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

This paper demonstrates that the Cosmic Neutrino Background significantly alters dark matter self-interactions mediated by neutrino forces through a screening effect arising from the interplay of vacuum and background potentials, thereby reshaping viable coupling ranges and suppressing Sommerfeld enhancement for dark matter annihilation.

The Gist

Imagine the universe is filled with a vast, invisible ocean. Most of us think of this ocean as being made of empty space, but according to this paper, it's actually teeming with ghostly particles called neutrinos. These are the "Cosmic Neutrino Background" (CνB), a leftover soup from the Big Bang that permeates everything.

The paper asks a simple question: How does this ghostly ocean affect the behavior of Dark Matter?

Dark Matter is the invisible stuff that holds galaxies together. Scientists have been puzzled because, on small scales (like inside individual galaxies), the standard theory of Dark Matter doesn't quite match what we see in telescopes. One popular idea to fix this is Self-Interacting Dark Matter (SIDM)—the idea that Dark Matter particles bump into each other, like cars in traffic, rather than just passing through like ghosts.

Here is how the paper explains the new twist in this story, using simple analogies:

1. The Invisible Force Field

Usually, scientists thought Dark Matter particles could talk to each other by exchanging pairs of neutrinos. Think of this like two people on a frozen lake throwing a heavy ball back and forth. The act of throwing and catching creates a force that pulls them together.

• The Vacuum Force: In empty space (the "vacuum"), this neutrino exchange creates an attractive force. It's like a magnet pulling two Dark Matter particles together. This helps explain why galaxies have "soft" centers (solving the "core-cusp" problem).

2. The Ocean Gets in the Way

The paper introduces a new factor: the Cosmic Neutrino Background. Imagine that the two people on the frozen lake aren't just in empty air; they are standing in a dense, churning crowd of other invisible people (the background neutrinos).

• The Screening Effect: When the Dark Matter particles try to pull each other together using their neutrino "ball," the crowd of background neutrinos pushes back.
• The Result: The paper finds that this background crowd creates a repulsive force that acts like a shield. It effectively "screens" or cancels out the attractive magnetism between the Dark Matter particles.

3. The "Goldilocks" Zone of Mass

The paper discovers that this shielding effect only happens under specific conditions, depending on the "weight" (mass) of the Dark Matter particles:

• Heavy Dark Matter: If the Dark Matter particles are very heavy, they are like big, strong swimmers. The crowd of background neutrinos is too weak to stop them. They still feel the attractive force, and the old theories work fine.
• Light Dark Matter: If the Dark Matter particles are light (comparable to the temperature of the neutrino background), they are like tiny leaves in a storm. The background crowd completely overwhelms their attraction. The force between them vanishes.
• The "Just Right" Zone: There is a specific range of light masses where the background neutrinos perfectly cancel out the attraction. In this zone, the Dark Matter stops interacting with itself entirely.

4. What About "Sommerfeld Enhancement"?

In physics, sometimes forces can make particles collide and annihilate (destroy each other) much more efficiently than expected. This is called "Sommerfeld Enhancement."

• The Paper's Finding: The authors found that the background neutrino crowd acts like a "force field" that blocks this efficiency. It completely shuts down the enhancement. If Dark Matter is light enough to feel the background, it won't get that extra boost in collisions.

5. The Bottom Line

The paper concludes that the "Cosmic Neutrino Background" is a major player that we can't ignore.

• It changes the rules of the game for light Dark Matter.
• It forces scientists to rethink which models of Dark Matter are possible. If the Dark Matter is too light, the background neutrinos will hide its self-interactions, making it behave like "normal" non-interacting Dark Matter.
• However, for Dark Matter in a specific mass range, this screening effect actually helps solve the "core-cusp" problem (the mismatch between theory and observation) by adjusting how strongly the particles interact.

In summary: The universe isn't just empty space where Dark Matter particles float freely. It's a crowded room. If the Dark Matter particles are light, the crowd (the neutrino background) pushes them apart, canceling out the forces that were supposed to hold them together. This changes the map of where we should look for the solution to the universe's small-scale mysteries.

Technical Summary

Technical Summary: Effect of Cosmic Neutrino Background on Dark Matter Self-Interaction via Neutrino Force

Problem Statement
While the Lambda-Cold Dark Matter ($\Lambda$CDM) model successfully describes large-scale structure, it faces discrepancies on small scales, such as the "core-cusp," "missing satellite," and "too big to fail" problems. Self-Interacting Dark Matter (SIDM) offers a potential resolution by introducing non-gravitational forces. A specific mechanism involves DM self-interactions mediated by the exchange of light neutrino pairs, generating an effective potential. However, previous studies often neglected the presence of the Cosmic Neutrino Background (C$\nu$B). This paper investigates how the C$\nu$B modifies the neutrino-mediated force between scalar dark matter particles, specifically examining the interplay between the vacuum potential and the background potential, and its subsequent impact on DM self-scattering and annihilation phenomenology.

Methodology
The authors analyze a model where a CP-even complex scalar dark matter particle ($\chi$) interacts with massive Majorana neutrinos ($\nu$) via scalar ($G_s$) and pseudoscalar ($G_p$) contact interactions. The study proceeds through the following steps:

1. Potential Derivation:

   • Vacuum Potential ($V_{\text{vac}}$): Calculated from the double neutrino exchange diagram in a vacuum. The amplitude is derived using the optical theorem and Fourier transformed to coordinate space.
   • Background Potential ($V_{\text{bkg}}$): Calculated by modifying the neutrino propagator to include the C$\nu$B distribution (Fermi-Dirac distribution). The total amplitude is treated as the sum of vacuum and background contributions, where the background term arises from replacing one virtual neutrino leg with an on-shell neutrino from the background.
   • Regimes: The potentials are analyzed in both relativistic ($m_\nu \ll T$) and non-relativistic ($m_\nu \gg T$) limits, where $T$ is the C$\nu$B temperature.

2. Phenomenological Calculation:

   • Self-Scattering: The scattering cross-section is computed by solving the non-relativistic Schrödinger equation for the two-particle reduced system. The singular nature of the potential ($\sim 1/r^5$) at short distances is handled via Wilsonian renormalization, introducing a cutoff $R = m_\chi^{-1}$ and a flat potential $V_0$ for $r \leq R$.
   • Annihilation: The Sommerfeld enhancement factor ($S$) is calculated to determine the modification of the DM annihilation cross-section due to the neutrino force.
   • Parameter Space: The authors identify regions in the $(m_\chi, G_s)$ plane where the self-scattering cross-section per unit mass ($\sigma/m_\chi$) falls within the range $0.03 - 1 \, \text{cm}^2/\text{g}$, which is relevant for solving small-scale structure problems.

3. UV Completion and Constraints:

   • The effective operators are embedded into UV-complete models involving heavy fermions (s-channel) or heavy scalars (t-channel).
   • Constraints from Standard Model invisible decays ($Z \to \text{invisible}$, $h \to \text{invisible}$) and flavor-dependent leptonic kaon decays ($K^+ \to l^+ \chi \bar{N}$) are applied to the parameter space.

Key Results

• Screening Effect: A critical finding is the sign difference between the potentials. The vacuum potential $V_{\text{vac}}$ is attractive, while the background potential $V_{\text{bkg}}$ is repulsive in the relativistic limit ($m_\nu \ll T$) at intermediate ranges ($T^{-1} \ll r \ll m_\nu^{-1}$).
• Mass Hierarchy Dependence:
  • $m_\chi \lesssim T$: In regimes where the DM mass is comparable to or smaller than the C$\nu$B temperature, the repulsive background potential significantly screens the attractive vacuum potential. This leads to a reduction in the net interaction strength.
  • $m_\chi \gg T$: For heavier DM, the background effect is negligible, and the scattering behavior resembles the vacuum case.
• Impact on Self-Scattering: The screening effect shifts the viable parameter space for addressing the core-cusp problem toward larger coupling constants ($G_s$). Specifically, for $m_\chi \lesssim T$, the cancellation of potentials requires stronger couplings to achieve the necessary cross-sections.
• Impact on Annihilation: The C$\nu$B screening completely suppresses the Sommerfeld enhancement induced by the neutrino force in the annihilation channel. In the relativistic limit with high temperatures, the enhancement factor vanishes, rendering the neutrino force ineffective for boosting annihilation rates in these regimes.
• Scalar vs. Pseudoscalar: In the relativistic limit, scalar and pseudoscalar interactions yield indistinguishable parameter spaces. In the non-relativistic limit, pseudoscalar interactions are more suppressed due to the $m_\nu T^{-1}$ factor.
• UV Constraints:
  • For the s-channel mediator model, the inclusion of C$\nu$B effects shifts the preferred parameter space to larger couplings, which are subsequently ruled out by flavor-dependent constraints from kaon decays.
  • For the t-channel mediator model, the parameter space remains viable for $m_\chi \gtrsim T$, as the screening effect is negligible in this mass regime.

Significance and Claims
The paper claims that the Cosmic Neutrino Background substantially reshapes the phenomenology of neutrino-mediated self-interacting dark matter. The authors assert that the interplay between the attractive vacuum potential and the repulsive background potential creates a screening effect that is highly dependent on the mass hierarchy of the neutrino ($m_\nu$), dark matter ($m_\chi$), and the background temperature ($T$).

The study concludes that while the C$\nu$B can render DM self-interactions negligible or require significantly larger couplings in the low-mass regime ($m_\chi \lesssim T$), the scalar DM-neutrino framework remains a viable solution to small-scale structure problems (such as the core-cusp problem) for a broad range of DM masses, provided the model is consistent with current experimental constraints. The work highlights that neglecting the C$\nu$B can lead to incorrect conclusions regarding the viable coupling ranges and the magnitude of Sommerfeld enhancement in DM annihilation.