Non-minimally flavour violating dark matter

Flavour symmetries provide an appealing mechanism to stabilize the dark matter particle. I present a simple model of quark flavoured dark matter that goes beyond the framework of minimal flavour violation. I discuss the phenomenological implications for direct and indirect dark matter detection experiments, high energy collider searches as well as flavour violating precision data. 1. Flavour symmetries in the dark sector While astrophysical and cosmological observations provide convincing evidence for the existence of dark matter (DM), little is known about its particle properties. Besides its gravitational interactions, appealing arguments exist that the DM particles should interact weakly with the Standard Model (SM). The reason for this belief is referred to as the “WIMP miracle”: a DM particle with weak scale mass, mDM ∼ O(10 2 GeV) and weak coupling automatically generates the right DM relic abundance. The WIMP hypothesis receives further support from the electroweak (EW) naturalness problem, requiring an extension of the SM at the TeV scale in order to stabilize the (EW) symmetry breaking scale. Adopting the WIMP hypothesis many properties of the DM particle are still unknown. It has to be neutral under strong and electromagnetic interactions, yet its transformation under EW symmetry can be non-trivial. Indeed the WIMP hypothesis seems to suggest a coupling to the weak gauge bosons. Nevertheless it is equally justified to introduce some new type of interactions through which an EW singlet DM particle couples to the SM. Non-trivial symmetry transformation properties of DM, both for global and local groups, are possible and worthwhile to be studied. In this article, summarizing the results of [1], we focus on a particular type of global symmetry, namely a flavour group. The idea of flavoured DM is not new, see e. g. [2] for a review of early studies. However most studies so far assumed that the DM is charged under the SM flavour group and its interactions satisfy the Minimal Flavour Violation (MFV) [3, 4] hypothesis, so that the SM Yukawa couplings Yu,d remain the only source of flavour breaking. This approach has several benefits: apart from avoiding the stringent constraints from flavour changing neutral current (FCNC) processes, it can be shown [5] that the MFV principle implies the stability of DM, provided the latter transforms under certain representations of the flavour group. The drawback of the MFV assumption is that no interesting effects in flavour violating observables can be expected, thus closing a potential discovery channel of flavoured DM. Therefore in [1] we studied the possibility of non-minimally flavour violating DM. The results of that paper have been presented at the DISCRETE 2014 conference and are summarized in the present article. 2. Dark Minimal Flavour Violation and its implications 2.1. The Dark Minimal Flavour Violation hypothesis The Dark Minimal Flavour Violation (DMFV) hypothesis [1] is a conceptually straightforward extension of the well-known MFV principle to the DM sector. In complete analogy to the SM matter content we assume that the DM χ transforms under the fundamental representation of a new global flavour symmetry U(3)χ. The full flavour symmetry group 1 then reads GF = U(3)q × U(3)u × U(3)d × U(3)l × U(3)e × U(3)χ . (1) The crucial ingredient for DMFV is then that this global flavour symmetry is broken only by the SM Yukawa couplings Yu, Yd, Ye, and the DM coupling λ to the SM fermions. Depending on which type of SM fermion the DM field χ couples to, and depending on the Dirac structure of the coupling, different classes of DMFV models can be obtained. We are thus left with a huge variety of models with interesting and quite distinct phenomenological implications. It is important to note that while DMFV is conceptually close to the MFV ansatz, the phenomenology of DMFV models differs vastly from the MFV ones. This is due to the new coupling matrix λ whose structure is unrelated to the SM Yukawa couplings, and upon which no hierarchical structure is imposed. 2.2. A minimal model For concreteness, following [1], let us focus on a concrete class of DMFV models in what follows. We introduce DM as a Dirac fermion χ that transforms as a triplet under the global flavour symmetry U(3)χ, and that couples to right-handed down-type quarks via a scalar mediator φ. The field φ is singlet under the flavour group GF , however it transforms as