Technical Summary: CMB Limits on the Absorption of Light Vector and Axial-Vector Dark Matter

Problem Statement

The fundamental nature of dark matter (DM) remains an open question in cosmology and particle physics. While terrestrial and astrophysical searches have placed stringent bounds on DM interactions with Standard Model (SM) particles, cosmological observations offer a complementary probe, particularly for light DM candidates. This work focuses on sub-MeV spin-1 (vector and axial-vector) DM candidates that couple trilinearly to electrons (leptophilic DM).

In these models, tree-level decay into electron-positron pairs is kinematically forbidden for $m_{\text{DM}} \lesssim m_e$, and loop-induced decay into two photons is forbidden by angular momentum conservation. Consequently, the dominant energy injection mechanisms into the primordial plasma are distinct from the annihilation or decay channels typically studied. Instead, the relevant processes involve the conversion of DM into SM radiation via interactions with electrons:

1. Inelastic scattering: DM converts into a photon via scattering with a free electron ($V/A + e^- \to \gamma + e^-$).
2. Absorption: DM is absorbed by a bound atomic electron in neutral hydrogen, leading to ionization ($V/A + \text{H} \to p^+ + e^-$), analogous to the photoelectric effect.

The paper addresses the lack of constraints on these specific conversion channels using Cosmic Microwave Background (CMB) anisotropies, specifically for DM masses between 100 eV and 100 keV.

Methodology

The authors employ a multi-step computational framework to derive constraints on the DM-electron coupling constants ($g_{V\bar{e}e}$ and $g_{A\bar{e}e}$):

1. Cross Section Derivation:

   • Analytic expressions for the inelastic scattering cross sections ($\sigma_{V/A \, e^- \to \gamma e^-}$) are derived at tree level, expanded in the non-relativistic limit ($v_r \ll 1$).
   • Cross sections for hydrogen ionization via DM absorption ($\sigma_{V/A + \text{H} \to p^+ e^-}$) are calculated using the atomic form factor formalism. The authors compute the atomic form factors $Q_{V/A}(\epsilon)$ numerically using the Flexible Atomic Code (FAC), accounting for contributions from bound states (primarily the ground state $1S_{1/2}$) and continuum states.
   • The authors note that for the mass range considered ($m_{\text{DM}} \gg 13.6$ eV), the form factors are in the suppressed tail of the ionization response, with the axial-vector case exhibiting a sharper peak and less numerical noise due to monopole dominance compared to the dipole dominance in the vector case.

2. Energy Injection and Deposition:

   • The energy injection rates into the primordial plasma are calculated for both channels. For inelastic scattering, the injection includes both a photon and a "kicked" electron, with energies determined by momentum conservation. For absorption, the energy is assumed to be carried entirely by the outgoing electron.
   • The DarkHistory code (v2.0) is modified to include these specific conversion channels. This code computes the energy deposition functions $f_c(z)$, which describe the fraction of injected energy deposited into various channels (hydrogen/helium ionization, Lyman-$\alpha$ excitation, heating, and continuum photon production) as a function of redshift.

3. Cosmological Analysis:

   • The modified DarkHistory outputs are interfaced with the cosmological Boltzmann solver CLASS.
   • Markov Chain Monte Carlo (MCMC) analyses are performed using MontePython against Planck 2018 data (temperature, polarization, and lensing power spectra).
   • The analysis is conducted for three scenarios: DM absorption only, DM inelastic scattering only, and the combined effect of both channels.
   • Constraints are derived for discrete DM masses ($100$ eV, $1$ keV, $10$ keV, $100$ keV) and interpolated.

Key Contributions

• First CMB Constraints on Conversion Channels: This is the first study to quantify the impact of DM absorption and inelastic scattering (conversion to photons) on CMB anisotropies for sub-MeV vector and axial-vector DM.
• Dual-Channel Analysis: The work distinguishes between two distinct physical regimes:
  • High Mass ($m_{\text{DM}} \gtrsim 1$ keV): Inelastic scattering with free electrons dominates the constraints. The atomic form factor suppression makes hydrogen absorption negligible in this regime.
  • Low Mass ($m_{\text{DM}} \lesssim 1$ keV): Hydrogen absorption becomes the leading channel. This is driven by the reduced suppression of the atomic form factor at lower energies and the higher efficiency of post-recombination energy injection in modifying the free-electron fraction.
• Vector vs. Axial-Vector Comparison: The paper provides separate constraints for vector and axial-vector couplings, noting that axial-vector constraints are slightly stronger at sub-keV masses due to the enhancement of the corresponding atomic form factor.
• Implementation in DarkHistory: The authors extend the DarkHistory code to handle DM conversion processes where the injected particles are a photon and an electron (or just an electron), differing from standard decay/annihilation scenarios.

Results

Using Planck 2018 data, the authors derive 95% confidence level (C.L.) upper limits on the dimensionless DM-electron coupling constants:

• Mass Dependence: The constraints are approximately mass-independent for $m_{\text{DM}} \gtrsim 1$ keV (dominated by inelastic scattering). At lower masses, the constraints weaken as the hydrogen ionization channel becomes less efficient relative to the thermalization threshold, though it remains the dominant constraint mechanism in that regime.
• Magnitude: The derived bounds are approximately 8 to 9 orders of magnitude weaker than existing laboratory limits (e.g., XENON, DarkSide) and astrophysical limits (e.g., stellar cooling, INTEGRAL).
• Thermalization Tension: The authors note that the couplings constrained by this work lie 1–3 orders of magnitude above the threshold required to thermalize DM with the SM plasma prior to Big Bang Nucleosynthesis (BBN). This implies that a minimal scenario with constant DM properties is inconsistent with the non-thermal production assumption. The paper suggests that mechanisms such as a dark-sector phase transition or in-medium suppression (kinetic mixing) are required to reconcile these bounds with BBN constraints.

Significance and Claims

The paper positions its results as a robust and independent cosmological probe of leptophilic DM interactions. While the limits are weaker than direct detection or astrophysical bounds, they rely exclusively on cosmological observables (CMB anisotropies) and do not depend on assumptions regarding laboratory detector efficiencies or stellar modeling.

The authors emphasize that:

1. CMB anisotropies remain a sensitive probe for leptophilic DM even in scenarios where the dominant energy injection is not decay or annihilation, but rather conversion processes.
2. These constraints provide the only limits in the sub-MeV mass regime that are derived solely from cosmological data.
3. The work complements previous constraints on scalar and pseudo-scalar DM (where loop-induced two-photon decay was dominant), demonstrating that CMB anisotropies can constrain spin-1 candidates even in the absence of loop-induced photon decays.

The paper concludes that while the derived bounds do not currently challenge existing laboratory limits, they establish a necessary baseline for cosmological consistency and offer a unique window into DM interactions that are otherwise inaccessible to terrestrial experiments in this specific mass and coupling regime.