Nuclear Production and Analytic Attenuation of Energetic MeV Solar Dark Matter

TL;DR

The paper addresses the challenge of detecting sub-GeV dark matter by proposing a solar-origin mechanism that yields MeV-scale DM from the Sun's $pp$-chain fusion, specifically via $p+d \to {}^3{\rm He}+\chi^*\chi$ with a $5.5\,\mathrm{MeV}$ energy release. It introduces a three-stage framework: solar production, solar attenuation, and Earth-based detection, and develops a three-dimensional analytic Boltzmann formalism to accurately propagate and attenuate the DM flux inside the Sun, linking DM production to photon production through $S$-factors. The work provides explicit expressions for the production rate, derives an attenuation-driven flux at Earth, validates the approach against Monte Carlo simulations, and forecasts the detection prospects for DarkSide-LowMass, showing sensitivity to $10^{-35}\ \mathrm{cm}^2 \lesssim σ_{χp}^{LO} \lesssim 4\times10^{-34}\ \mathrm{cm}^2$ in the sub-MeV regime. It also discusses cosmological constraints, notably BBN, and the role of dilution in ensuring viability, suggesting that the solar DM channel offers a complementary and potentially detectable probe of light DM with MeV-scale energies. Overall, the paper demonstrates a novel solar-produced DM pathway and a practical detection strategy for next-generation low-threshold experiments.

Abstract

We propose a solar production mechanism of MeV dark matter to overcome the energy threshold in direct detection experiments. In particular, the proton and deuteron fussion to ${}^3 \mathrm{He}$ of the $pp$ chain that produces energetic neutrino and gamma photon with 5.5$\,$MeV of energy release can also produce a pair of dark matter particles. Besides, we establish an analytical formalism of using the Boltzmann equation to study the solar attenuation effect on the produced dark matter flux. The projected sensitivity is illustrated with Argon target at the DarkSide-LowMass experiment.

Figures (5)

• Figure 1: Schematic illustration of the production, attenuation and detection of energetic solar DM.
• Figure 2: The ratio of the DM and photon production $S$-factors for the $p$-$d$ fusion.
• Figure 3: Illustration of the geometric meaning of $x$ and $y$. $x'$ denotes the integration variable in the integral equation form of the Boltzmann equation. $-x_0$ is on the solar surface.
• Figure 4: The solar DM flux spectrum arriving at Earth for $m_\chi = 1\, \mathrm{MeV}$ and $\sigma_{\chi p}^{\mathrm{LO}} = 10^{-34} \, \mathrm{cm}^2$. The red curve is from the analytic Boltzmann equation method while the black curve is from Monte Carlo simulation based on DarkPropDarkProp:v0.3. The blue dashed curve is obtained assuming no attenuation.
• Figure 5: The projected exclusion regions for the solar DM parameter space at DarkSide-LowMass with a ${}^{39} \mathrm{Ar}$ background level of $73\,\mu \mathrm{Bq/kg}$ (red) or $7.3\,\mu \mathrm{Bq/kg}$ (blue). For comparison, the exclusion limits from PandaX PandaX-II:2021kai and Super-Kamiokande Super-Kamiokande:2022ncz on the cosmic-ray boosted DM, SENSEI SENSEI:2023zdf, as well as the BBN constraint are also shown.