Testing Dark Matter with the Anomalous Magnetic Moment in a Dark Matter Quantum Electrodynamics Model Ashok K. Das, 1, 2, ∗ Jorge Gamboa, 3, † Fernando M´ endez, 3, ‡ and Natalia Tapia 3, § 1 Department of Physics and Astronomy, University of Rochester, Rochester, NY 14627-0171, USA 2 Institute of Physics, Sachivalaya Marg, Bhubaneswar 751005, India 3 Departamento de F´ ısica, Universidad de Santiago de Chile, Casilla 307, Santiago, Chile (Dated: October 17, 2018) We consider a model of dark quantum electrodynamics which is coupled to a visible photon through a kinetic mixing term. We compute the gχ - 2 for the dark fermion, where gχ is its gyromagnetic factor. We show that the gχ - 2 of the dark fermion is related to the g ′ χ - 2 of (visible) quantum electrodynamics through a constant which depends on the kinetic mixing factor. We determine gχ - 2 as a function of the mass ratio κ = mB/mχ where mB and mχ denote the masses of the dark photon and the dark fermion respectively and we show how gχ - 2 become very different for light and heavy fermions around mB ≤ 10 −4 eV. I. INTRODUCTION The search for dark matter is one of the important challenges in physics today because its existence may explain some of the puzzles of conventional physics, such as the rotation curves of the galaxies, the new phenomenon of emission of light from the center of galaxies. It can also provide new insights into old problems such as matter- antimatter asymmetry, primordial magnetic fields and so on. Dark matter can also open up new areas of research in particle physics, astrophysics and cosmology [1–6]. The dark matter interacts very weakly with conventional matter and the effects produced by either light or heavy dark fermions are small in general. On the other hand, some properties, such as the magnetic dipole moment for electron/muon like dark fermions may depend dramatically on the mass of the dark fermion as well as the way they couple to the visible sector. (The Pauli coupling, for example, depends on the fermion mass with the mass in the denominator.) The possibility of a mass dependence for such effects makes the heavy and the light fermion regimes very different since they correspond to different parameter spaces. Precisely for this reason, the distinction between weakly interacting slightly particle (WISP) and weakly interacting massive particle (WIMP) is introduced in these studies. Although the observational and theoretical reasons for the existence of dark matter are many (for a review see [7, 8]), there are issues that still need to be addressed. For example, for models mirroring the visible sector, such as the one considered in the present work, it would be interesting to find the effects of such dark systems on some of the high-precision measurements in particle physics [9, 10]. The electron gyromagnetic factor is one of the greatest triumphs of quantum field theory (quantum electrodynamics) and, therefore, the study of the magnetic moment of a dark Dirac fermion would be a very relevant and important issue in this context. However contrary of the conventional standard model calculations, the calculation for the magnetic moment of dark fermions must take into account the range of masses in which the theory is considered. For the case of WISP the typical fermion masses are m wisp ∼ 10 −3 eV or less, while in the case of WIMP the fermion masses are typically m wimp ∼ 10 2 GeV or more and, therefore the magnetic moment of a WISP and a WIMP can be very different. In this paper we would like to concentrate mainly on the sector of WISP where the space of parameters can be tested in a family of experiments running at present [11, 12]. The masses of dark light fermions are bounded typically as m χ < 10 −3 eV which can be easily studied in these experiments. In the low energy sector, which is the region to be discussed in this paper, there are still a number of important phenomena that require careful study such as the distortion of cosmic microwave radiation [13], deviations from Coulomb’s law [14, 15], the distortion of planetary magnetic fields [16], the level shifts in atomic physics [17] and so on. The ranges of parameters that may be relevant in these studies are m χ ∼ 10 −8 − 10 6 eV for dark fermion masses ∗ Electronic address: das@pas.rochester.edu † Electronic address: jorge.gamboa@usach.cl ‡ Electronic address: fernando.mendez@usach.cl § Electronic address: natalia.tapiaa@usach.cl arXiv:1612.03682v2 [hep-ph] 17 Oct 2017