An Effective Theory of Dirac Dark Matter

TL;DR

The paper introduces a stable Dirac fermion dark matter candidate interacting with Standard Model leptons via dimension-6 four-fermion operators, yielding a non-suppressed annihilation cross section that fixes the thermal relic density and links to present-day galactic signals. It argues that leptophilic couplings naturally avoid direct detection constraints and can account for the PAMELA positron excess with minimal boost factors, while making concrete predictions for gamma-ray features observable by Fermi/GLAST. A Dirac bino UV completion is presented as a natural realization, predicting light sleptons and a dominant leptonic annihilation channel, with measurable implications for the LHC and direct detection constraints. The framework ties cosmology, indirect detection, and collider phenomenology into a testable scenario and discusses extensions to reconcile additional experimental hints such as ATIC/PPB-BETS and DAMA.

Abstract

A stable Dirac fermion with four-fermion interactions to leptons suppressed by a scale Lambda ~ 1 TeV is shown to provide a viable candidate for dark matter. The thermal relic abundance matches cosmology, while nuclear recoil direct detection bounds are automatically avoided in the absence of (large) couplings to quarks. The annihilation cross section in the early Universe is the same as the annihilation in our galactic neighborhood. This allows Dirac fermion dark matter to naturally explain the positron ratio excess observed by PAMELA with a minimal boost factor, given present astrophysical uncertainties. We use the Galprop program for propagation of signal and background; we discuss in detail the uncertainties resulting from the propagation parameters and, more importantly, the injected spectra. Fermi/GLAST has an opportunity to see a feature in the gamma-ray spectrum at the mass of the Dirac fermion. The excess observed by ATIC/PPB-BETS may also be explained with Dirac dark matter that is heavy. A supersymmetric model with a Dirac bino provides a viable UV model of the effective theory. The dominance of the leptonic operators, and thus the observation of an excess in positrons and not in anti-protons, is naturally explained by the large hypercharge and low mass of sleptons as compared with squarks. Minimizing the boost factor implies the right-handed selectron is the lightest slepton, which is characteristic of our model. Selectrons (or sleptons) with mass less than a few hundred GeV are an inescapable consequence awaiting discovery at the LHC.

Figures (8)

• Figure 1: Cutoff scale $\Lambda$ as a function of the Dirac dark matter fermion mass $M$ that gives the thermal relic abundance $\Omega h^2 = 0.114$, consistent with cosmological data. The top curve corresponds to the flavor-democratic scenario, $c_{e_R} = c_{\mu_R} = c_{\tau_R} = 1$, while the lower curve corresponds to electrons only $c_{e_R} = 1$. In both cases we took only right-handed leptons for simplicity; adding left-handed leptons is trivial.
• Figure 2: The positron ratio assuming background only as calculated by Galprop for the 3 propagation models described in the text, DC (solid), DR (long dashed) and DRB(short dashed). The central thick lines assume an electron spectral spectrum $\Phi_{e^-}(E) \propto E^{-3.15}$ whereas the thinner lines above and below show the affect of varying the electron spectrum by $\Phi_{e^-}(E) \propto E^{-3.5}$ and $E^{-2.8}$, respectively, within the range as determined by Table \ref{['electron-data-table']}. The data is taken from the recent PAMELA observations Adriani:2008zr.
• Figure 3: The positron fraction from a 100 GeV Dirac dark matter particle that annihilates to right handed electrons. Three propagation models are plotted: DC (solid), DR (long dash), and DRB (short dash), as well as the uncertainty due to variation of the electron spectral slope. No boost factor was employed for this figure. Within the present astrophysical uncertainties, the PAMELA data can be explained so long as the electron spectrum is quite steep, $\Phi_{e^-} \propto E^{-3.5}$, corresponding to the top of the shaded blue band.
• Figure 4: Same as Fig. \ref{['e100noboost']}, except for $M = 150$ GeV and a boost factor of $5$.
• Figure 5: Same as Fig. \ref{['e150boost5']}, except with a boost factor of $15$.