[Paper Review] Effects of new long-range interaction: Recombination of relic Heavy neutrinos and antineutrinos

K. M. Belotsky, Maxim Khlopov+2 more|arXiv (Cornell University)|Apr 27, 2005

Neutrino Physics Research11 citations

TL;DR

This paper proposes that stable heavy neutrinos from the fourth fermion generation, if endowed with a new long-range U(1) gauge interaction (y-interaction), can form bound states (N-recombination) in the early Universe and later in galactic dark matter halos. These bound states annihilate efficiently, producing high-energy gamma rays that can account for the diffuse extragalactic gamma-ray background observed by EGRET, with a predicted flux matching data for a neutrino mass of ~50 GeV and fine-structure constant α_y ≈ 1/137.

ABSTRACT

If stable Heavy neutrinos of 4th generation possess their own Coulomb-like interaction, recombination of pairs of Heavy neutrinos and antineutrinos can play important role in their cosmological evolution and lead to observable consequences. In particular, effect of this new interaction in the annihilation of neutrino-antineutrino pairs can account for $γ$-flux observed by EGRET.

Motivation & Objective

• To investigate the cosmological impact of a new long-range U(1) gauge interaction (y-interaction) on stable heavy neutrinos from the fourth fermion generation.
• To assess whether neutrino-antineutrino recombination due to y-interaction can suppress relic density and produce observable high-energy gamma-ray emission.
• To determine if the resulting gamma-ray flux can explain the diffuse extragalactic gamma-ray background measured by EGRET.
• To evaluate the role of galactic dark matter clumps in enhancing N-recombination and gamma-ray production compared to homogeneous cosmological recombination.
• To explore theoretical consistency of the y-interaction, including anomaly freedom and unification with other gauge interactions in GUT models.

Proposed method

• Model the y-interaction as a U(1) gauge theory with a massless y-photon and y-charge, analogous to electromagnetism but specific to the fourth generation.
• Calculate the annihilation rate of neutrino-antineutrino pairs via y-photon emission (N N̄ → yy), using a cross-section scaling as τ_ann ∝ m²a_b³/α_y².
• Apply Sakharov enhancement via the Coulomb factor C₀ = 2πα_y/v to increase cross-sections for slow, non-relativistic neutrinos.
• Compute the relic number density of 4th neutrinos using the ratio r = n/s, accounting for y-interaction effects during freeze-out at T ≈ m/30.
• Model the formation of bound states (N-recombination) after decoupling from y-radiation, with annihilation timescale τ_ann ∝ m²a_b³/α_y².
• Estimate the gamma-ray flux from galactic halo clumps using I(E) = η·(B_Z⟨σv⟩/4π)f_γ(E)∫(ρ/m)²dl, with η ≈ 200–240 for m=50 GeV and α_y=1/137.

Experimental results

Research questions

• RQ1 Can a new long-range U(1) interaction (y-interaction) between 4th-generation heavy neutrinos and antineutrinos lead to significant N-recombination and annihilation in the early Universe?
• RQ2 To what extent does N-recombination suppress the relic density of stable heavy neutrinos compared to standard freeze-out?
• RQ3 Can the gamma-ray emission from N-recombination in galactic dark matter halos reproduce the high-energy diffuse extragalactic gamma-ray background observed by EGRET?
• RQ4 How sensitive is the predicted gamma-ray flux to variations in the y-interaction strength (α_y) and neutrino mass (m)?
• RQ5 What are the theoretical constraints on the y-interaction, such as anomaly freedom and unification with other gauge groups in GUT models?

Key findings

• The inclusion of y-interaction increases the annihilation rate of 4th-generation neutrino-antineutrino pairs during freeze-out, reducing their relic density by a factor of 2–10.
• N-recombination leads to efficient annihilation of bound neutrino-antineutrino pairs, with annihilation timescale τ_ann ∝ m²a_b³/α_y², making it a dominant suppression mechanism.
• For a neutrino mass of 50 GeV and α_y = 1/137, the predicted gamma-ray flux from galactic halo clumps matches the high-energy diffuse extragalactic background observed by EGRET with an enhancement factor η ≈ 200.
• A slightly larger α_y = 1/30 requires η ≈ 240 to match EGRET data, indicating weak dependence of the flux on α_y due to the dominant role of B_Z(α_y) and resonance effects near m ≈ 46 GeV.
• The model predicts that the contribution from N-recombination in galactic clumps dominates over homogeneous cosmological recombination, especially in the high-energy gamma-ray band.
• Theoretical consistency requires anomaly-free y-charge assignments (e.g., e_yN = e_yE = -e_yU/3 = -e_yD/3) and possible extensions like SUSY or E₆ GUTs to avoid gauge anomalies and mixings.