Kinetic Mixing as the Origin of Light Dark Scales

TL;DR

The paper introduces a minimalist SUSY dark sector with an abelian U(1)_d gauge symmetry that is kinetically mixed with SM hypercharge. This mixing generates GeV-scale dynamics and MeV-scale splittings, enabling explanations of PAMELA/ATIC via a GeV mediator and DAMA/XDM via iDM or XDM, while making sharp, testable predictions—such as lepton jets from dark-photon cascades and a direct link between DAMA cross-sections and MSSM D-terms. The framework fixes key parameters through relic abundance and cosmic-ray observations, and anticipates observable signals across direct detection, indirect detection, and collider experiments. While highly predictive, it also highlights potential tensions and the need for modest extensions to address lifetime constraints and cross-section magnitudes. Overall, the work offers a simple, testable mechanism for generating the required dark-sector scales from kinetic mixing alone.

Abstract

We propose a model in which supersymmetric weak scale dark matter is charged under a U(1)_d dark gauge symmetry. Kinetic mixing between U(1)_d and hypercharge generates the appropriate hierarchy of scales needed to explain PAMELA and ATIC with a GeV scale force carrier and DAMA (or INTEGRAL) using the proposals of inelastic (or, respectively, exciting) dark matter. Because of the extreme simplicity of this setup, observational constraints lead to unambiguous determination of the model parameters. In particular, the DAMA scattering cross section is directly related to the size of the hypercharge D-term vacuum expectation value. The known relic abundance of DM can be used to fix the ratio of the dark sector coupling to the dark matter mass. Finally, the recent observation of cosmic ray positron and electron excesses can be used to fix the mass of the dark matter through the observation of a shoulder in the spectrum and the size of the kinetic mixing by fitting to the rate. These parameters can be used to make further predictions, which can be checked at future direct detection, indirect detection, as well as collider experiments.

Figures (2)

• Figure 1: A contour plot of the Sommerfeld enhancement nima_paper as a function of $M$ (or $\alpha_d$, related through Eq. (\ref{['eqn:freezeCS']})) and $\sqrt{\xi_Y}$, with $\epsilon=10^{-4}$ and $\tan \beta = 40$. The solid black lines correspond to fixed $m_b$. The dark matter velocity is taken to be $v =150 \textrm{ km/s}$. On the right we indicate the boost required for PAMELA for three reference values of $M$, for the process $\Phi \Phi \rightarrow \gamma^\prime \gamma^\prime$ followed by $\gamma' \rightarrow e^+ e^-$boost. The boost is relative to $\langle \sigma v \rangle = 3 \times 10^{-26} \textrm{ cm}^3 \textrm{ s}^{-1}$, assuming local dark matter density $\rho_0 = 0.3 \textrm{ GeV} \textrm{ cm}^{-3}$.
• Figure 2: The DAMA cross-section as a function of the effective FI parameter with $\tan \beta = 2$ (red, dashed) and $\infty$ (blue, line). The horizontal lines indicate the preferred range for the WIMP-nucleon cross-section idm.