Constraints on electromagnetic form factors of sub-GeV dark matter from the Cosmic Microwave Background anisotropy

Abstract

We consider dark matter which have non-zero electromagnetic form factors like electric/magnetic dipole moments and anapole moment for fermionic dark matter and Rayleigh form factor for scalar dark matter. We consider dark matter mass $m_{\chi }>\mathcal{O}(\mathrm{MeV})$ and put constraints on their mass and electromagnetic couplings from CMB and LSS observations. Fermionic dark matter with non-zero electromagnetic form factors can annihilate to $e^{+}{e}^{-}$ and scalar dark matter can annihilate to $2\gamma$ at the time of recombination and distort the CMB. We analyze dark matter with multipole moments with Planck and BAO observations. We find upper bounds on anapole moment $g_A<7.163\times 10^3{\text{GeV}}^{-2}$, electric dipole moment $\mathcal{D}<7.978\times 10^{-9}\text{e-cm}$, magnetic dipole moment $\mu <2.959\times 10^{-7}{\mu }_B$, and the bound on Rayleigh form factor of dark matter is $g_4/{\Lambda }_4^2<1.085\times 10^{-2}{\text{GeV}}^{-2}$ with $95\%$C.L.

Comments: Version to appear in Physical Review D