Abstract
We perform a systematic study of the electric and magnetic dipole moments of dark matter (DM) that are induced at the one-loop level when DM experiences four-fermion interactions with Standard Model (SM) charged fermions. Related to their loop nature these moments can largely depend on the UV completion at the origin of the four-fermion operators. We illustrate this property by considering explicitly two simple ways to generate these operators, from t- or s-channel tree-level exchange. Fixing the strength of these interactions from the DM relic density constraint, we obtain in particular a magnetic moment that, depending on the interaction considered, lies typically between 10−20 to 10−23 ecm or identically vanishes. These non-vanishing values induce, via photon exchange, DM-nucleus scattering cross sections that could be probed by current or near future direct detection experiments.
Highlights
In this work we are interested in effective interactions involving charged Standard Model (SM) fermions (f ) and dark matter (DM) fermions (χ), of the general form L ⊃ GχOχf O f with O and O any possible operators
The question we ask is: once the coefficients of the effective operators are fixed by the relic density, what are the values of the dipoles one can expect at the one-loop level and what are their phenomenological consequences? The answer to this question is not straightforward because a procedure which would consist in computing the loop diagram resulting from closing the charged fermion line of the 4-fermion operator, and attaching an external photon to this fermion line, does not necessarily lead to the dipoles that would be generated in the UV complete theory that is at the origin of these operators
As compared to a standard WIMP case, where the particle exchanged with the nucleon has typically an electroweak scale mass, this will largely boost the number of events in direct detection events, since the recoil energy considered in these experiments is typically of order 5-50 keV
Summary
We start with the most general four-fermion interactions of Dirac DM (χ) and SM fermions (f ) [16, 34,35,36,37,38]:. Note that in eq (2.1) we have inserted an ia factor, which is defined as iS,P,T = i and iV,A = 1, so that the various terms are hermitian, with a anda real numbers — for further discussions see e.g. refs. Eq (2.1) provides a complete description of all possible Lorentz-invariant four-fermion interactions. This set of effective operators has been frequently used for DM collider searches and direct detection — see e.g. refs. Are real and independent of each other, and in the chiral basis are either complex conjugate of each other. ’s in the chiral basis still contains 10 real independent parameters
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