Momentum Dependent Dark Matter Scattering

TL;DR

This work shows that dark matter direct detection can be markedly altered if interactions are momentum dependent, dominated by operators beyond the standard spin-independent and spin-dependent forms when a GeV-scale mediator is present. The authors formulate a compact parameterization of the recoil rate, $dR_i^{\text{MDDM}}/dE_R=\left(q^{2}/q^{2}_{\text{ref}}\right)^{n}\left(\dfrac{q^{2}_{\text{ref}}+m^{2}_{\phi}}{q^{2}+m^{2}_{\phi}}\right)^{2}dR_i/dE_R$, with $n=1$ for $\mathcal{O}_1,\mathcal{O}_2$ and $n=2$ for $\mathcal{O}_3$, and $q^2_{\text{ref}}=(100\,\text{MeV})^2$. In the heavy mediator limit this reduces to a simple power law, but for a light mediator the spectra peak at nonzero recoil energy and can be substantially altered in both shape and normalization. Applying this framework to existing constraints, they find that momentum dependence can weaken low-threshold experiments and, in SD-proton scenarios with $q^4$ suppression, can open DAMA-compatible regions around $m_{\chi} \sim 40$–60 GeV (and down to ~10 GeV for very light mediators). They also discuss the necessary model-building ingredients and experimental bounds on light mediators, emphasizing that such momentum-dependent interactions offer a rich and testable expansion of direct detection phenomenology.

Abstract

It is usually assumed that WIMPs interact through spin-independent and spin-dependent interactions. Interactions which carry additional powers of the momentum transfer, q^2, are assumed to be too small to be relevant. In theories with new particles at the ~ GeV scale, however, these q^2-dependent interactions can be large, and, in some cases dominate over the standard interactions. This leads to new phenomenology in direct detection experiments. Recoil spectra peak at non-zero energies, and the relative strengths of different experiments can be significantly altered. We present a simple parameterization for models of this type which captures much of the interesting phenomenology and allows a comparison between experiments. As an application, we find that dark matter with momentum dependent interactions coupling to the spin of the proton can reconcile the DAMA annual modulation result with other experiments.

Figures (3)

• Figure 1: Germanium spectra plots with arbitrary normalization versus energy recoil for SI momentum dependent scattering of a 100 GeV dark matter mass. Plot a) displays the effect of additional powers of $q^2$ with $q^0,q^2,{\rm and\;} q^4$ in solid, long dash and short dash. Plot b) illustrates the effect of $m_\phi$ on the $q^4$ suppressed scenario with $m_\phi=(1,.1,.01)\; {\rm GeV}$ in solid, long dash and short dash.
• Figure 2: Plots of the SI nucleon cross section $\sigma_p$ vs DM mass $m_\chi$ without (a) and with $q^2$ suppression (b). The colored regions show the 68, 90, and 99% CL regions for the best DAMA fit. The 90% exclusions limits are KIMS (orange dashed), CDMS Si (red solid), CDMS Ge (red dotted) and XENON10 (brown dot-dashed). We have taken $f_p=f_{n}$.
• Figure 3: Plots of the SD-proton cross section $\sigma_p$ vs DM mass $m_\chi$ without (a) and with $q^4$ suppression (b) and (c), where the mediator mass is 1 GeV (b) and 100 MeV (c). The colored regions show the 68, 90, and 99% CL regions for the best DAMA fit. The 90% exclusions limits are PICASSO (gray solid), KIMS (orange dashed), XENON10 (brown dot-dashed), and CDMS (red dotted).