Opening the Parameter Space of sub-GeV Inelastic Dark Matter through Parity Violation

TL;DR

Sub-GeV inelastic DM can evade indirect-detection constraints through parity-violating interactions that induce small diagonal couplings. The authors develop a framework combining the Boltzmann equation for the excited-state fraction with a detailed treatment of dark-sector temperature evolution to determine the relic fraction and excited-state abundance, showing that parity violation opens large regions of parameter space previously excluded. They project that forthcoming experiments like LDMX can probe much of this space, and the approach is readily applicable to other exothermic sub-GeV DM scenarios. Overall, the work demonstrates that parity-violating inelastic DM is a compelling, testable framework for light DM with distinctive up/down-scattering dynamics and observable consequences.

Abstract

Sub-GeV dark matter (DM) has emerged as a particularly compelling target in light of the persistent null results from conventional DM searches. While s-wave annihilating DM candidates with masses below the GeV are strongly constrained by indirect-detection bounds, inelastic scenarios can naturally evade these limits. In this work, we show that parity violation can play an important role in inelastic DM models featuring long-lived excited states by inducing small diagonal couplings that significantly relax experimental constraints. A precise determination of the excited-state abundance is essential for assessing the phenomenology of such models. To this end, we solve the integrated Boltzmann equation, fully accounting for up- and down-scattering with electrons and positrons as well as dark-sector conversion processes. Using the resulting abundance, we update the viable parameter space in light of the most recent experimental constraints and demonstrate that parity-violating interactions can reopen broad regions of parameter space that would otherwise be excluded. Moreover, the forthcoming LDMX experiment will probe a significant portion of the parameter space. The framework developed in this work can be readily applied to other exothermic sub-GeV DM scenarios.

Figures (12)

• Figure 1: Contours of the excited-state lifetime $\tau_\ast \times(\alpha' \epsilon^2)$ are shown as colored lines, computed using the approaches of Ref. Batell:2009vb (solid) and Ref. Bernal:2017mqb (dashed). For the small mass splittings considered ($\delta / m_{\chi} \ll 1$), we have $\alpha' \simeq \alpha'_{\rm inel}$, and the results are effectively independent of $\delta_y$. The horizontal solid black line marks the value of $\delta$ below which the decay into neutrinos, $\chi^\ast \to \chi 2\nu$, dominates, while above the decay into photons $\chi^\ast \to \chi 3\gamma$ becomes dominant (and similarly for the horizontal dashed line). Note that kinetic mixing values in the range $\epsilon \sim 10^{-6}$--$10^{-4}$ are typically required to reproduce the observed DM relic abundance via standard thermal freeze-out, assuming benchmark choices of $\alpha' \sim 0.1- 0.5$ and $m_{A'} \simeq 3 \,m_\chi$, for the DM masses considered in this work---see \ref{['fig:relicAbundance']}.
• Figure 2: Key processes governing number evolution and state populations: (a) Annihilation and coannihilation into SM electrons and positrons; (b) DM–electron/positron inelastic scattering; Dark sector self-scatterings and conversions in $s$-channel (c) and $t$-channel (d).
• Figure 3: Thermal targets ($\Omega h^2 \simeq 0.12$Planck:2018vyg) for the benchmark choices $\alpha'=0.1$ (left) and $\alpha'=0.5$ (right) with $m_{A'}=3m_{\chi}$. We show results for both parity-conserving $\delta_y=0$ (dashed) and parity-breaking $\delta_y\gg1$ (solid) (not-so-)inelastic DM models for various mass splittings $\delta = \{10\text{ keV},\, 100\text{ keV},\, 500\text{ keV},\, 1\text{ MeV}\}$ in different colors.
• Figure 4: Evolution of the ratio between the relevant rates and the Hubble parameter, $\Gamma/H$ (upper panels), and of the excited-state fraction $f$ (lower panels) as a function of $x \equiv m_\chi/T_{\rm SM}$. Here, $\gamma_{\chi^\ast e^\pm \to \chi e^\pm}$ denotes the momentum exchange rate (see \ref{['eq:transf_momenta']}). The left panel corresponds to $\delta_y = 0$, where only off-diagonal (inelastic) interactions are present, while the right panel shows the maximal parity-violating case $\delta_y \gg 1$, in which diagonal processes are also active. The parameters are fixed as follows: $m_\chi = 10~\text{MeV}$, $\delta = 100~\text{keV}$, $\alpha' = 0.5$, $m_{A'}=3m_\chi$ and $\epsilon$ is chosen to reproduce $\Omega_{\rm obs} h^2$. Note that we do not include $\chi^\ast$ decay processes, as they are suppressed.
• Figure 5: Contours of the fraction of excited states at the freeze-out of $\chi^\ast\leftrightarrow\chi$ conversion processes ($f_0$) in the plane of mass splitting $\delta$ and DM mass $m_\chi$ (top) as well as in the plane of the dark fine-structure constant $\alpha'$ and DM mass $m_\chi$ (bottom). The solid translucent (dashed opaque) lines correspond to parity-violating (-conserving) interactions. The top left (top right) panel corresponds to $\alpha'=0.1$ ($\alpha'=0.5$), while the bottom left (bottom right) to $\delta=100$ keV ($\delta=500$ keV). At each point, the value of the kinetic mixing $\epsilon$ is such that the DM relic abundance is reproduced. Additionally, we take $m_{A'}=3m_\chi$.