Abstract
We present an effective field theory describing the relevant interactions of the Standard Model with an electrically neutral particle that can account for the dark matter in the Universe. The possible mediators of these interactions are assumed to be heavy. The dark matter candidates that we consider have spin 0, 1/2 or 1, belong to an electroweak multiplet with arbitrary isospin and hypercharge and their stability at cosmological scales is guaranteed by imposing a ℤ2 symmetry. We present the most general framework for describing the interaction of the dark matter with standard particles, and construct a general non-redundant basis of the gauge-invariant operators up to dimension six. The basis includes multiplets with non-vanishing hypercharge, which can also be viable DM candidates. We give two examples illustrating the phenomenological use of such a general effective framework. First, we consider the case of a scalar singlet, provide convenient semi-analytical expressions for the relevant dark matter observables, use present experimental data to set constraints on the Wilson coefficients of the operators, and show how the interplay of different operators can open new allowed windows in the parameter space of the model. Then we study the case of a lepton isodoublet, which involves coannihilation processes, and we discuss the impact of the operators on the particle mass splitting and direct detection cross sections. These examples highlight the importance of the contribution of the various non-renormalizable operators, which can even dominate over the gauge interactions in certain cases.
Highlights
Been considered, see refs. [20, 21] for recent accounts
We present an effective field theory describing the relevant interactions of the Standard Model with an electrically neutral particle that can account for the dark matter in the Universe
Among the simplest and most economical of these EFTs are the Higgs-portal models, in which a single DM particle is introduced in addition to the SM particles; it interacts in pairs only with the Higgs sector of the theory, which is assumed to be minimal [22] and, involves only the unique Higgs boson observed at the LHC [23, 24]; see refs. [25, 26] for recent reviews
Summary
Our aim in this study is to set up a general framework for the description of the interactions between the DM and the SM particles in the case in which the possible mediators of the interactions are heavier than these particles and than the energies which are expected to be probed This DM-EFT can be obtained by extending the SMEFT (the effective field theory constructed with the SM fields only) with an extra field content, a multiplet that we will generically denote X , that involves the DM particle, X0, and it possible companions. The minimal field content of multiplets with vanishing hypercharge and integer isospin corresponds to irreducible representations carried by real scalars, Majorana spinors or real vectors. These tables comprise a non-redundant basis of operators: gauge-invariant operators not written here can be expressed as linear combinations of these by the use of algebraic identities, integration by parts and field redefinitions
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