Exploring Leptogenesis, WIMP Dark Matter, and Gravitational Waves in an extended Scalar Framework

TL;DR

This work develops a unified framework that links neutrino mass generation, leptogenesis, and dark matter within an extended type-I seesaw model featuring a scalar mediator $\Phi$ and a complex DM field $S$ under a $\mathcal{Z}_4\times CP$ symmetry. Neutrino masses arise from a dimension-5 operator generated after $\Phi$ acquires a VEV, while leptogenesis proceeds via RHN decays and $N_i\Phi$-driven scatterings at a high symmetry-breaking scale $v_{\phi}$, with $v_{\phi} \gtrsim 10^9$ GeV ensuring the observed BAU. The model also predicts domain-wall formation and annihilation, producing a stochastic gravitational-wave background whose peak features depend on $v_{\phi}$, $v_s$, and the domain-wall tension $\sigma$, offering a novel cosmological probe. The DM sector exhibits WIMP-like phenomenology with an induced VEV for one component of $S$, yielding two distinct relic-density behaviors ( Case-I and Case-II) and connecting direct-detection prospects to the scalar mixing and induced-VEV dynamics, all while remaining testable through future GW experiments and collider studies.

Abstract

We explore extensions of type I seesaw framework with a scalar mediator ($Φ$) connecting to a complex scalar dark field ($S$), and right handed neutrinos ($N_i$), with an aim to correlate neutrino mass generation, leptogenesis, and dark matter. $\mathcal{Z}_4\times CP$ turns out to be a phenomenologically viable choice of the extended symmetry, which can accommodate a dimension five effective interaction $\bar{l}_L^α\tilde{H}ΦN_i$, involving the SM lepton isodoublet ${l}_L$, and Higgs $H$; prohibiting the canonical Yukawa term $\bar{l}_L^α\tilde{H} N_i$. The $\mathcal{Z}_{4}$ symmetry is spontaneously broken via the vacuum expectation value (VEV) of the $Φ$ filed, which directly affects neutrino mass generation and leptogenesis; while the $CP$ symmetry stabilises one component of $S$, making it a viable dark matter candidate. The discrete symmetry breaking creates domain wall, which needs to be annihilated before the over-closure of the Universe. This paves the way for gravitational wave signal associated with the model set up, which probes the symmetry breaking scale, and indirectly connects to the other phenomena.

Figures (11)

• Figure 1: Various tree and one-loop diagrams that contribute to the CP asymmetry parameters $\varepsilon_D$ and $\varepsilon_S$.
• Figure 2: Left: Plot for total lepton asymmetry $|Y_{\Delta L}|$ for different $v_{\phi}$ values. The dashed gray line indicates the correct lepton asymmetry necessary to create the observed baryon asymmetry. Right: Plot for total lepton asymmetry $|Y_{\Delta L}|$ for different $M_1$ values.
• Figure 3: Variation of the DM relic density with DM mass ($M_{s_1}$) for two cases of our interest, case-I: large $v_s$ on let left, and case-II: small $v_s$ on the right. We also varied the parameter $v_{s}$ for both cases, shown by red, green and blue representing increasing values of $v_{s}$. Parameters kept fixed are mentioned in the heading and inset.
• Figure 4: Plots for relic density as a function of DM mass are shown for different ranges of $M_{\mathbf{s}_{2}^{}}$. The upper row illustrates case-I, with the left (right) panel corresponding to $v_{s}^{}= 40 (200)$ TeV. The lower row represents case-II, with the left (right) panel corresponding to $v_{s}^{}= 0.3 (1)$ TeV.
• Figure 5: Plots for parameter space in the $M_{\mathbf{s}_{1}^{}}-M_{\mathbf{s}_{2}^{}}$ plane satisfying the observed DM relic ($\rm\Omega_{DM}h^{2}=0.1200\pm 0.0012$) for case-I and case-II. The left panel plot corresponds to case-I with $v_{s}^{}=40$ TeV (represented by blue points) and $v_{s}^{}=200$ TeV (represented by magenta points). The right panel plot corresponds to case-II with $v_{s}^{}=0.3$ TeV (represented by blue points) and $v_{s}^{}=1$ TeV (represented by magenta points).