Leptogenesis and Dark Matter in an Inverse Seesaw from gauged B-L breaking

TL;DR

The paper presents a coherent framework where a low-scale Inverse Seesaw is realized through a gauged and dynamically broken $U(1)_{B-L}$, with anomaly cancellation introducing a dark sector that includes a stable DM candidate and a massless partner contributing to dark radiation. The DM is produced via freeze-in through the $Z'$ mediator in a regime of feeble gauge coupling, while ARS leptogenesis remains viable due to suppressed thermalization of heavy neutral leptons. The analysis integrates dark matter abundance calculations, dark radiation constraints ($N_{ m eff}$), and leptogenesis requirements to delineate a predictive parameter space that is testable with future cosmic surveys and intensity-frontier experiments like SHiP, albeit with challenging direct-detection prospects. A notable feature is the potential dilution of $N_{ m eff}$ from late decays of heavy neutrinos, which can widen the experimentally accessible regions, highlighting the model’s rich interplay between cosmology and laboratory probes.

Abstract

We study a dynamical realization of the low-scale Inverse Seesaw mechanism in which the approximate $B-L$ symmetry is gauged and spontaneously broken. Anomaly cancellation requires additional chiral fermions, one of which becomes a stable dark matter candidate after symmetry breaking, while another remains massless and contributes to dark radiation. Focusing on the regime of feeble gauge interactions, we compute the dark matter relic abundance produced via the freeze-in mechanism through the $B-L$ gauge boson and identify the parameter space consistent with cosmological and laboratory constraints. We show that the same region naturally avoids thermalization of heavy neutral leptons, preserving the viability of ARS leptogenesis. The interplay between dark matter production, dark radiation constraints, and leptogenesis requirements leads to a predictive scenario where future cosmological surveys and intensity-frontier experiments such as SHiP can probe significant portions of the viable parameter space.

Figures (8)

• Figure 1: First and second rows represent the main DM production channels: s-channel for (a) SM fermion, (b) Higgs doublet, and (c) massless fermion $\omega$; and (d) $Z'$ annihilation through $t$-, $u$-, and $s$-channel processes. Diagrams (e) and (f) represent the dominant production channels for the mediator via, respectively, top quark pair annihilation into $Z'$ and $H$, and fermion annihilation into $Z'$ and a gauge boson $V = B, W$ (before EWSSB), or $V = \gamma$ (after EWSSB). Crossed-channel contributions are not shown. The last diagram illustrates the production or annihilation of $\omega$'s through an $s$-channel $Z'$ mediator. Vertex color code indicates coupling strengths: blue scales with $g_{\scaleto{B-L}{5pt}}$, purple with $\lambda_{1H}$, pink with the DM Yukawa coupling $y_\chi$, and green with SM couplings.
• Figure 2: The upper panel shows the yields of the dark sector species: ${ \textcolor{myblue}{Y_{\rm DM} } }$ (solid blue), ${ \textcolor{myred}{Y_{\omega} } }$ (solid red), and ${ \textcolor{mygreen}{Y_{Z'} } }$ (solid green), as a function of $x$ (lower x-axis) and temperature $T$ (upper x-axis). The masses were fixed to $m_\chi = 400 \,\mathrm{GeV}$ and $m_{Z'} = 3 \,\mathrm{GeV}$, and the gauge coupling is chosen to reproduce the observed DM relic abundance. Dashed lines represent the corresponding equilibrium yields. The lower panel presents the rates, normalized to the Hubble rate, of the processes that govern the evolution of the yields: DM production via fermion annihilation (light blue) and $Z' Z'$ annihilation (purple), $Z'$ production (light green), $\omega$ coalescence (orange), and $Z' \to \omega \bar{\omega}$ decays (dashed yellow). The black cross indicates the moment when the massless fermion $\omega$ freezes out.
• Figure 3: Left: region of the $g_{\scaleto{B-L}{5pt}}-m_{Z'}$ plane reproducing the observed DM relic abundance for DM masses in the $(400, 10^5)$ GeV range. The red shaded area shows current bounds from $\Delta N_{\rm eff}$, including how it could be relaxed due to the dilution from HNL decays (see Sec. \ref{['sec:Neff']}), while the dashed line represents future prospects. Right: gauge coupling $g_{\scaleto{B-L}{5pt}}$ as a function of the scalar mixing $\lambda_{1H}$ that reproduces the observed DM relic abundance, for three different mediator masses and fixed values of $m_\chi$ and $\lambda_1$.
• Figure 4: Parameter space where the $Z'$ mediator and HNLs thermalize with the SM plasma above or near the electroweak phase transition ($T\gtrsim 140\,{\rm GeV}$), spoiling ARS leptogenesis. The change in slope of the dashed $Z'$ line corresponds to the kinematical threshold of the coalescence channel $f\bar{f}\to Z'$, whereas the change in the solid $N_i$ lines corresponds to the threshold for the decay $Z'\to N_i \bar{N}_i$. We also show the region in which the DM abundance can be generated via freeze-in when gauge interactions dominate its production.
• Figure 5: Main diagrams contributing to the thermalization of the heavy neutrinos $N$ when $Z'$-decays are kinematically forbidden. The $s$-channel process $Z'Z'\to\varphi_2\to \bar{N}N$ is suppressed with respect to the above diagrams by the very small $\varphi_1-\varphi_2$ mixing.