Effect of Cosmic Neutrino Background on the Dark Matter Self-interaction via Neutrino force

TL;DR

The paper investigates how the cosmic neutrino background (CνB) modifies neutrino-mediated dark matter self-interactions for scalar and pseudoscalar portals. It derives the vacuum potential V_vac and the background potential V_bkg and shows that the CνB can screen the attractive vacuum interaction, particularly when m_nu ≲ m_chi ≲ T_CνB. By solving the nonrelativistic Schrödinger equation with a singular 1/r^5 potential (regularized by a cutoff R = 1/m_chi) and evaluating the Sommerfeld enhancement, the authors find that the background can suppress or erase annihilation enhancements and significantly alter the allowed parameter space for self-interactions. They also discuss UV completions and show that, while s-channel realizations can be severely constrained by SM decays and flavor bounds, t-channel realizations remain viable in portions of parameter space, making the scalar DM–neutrino framework a plausible route to address small-scale structure problems.

Abstract

Neutrino-pair exchange induces a neutrino force that can drive dark matter (DM) self-interactions and impact small-scale structure formation. In the presence of the cosmic neutrino background (C$ν$B), this force can be modified, with important consequences for DM phenomenology. We study the effect of the C$ν$B on neutrino forces, generated by the scalar and pseudoscalar interactions. We explore the significance of the background neutrino force on the scalar DM-neutrino portal model, including DM self-scattering and annihilation. Our results show that the interplay between attractive vacuum potential and repulsive background potential leads to a screening effect that varies across DM mass ($m_χ$) regimes, strongly affecting DM self-scattering in the DM mass $m_ν\lesssim m_χ\lesssim T_{C νB}$. Meanwhile, for DM annihilation, the screening completely vanishes the Sommerfeld Enhancement induced by the neutrino force. Overall, the C$ν$B substantially reshapes the viable coupling range for DM self-interactions while remaining compatible with current constraints, offering a pathway to small-scale structure problems.

Figures (13)

• Figure 1: Scalar DM self-scattering via double neutrino exchange.
• Figure 2: Magnitude of the vacuum potential $V^{s,p}_\text{vac}(r)$ (blue) and background potential $V^{s,p}_\text{bkg}(r)$ (orange) from both the scalar and the pseudoscalar interactions. The potential is plotted for $m_\chi = 10^{3}$ eV, $m_\nu = 10^{-6}$ eV, and $T = 1.7 \times 10^{-4}$ eV. The potential is in the relativistic limit ($T \gg m_\nu$) and the change in behavior is seen at $rm_{\chi} \sim 10^6$. In this limit, the scalar potential is the same as the pseudoscalar.
• Figure 3: Magnitude of the vacuum potential $V^{s,p}_\text{vac}(r)$ (blue), along with background potential $V^{s}_\text{bkg}(r)$ (orange) and $V^{p}_\text{bkg}(r)$ (green) from both the scalar and pseudoscalar interactions, respectively. The potential is plotted for $m_\chi = 10^{3}$ eV, $m_\nu = 0.05$ eV, and $T = 1.7 \times 10^{-4}$ eV. The potential is in the non-relativistic limit ($m_\nu \gg T$), showing the suppressed pseudoscalar potential compared to scalar
• Figure 4: Magnitude of the vacuum potential $V^{s,p}_{\text{vac}}(r)$ (blue) and background potential $V^{s,p}_{\text{bkg}}(r)$ (orange) from both the scalar and pseudoscalar interactions. The potential is plotted for $m_\chi = 10^{3}$ eV, $m_\nu = 10^{-6}$ eV, and $T = 10^4 \times T_0$. The potential is in the relativistic limit ($T \gg m_\nu$). In this limit, $V_{\text{vac}}$ is completely opposed to $V_{\text{bkg}}$ up to the short range.
• Figure 5: Multiple exchange of the neutrino/antineutrino pair, resulting in the ladder diagram.