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Lepton parity dark matter and naturally unstable domain walls

Ernest Ma, Partha Kumar Paul, Narendra Sahu

Abstract

We propose a simple and predictive setup that connects neutrino masses, dark matter (DM), and gravitational waves. A minimal lepton parity DM scenario is considered where the residual symmetry $(-1)^L$ from the type I seesaw acts as the dark parity $D=(-1)^{L+2j}$, ensuring DM stability without imposing any new symmetry. A singlet Majorana fermion $S$ with even lepton parity serves as the DM candidate, interacting via a real scalar $σ$ which is also even lepton parity. The scalar potential possesses an accidental $\mathcal{Z}_2$ symmetry, whose spontaneous breaking gives rise to unstable domain walls (DW) in the presence of explicit $\mathcal{Z}_2$ breaking terms allowed by the lepton parity. The subsequent DW annihilation generates a stochastic gravitational wave (GW) background potentially observable at different GW experiments.

Lepton parity dark matter and naturally unstable domain walls

Abstract

We propose a simple and predictive setup that connects neutrino masses, dark matter (DM), and gravitational waves. A minimal lepton parity DM scenario is considered where the residual symmetry from the type I seesaw acts as the dark parity , ensuring DM stability without imposing any new symmetry. A singlet Majorana fermion with even lepton parity serves as the DM candidate, interacting via a real scalar which is also even lepton parity. The scalar potential possesses an accidental symmetry, whose spontaneous breaking gives rise to unstable domain walls (DW) in the presence of explicit breaking terms allowed by the lepton parity. The subsequent DW annihilation generates a stochastic gravitational wave (GW) background potentially observable at different GW experiments.

Paper Structure

This paper contains 6 sections, 42 equations, 6 figures, 1 table.

Table of Contents

  1. LEPTON PARITY $(-1)^L$ IDENTIFIED AS DARK PARITY, $D=(-1)^{L+2j}$
  2. SCALAR MIXING
  3. DOMAIN WALL FROM $\mathcal{Z}_2$ SYMMETRY BREAKING AND PRODUCTION OF GRAVITATIONAL WAVES
  4. THERMALLY AVERAGED CROSS-SECTION
  5. DECAY WIDTH OF THE SCALAR
  6. EVOLUTION OF DARK MATTER RELIC AND INTERACTION RATES FOR BP2, BP3, AND BP4

Figures (6)

  • Figure 1: Left: Cosmological evolution of the DM ($S$) and the singlet scalar ($\sigma$) with respect to $z=M_\sigma/T$ for BP1 as mentioned in Table \ref{['tab:tab1']}. The blue dashed line represents the equilibrium abundance of $\sigma$, and the blue solid line represents the actual abundance of $\sigma$. The DM abundance is shown with the red solid line mentioned in the figure. The gray dashed line represents the correct relic of DM. Right: Comparison of the interaction rates of different processes involved in the BE with the Hubble is shown with different colors as mentioned in the inset of the figure.
  • Figure 2: GW spectrum is shown for BP1, BP2, BP3 and BP4 as mentioned in Table \ref{['tab:tab1']}. The sensitivities from different GW experiments are shown with different colored lines.
  • Figure 3: Allowed values of $\mu_1$ and $\mu_2$ which give the chosen $T_{\rm ann}$ as mentioned in Table \ref{['tab:tab1']} for four BPs.
  • Figure 4: Left: Cosmological evolution of the DM, $S$ and the singlet scalar, $\sigma$ with respect to $z=M_\sigma/T$ for BP2 as mentioned in Table \ref{['tab:tab1']}. Right: Comparison of the interaction rates of different processes is shown with different colors as mentioned in the inset of the figure.
  • Figure 5: Left: Cosmological evolution of the DM, $S$ and the singlet scalar, $\sigma$ with respect to $z=M_\sigma/T$ for BP3 as mentioned in Table \ref{['tab:tab1']}. Right: Comparison of the interaction rates of different processes is shown with different colors as mentioned in the inset of the figure.
  • ...and 1 more figures