also points towards the violation of LFU [35].

Summarizing, there are at present two sets of experimental anomalies in processes involving transitions at the quark level. While the relevance of the first set is currently a matter of discussion due to the possibility of unknown QCD effects faking the deviations from the SM, the second can only be explained by NP violating LFU. In principle, these two classes of anomalies can be completely unrelated but, as we will see in the next section, global analyses of all experimental data in transitions indicate that a common explanation (in terms of a single effective operator) can address both sets in a satisfactory and economical way. This intriguing result has made the anomalies a topic of great interest currently.

Finally, it is very interesting to note the existence of an independent set of anomalies in transitions. Several experimental measurements of the ratios and have been found to depart from their SM predictions, with a global discrepancy at the level [44]. Recently, the ratio has also been measured by the LHCb collaboration, finding again a deviation from the SM expected value [45]. Compared to the anomalies, the anomalies are of a different nature and, if real, they could have a completely different origin. For instance, they would involve a new charged current, instead of a neutral one, hence requiring the new mediators to be much lighter to be able to compete with the SM boson tree-level exchange. However, many authors have proposed models that can simultaneously address both sets of anomalies. We refer to [46] for a general discussion on combined explanations and ignore the anomalies for the rest of this paper.

#### 3. Model Independent Interpretation

The experimental tensions discussed in the previous section must be properly quantified and interpreted.** Quantification** is crucial to determine whether the anomalies can be explained by fluctuations in the data or they truly indicate a statistically significant deviation from the SM. Assuming that these tensions are caused by genuine NP, the ultimate goal is to construct a specific model in which they are solved. However, the first step in this direction must be a** model independent interpretation** of the experimental data in order to identify the ingredients that this new scenario must include. This is achieved by adopting an approach based on effective operators, valid under the assumption that all NP degrees of freedom lie at energies well above the relevant energy scales for the observables of interest.

The effective Hamiltonian for transitions is usually written asHere is the Fermi constant, the electric charge, and the Cabibbo-Kobayashi-Maskawa (CKM) matrix. and are the effective operators that contribute to transitions, and and their Wilson coefficients. The most relevant operators for the interpretation of the anomalies areHere . In fact, the operators and Wilson coefficients carry flavor indices and we are omitting them to simplify the notation. When necessary, we will denote a particular lepton flavor with a superscript, e.g., and , for muons. It is also convenient to split the Wilson coefficients in two pieces: the SM contributions and the NP contributions, defining the following (similar splittings could be defined for the Wilson coefficients of the primed operators, and , but in this case the SM contributions are suppressed and one has and ):The SM contributions have been computed at NNLO at GeV, obtaining and (see [29] and references therein), leaving the NP contributions as parameters to be determined (or at least constrained) by using experimental data.

It is in principle possible to derive limits for the NP contributions considering each observable independently, but this approach would completely miss the global picture. The effective operators in (4) contribute to several observables and one expects the presence of NP to be revealed by a pattern of deviations from the SM expectations, rather than by a single anomaly. For this reason, global fits constitute the best approach to analyze the available experimental data. Interestingly, several independent fits [47–54] have found a remarkable tension between the SM and experimental data on transitions which is clearly reduced with the addition of NP contributions. Although the numerical details (such as statistical significance) differ among different analyses, there is a general consensus on the following qualitative results:(i)Global fits improve substantially with a negative contribution in , with , leading to a total Wilson coefficient significantly smaller than the one in the SM.(ii)NP contributions in other Wilson coefficients can also improve the fit, but only in a subdominant way. For instance, the anomalies can also be accommodated in scenarios with or , without a clear statistical preference with respect to the scenario with NP only in . (Such patterns for the Wilson coefficients are automatically obtained if the NP states coupled to SM fermions with specific chiralities. For instance, the relation is obtained in models where the NP states only couple to the* left-handed* muons. Two examples of this class of models are shown in Sections 5 and 6.)(iii)Other operators involving muons are perfectly compatible with their SM values. Similarly, no NP is required for operators involving electrons or tau leptons.

Armed with these results, model builders can construct specific models where all requirements are met and the anomalies explained. Similarly, one can extract interesting implications for model building by explaining the anomalies in terms of gauge invariant effective operators; see [55] for a recent analysis. Either way, the resulting profile of NP contributions reveals a pattern that was not predicted by any theoretical framework, such as supersymmetry, and many new models have been put forward. In the next Section we will discuss some of these models, in particular those linking the anomalies to dark matter.

#### 4. Linking the Anomalies to Dark Matter

After discussing the current experimental situation in transitions, let us focus on possible connections to the dark matter problem. These have been explored in [2–20]. In general, the proposed models that solve the anomalies and explain the origin of the dark matter of the Universe can be classified into two principal categories:(i)**Portal models:** models in which the mediator responsible for the NP contributions to transitions also mediates the DM production in the early Universe.(ii)**Loop models:** models that induce the required NP contributions to transitions with loops containing the DM particle.

In the case of** portal models**, the usual scenario considers a gauge extension of the SM that leads to the existence of a new massive gauge boson after spontaneous symmetry breaking. The resulting boson induces a new neutral current contribution in transitions and mediates the production of DM particles in the early Universe via a portal interaction. This setup was first considered in [2]. In this particular realization of the general idea, the SM fermions were assumed to be neutral under the new gauge symmetry and the couplings to quarks () and leptons (), necessary to explain the anomalies, are generated at tree-level via mixing with new vector-like (VL) fermions. Additionally, the boson also couples to the scalar field , the DM candidate in this model, automatically stabilized by an remnant symmetry after breaking. This model will be reviewed in more detail in Section 5. Variants of this setup with fermionic DM also exist. In [6], a horizontal gauge symmetry is introduced, with being the baryon number of the ith fermion family. The resulting boson couples directly to the SM quarks, while the coupling to muons is obtained by introducing a VL lepton. This allows accommodating the anomalies in transitions. Furthermore, the model also contains a Dirac fermion that is stable due to a remnant symmetry, in a similar fashion as in [2], which becomes the DM candidate. Similarly, [7] builds on the well-known model of [56] and extends it to include a stable Dirac fermion with a relic density also determined by portal interactions, while [20] considers a similar model but makes use of kinetic mixing between the and the SM neutral gauge bosons. Reference [19] considers vector-like neutrino DM in a setup analogous to [2] extended with additional VL fermions. Reference [10] explored a pair of scenarios based on a gauge symmetry supplemented with VL fermions and a fermionic DM candidate, of Dirac or Majorana nature. This paper focuses on effects in indirect detection experiments, aiming at an explanation of the excess of events in antiproton spectra reported by the AMS-02 experiment in 2016 [57]. Other works that adopt the standard portal setup are [4, 12]. Finally, [11] considers a light mediator (not the usual heavy ) that contributes to transitions and decays predominantly into invisible final states, possibly made of light DM particles.

It is important to note that the phenomenology of these portal models differs substantially from the standard portal phenomenology. This is due to the fact that the bosons in these models couple with different strengths to different fermion families, as required to accommodate the LFUV hints observed by the LHCb collaboration ( and ). For instance, DM annihilation typically yields muon and tau lepton pairs, but not electrons and positrons. Direct detection experiments are also more challenging in the standard portal scenario, since the DM candidate typically does not couple to first generation quarks, more abundant in the nucleons.

In what concerns** loop models**, many variations are possible. To the best of our knowledge, the first model of this type that appeared in the literature is [13], based on previous work on loop models for the anomalies, without connecting to the DM problem, in [58, 59]. In this model the SM particle content is extended with two VL pairs of doublets, with the same quantum numbers as the SM quark and lepton doublets, but charged under a global symmetry. The model also contains the complex scalar , singlet under the SM gauge symmetry and also charged under . With these states, one can draw a 1-loop diagram contributing to the observables relevant to explaining the anomalies. Furthermore, if the global is conserved, the lightest -charged state becomes stable. In this work, this state is assumed to be , hence the DM candidate in the model. A more detailed discussion about this model can be found in Section 6. Two similar setups can be found in [18], where a different set of global symmetries are considered ( and ) in order to stabilize a scalar DM candidate. This paper also includes right-handed neutrinos in order to accommodate nonzero neutrino masses with the type-I seesaw mechanism and explores the lepton flavor violating phenomenology of the model in detail. A Majorana fermionic DM candidate was considered in [16]. Similarly to the previously mentioned models, this scenario also addresses the anomalies at 1-loop level introducing a minimal number of fields: just a VL quark () and an inert scalar doublet (), in addition to the fermion singlet that constitutes the DM candidate. The model is supplemented with a discrete symmetry to ensure the stability of the DM particle. Interestingly, the model can be tested in direct DM detection experiments as well as at the Large Hadron Collider (LHC), where the states and can be pair-produced and lead to final states with hard leptons and missing energy. Finally, an extended loop model for the anomalies, which also has an additional gauge symmetry, contains a scalar DM candidate and explains neutrino masses that can be found in [17].

Finally, let us comment on other models and works that do not easily fit within any of the two categories mentioned above. The model in [3] is very similar to the model in [2]. It also extends the SM with a complex scalar, VL quarks, and leptons and a new gauge symmetry that breaks down to a parity. However, the VL leptons carry different charges, leading to a loop-induced coupling. This changes the DM phenomenology dramatically. The dominant mechanism for the DM production in the early Universe is not a portal interaction, but t-channel exchange of VL leptons. The model in [9] can be regarded as a* hybrid* model, with features from both portal and loop models. The SM symmetry group is extended with a new piece. The first factor leads to the existence of a massive boson while the second one stabilizes a scalar DM candidate. The coupling is generated with a loop containing the -odd fields and the dominant DM production mechanism is a portal interaction, mainly with leptons. The coupling is also loop-generated in [14], but in this case production of DM particles takes place via a Higgs portal. Reference [8] proposes an extended Scotogenic model for neutrino masses [60] supplemented with a nonuniversal gauge group. The DM candidate in this case is the lightest fermion singlet and is produced by Yukawa interactions. Finally, two models that address the anomalies with leptoquarks and include DM candidates were introduced in [5, 15]. In the former the DM candidate is a component of an multiplet introduced to enhance the diphoton rate of a scalar in the model, whereas in the latter the DM candidate is a baryon-like composite state in a model with strong dynamics at the TeV scale.

Having reviewed and classified the proposed models, we now proceed to discuss in some detail two specific examples. These illustrate the main features of portal and loop models.

#### 5. An Example Portal Model

We will now review the model introduced in [2], arguably one of the simplest scenarios to account for the anomalies with a dark sector. Some of the ingredients of this model were already present in the model of [56], which is extended in the quark sector (following the same lines as in the lepton sector). It also includes a dark matter candidate that couples to the SM fields via the same mediator that leads to an explanation of the anomalies, a heavy boson. A variation of this scenario with a loop-induced coupling to muons appeared afterwards in [3], whereas the phenomenology of an extension to account for neutrino masses will be discussed in [61].

The model extends the SM gauge group with a new dark factor, under which all the SM particles are assumed to be singlets. The* dark sector* contains two pairs of vector-like fermions, and , as well as the complex scalar fields, and . Tables 1 and 2 show all the details about the gauge sector and the new scalars and fermions in the model. and have the same representation under the SM gauge group as the SM doublets and , and they can be decomposed under asWith the electric charges of , , , and being , , , and , respectively. In contrast to their SM counterparts, and are vector-like fermions charged under the dark . In addition to the usual canonical kinetic terms, the new vector-like fermions and have Dirac mass terms,as well as Yukawa couplings with the SM doublets and and the scalar ,where and are 3 component vectors. The scalar potential of the model can be split into different pieces, is the usual SM scalar potential containing quadratic and quartic terms for the Higgs doublet . The new terms involving the scalars and areandAll couplings are dimensionless, whereas has dimensions of mass and and have dimensions of mass^{2}. We will assume that the scalar potential parameters allow for the vacuum configurationwhere is the neutral component of the Higgs doublet . The scalar does not get a vacuum expectation value (VEV). Therefore, the scalar will be responsible for the spontaneous breaking of . This automatically leads to the existence of a new massive gauge boson, the boson, with mass . In the absence of mixing between the gauge bosons, the boson can be identified with the original boson in Table 1. We note that a Lagrangian term of the form , where are the usual field strength tensors for the groups, would induce this mixing. In order to avoid phenomenological difficulties associated with this mixing we will assume that . Moreover, it can be shown that loop contributions to this mixing are kept under control if [2].