Exothermic Dark Matter

TL;DR

Exothermic dark matter (exoDM) offers a mechanism to explain the DAMA/LIBRA annual modulation without conflicting with other direct-detection results by using two light GeV-scale states with keV-scale mass splittings that down-scatters off nuclei. The resulting recoil spectrum peaks at $E_R \approx \delta m_\\chi / m_N$ and is enhanced for light targets with low thresholds, yielding a small but modulated signal compatible with DAMA and potentially CoGeNT while evading many bounds due to sub-keV energy deposition. The paper develops the kinematics, surveys a broad set of constraints, and provides a minimal UV completion based on a light dark photon that naturally generates the required splitting and cross sections, with clear predictions for upcoming low-threshold experiments. It emphasizes that the key test of exoDM lies in understanding detector response and channeling at keV energies, which will determine the viability of the scenario as new data accumulate from light-nucleus detectors.

Abstract

We propose a novel mechanism for dark matter to explain the observed annual modulation signal at DAMA/LIBRA which avoids existing constraints from every other dark matter direct detection experiment including CRESST, CDMS, and XENON10. The dark matter consists of at least two light states with mass ~few GeV and splittings ~5 keV. It is natural for the heavier states to be cosmologically long-lived and to make up an O(1) fraction of the dark matter. Direct detection rates are dominated by the exothermic reactions in which an excited dark matter state down-scatters off of a nucleus, becoming a lower energy state. In contrast to (endothermic) inelastic dark matter, the most sensitive experiments for exothermic dark matter are those with light nuclei and low threshold energies. Interestingly, this model can also naturally account for the observed low-energy events at CoGeNT. The only significant constraint on the model arises from the DAMA/LIBRA unmodulated spectrum but it can be tested in the near future by a low-threshold analysis of CDMS-Si and possibly other experiments including CRESST, COUPP, and XENON100.

Figures (7)

• Figure 1: Sample recoil energy spectra for downscattering off of sodium during winter when the Earth is moving with the DM halo (blue line) and during summer when it is moving against the halo (red dashed). The modulation spectrum is half of the difference between these two curves, shown here enlarged by a factor of 20 (purple dotted). Here we have taken a dark matter mass of $m_{\chi} = 3.5 \text{ GeV}$ and a splitting of $\delta = 6 \text{ keV}$ and chosen the cross-section to fit the DAMA modulation signal. Note that the modulation is $\sim 1\%$ of the the unmodulated rate. This is tolerable for this model because the scattering is below threshold at most experiments.
• Figure 2: A sample of possible components of the unmodulated energy spectra at DAMA, arising from sodium and iodine scatters and channeled and unchanneled recoils. The spectra from iodine scatters are shown at 1% of their actual scale. Here we have taken $m_{\chi} = 3.5\text{ GeV}$ and $\delta = 6\text{ keV}$ and chosen the cross-section to fit the DAMA modulation signal. The channeling fraction has been assumed to be constant with energy and equal to 30% for both sodium and iodine recoils. Note that only channeled sodium scatters are relevant for the energies where modulation data is available ($> 2\text{ keV}$). Channeled sodium also dominates the rate at $2 \text{ keV}$ where the constraint form the DAMA unmodulated rate is strongest.
• Figure 3: The parameter space in the mass/splitting plane for the downscattering fit to DAMA (68%, 90% and 99% confidence level regions shaded). In the lefthand plot we assume constant channeling fractions for both sodium and iodine, while on the right we take the channeling fraction given by Eq. \ref{['Eqn:DownturnChanneling']}. At each point in the $(m_{\chi},\delta)$ plane in this plot the cross-section has been chosen to give the best fit to DAMA. The halo model is Maxwell-Boltzmann with $v_0 = 220 \text{ }\frac{\text{km}}{\text{s}}$ and $v_{esc} = 480 \text{ }\frac{\text{km}}{\text{s}}$. The orange dashed line indicates the constraints from the DAMA unmodulated rate at 2 keV (requiring less than 1 count/day/kg/keV-- see Section \ref{['Sec:DAMAUnmod']}). The null results from XENON10, CDMS-Si and other direct detection experiments do not further constrain this parameter space for the DAMA fit.
• Figure 4: The parameter space in the mass/cross-section plane for the exoDM fit to DAMA (68%, 90% and 99% confidence level regions shaded in blue), with a mass splitting of $\delta=6\text{ keV}$ and assuming constant channeling fractions of 30% for both sodium and iodine. The halo model is Maxwell-Boltzmann with $v_0 = 220 \text{ }\frac{\text{km}}{\text{s}}$ and $v_{esc} = 480 \text{ }\frac{\text{km}}{\text{s}}$. The orange long-dashed, black short-dashed, red solid, green dot-dashed (dotted) and blue medium-dashed lines indicate respectively the constraints from the DAMA unmodulated rate at 2 keV, the DAMA unmodulated rate at 1.5 keV, the null results of CDMS (silicon), the null results at XENON10 for $\mathcal{L}_{eff} =$ .03 (.08), and the null results from the PICASSO experiment (see Section \ref{['Sec:Constraints']}). The CDMS and XENON10 bounds are at 95% confidence level, while the PICASSO curve is a conservative constraint in which we require the integrated rate from 2 to 5 keV to be less than 30 counts/day/kg. The red shaded region gives the parameter space to fit the CoGeNT excess at 90% C.L. assuming a constant 5% channeling fraction in germanium. The sharp cut-off of the DAMA fit region as the mass is increased is due to the leakage of the exponential tail of channeled iodine scatters into the modulation signal region as described in Section \ref{['Sec:Kinematics']}.
• Figure 5: The parameter space in the mass/cross-section plane for the elastic LDM (zero mass splitting) fit to DAMA (68%, 90% and 99% confidence level regions shaded in blue), assuming constant channeling fractions of 30% for both sodium and iodine. The halo model is Maxwell-Boltzmann with $v_0 = 220 \text{ }\frac{\text{km}}{\text{s}}$ and $v_{esc} = 480 \text{ }\frac{\text{km}}{\text{s}}$. The orange long-dashed, black short-dashed, red solid, and green dot-dashed (dotted) indicate respectively the constraints from the DAMA unmodulated rate at 2 keV, the DAMA unmodulated rate at 1.5 keV, the null results of CDMS (silicon), and the null results at XENON10 for $\mathcal{L}_{eff} =$ .03 (.08) (see Section \ref{['Sec:Constraints']}). The CDMS and XENON10 bounds are at 95% confidence level. The red shaded region gives the parameter space to fit the CoGeNT excess at 90% C.L. assuming a constant 5% channeling fraction in germanium.