When inverse seesaw meets inverse electroweak phase transition: a novel path to leptogenesis

1. Problem Statement

The observed Baryon Asymmetry of the Universe (BAU), $Y_B \approx 8.58 \times 10^{-11}$, remains unexplained by the Standard Model (SM). Leptogenesis is a leading solution, typically involving the out-of-equilibrium decay of heavy Right-Handed Neutrinos (RHNs). However, traditional thermal leptogenesis faces challenges at the TeV scale:

• Thermal Washout: At temperatures near the electroweak scale, inverse decays and scattering processes tend to erase any generated lepton asymmetry.
• Sphaleron Efficiency: In a standard direct Electroweak Phase Transition (EWPT), the transition goes from a symmetric phase ($\langle h \rangle = 0$) to a broken phase ($\langle h \rangle \neq 0$). The interior of the bubbles is the broken phase where sphaleron processes are suppressed, preventing the conversion of lepton asymmetry into baryon asymmetry.
• Nonthermal Production: While cosmic first-order phase transitions (FOPTs) can produce heavy particles nonthermally, standard EWPTs do not support the necessary conditions (active sphalerons inside bubbles) for successful leptogenesis.

2. Methodology and Model Construction

The authors propose a nonthermal leptogenesis mechanism triggered by a cosmic first-order inverse EWPT, realized by extending the SM with two generations of Vector-Like Leptons (VLLs).

The Model

• First Generation of VLLs (Inverse EWPT Trigger):

  • Consists of a vector-like doublet $F$, a singlet $N$, and a singlet $E$.
  • These particles have TeV-scale masses ($\sim 1$ TeV) and large Yukawa couplings to the Higgs.
  • Mechanism: As the universe cools, the thermal corrections from these heavy VLLs modify the Higgs effective potential. Unlike the standard scenario where symmetry is restored at high $T$, here the VLLs induce a potential barrier that causes the Higgs VEV to transition from a non-zero value ($\langle h \rangle = v_{n1}$) back to zero ($\langle h \rangle = 0$) at $T_{n1} \sim 200$ GeV. This is an Inverse EWPT.
  • Dynamics: The transition is not supercooled. However, because SM particles lose mass upon entering the bubble (where $\langle h \rangle = 0$), the bubble walls expand at relativistic velocities ($v_w \approx 1$, $\gamma_w \sim 10^2$).

• Second Generation of VLLs (Inverse Seesaw & Leptogenesis):

  • Consists of heavier VLLs ($F', N', E'$) with masses $\sim 4$ TeV.
  • They are embedded into the Inverse Seesaw Mechanism to explain small neutrino masses.
  • Mass Hierarchy: $m'_{E} > m'_{F} > m'_{N} \sim 4$ TeV.
  • Couplings: The couplings to SM leptons are constrained by neutrino data, but the coupling between the charged singlet $E'$ and SM leptons ($\lambda_D$) can be relatively large ($\mathcal{O}(0.1)$) without violating constraints.

Leptogenesis Mechanism

1. Production: During the expansion of the inverse EWPT bubbles, SM left-handed leptons ($\ell_L$) scatter off the relativistic bubble walls. Due to the large Lorentz boost ($\gamma_w$), these leptons gain sufficient energy to transition into the heavy charged VLLs ($E'$) via the $\lambda_D$ coupling.
2. Cascade Decay: The produced $E'$ particles rapidly decay into $F'$, which subsequently decay into the lightest neutral VLLs ($N'$).
3. CP-Violating Decay: The $N'$ states (which act as RHNs) decay into SM leptons and Higgs bosons. Because the transition occurs in the EW-symmetric vacuum ($\langle h \rangle = 0$) inside the bubbles, the sphaleron processes remain active, efficiently converting the generated lepton asymmetry into baryon asymmetry.
4. Suppression of Washout: The heavy mass of the second-generation VLLs ($m'_{N} \sim 4$ TeV) ensures that the ratio $m'_{N}/T_{n1} \gtrsim 20$. This suppresses the thermal washout (inverse decay) that would otherwise destroy the asymmetry.

3. Key Contributions

• Inverse EWPT for Leptogenesis: The paper identifies and utilizes an inverse EWPT (transition from broken to symmetric phase) as the unique environment where bubble-assisted leptogenesis can succeed. This solves the "sphaleron inactivity" problem inherent in standard direct EWPTs.
• Two-Generation VLL Architecture: The authors demonstrate that a single generation of VLLs cannot simultaneously satisfy the requirements for a strong inverse EWPT and successful leptogenesis (due to conflicting mass/coupling constraints). They introduce a two-generation model where the first generation drives the phase transition and the second generates the asymmetry.
• Inverse Seesaw Advantage: By employing the inverse seesaw mechanism rather than the Type-I seesaw, the authors enhance the decay width of the RHNs relative to their annihilation cross-sections. This is crucial because, at the TeV scale, annihilation often dominates over decay, which would prevent asymmetry generation.
• Nonthermal Production via Boosted Scattering: The mechanism relies on the production of heavy particles via scattering with relativistic bubble walls, bypassing the Boltzmann suppression that would prevent thermal production of 4 TeV particles at 200 GeV.

4. Results

• Parameter Space: The authors performed a numerical scan over the model parameters.
  • Inverse EWPT: Successfully realized with first-generation VLL masses in the range $[0.8, 1.5]$ TeV and large Yukawa couplings.
  • Leptogenesis: Successful generation of the observed BAU ($Y_B \approx 8.58 \times 10^{-11}$) is achieved with second-generation VLL masses around 4 TeV.
  • CP Asymmetry: The unflavored CP asymmetry $\epsilon_i$ is found to be $\mathcal{O}(10^{-2})$, sourced by high-energy phases in the inverse seesaw parameters.
• Thermal Washout: The condition $m'_{N}/T_{n1} \gtrsim 20$ is satisfied, ensuring the thermal washout factor is sufficiently small to preserve the asymmetry.
• Gravitational Waves (GWs): The phase transitions are characterized by weak strength ($\alpha \lesssim 10^{-2}$) and rapid rates ($\beta/H_n \gtrsim 10^4$). Consequently, the resulting stochastic GW signal is weak, with only a small fraction of the parameter space yielding a Signal-to-Noise Ratio (SNR) $> 1$ for the future Big Bang Observer (BBO).
• Collider Signatures:
  • LHC: The first-generation VLLs ($\sim 1$ TeV) are within the direct reach of the High-Luminosity LHC. They modify the Higgs diphoton decay rate, predicting a signal strength deviation $\mu_{\gamma\gamma} > 1.05$.
  • Muon Collider: The second-generation VLLs ($\sim 4$ TeV) could be probed at a future 10 TeV muon collider. However, the CP asymmetries relevant for leptogenesis are calculated in the symmetric vacuum ($h=0$), while collider experiments probe the broken vacuum ($h=v$), leading to a suppression of observable asymmetries in the lab frame.

5. Significance

This work presents a novel and self-consistent framework for baryogenesis that bridges the gap between neutrino mass generation (Inverse Seesaw) and cosmological phase transitions.

• It resolves the long-standing tension between TeV-scale leptogenesis and thermal washout by utilizing a nonthermal production mechanism in a symmetric vacuum.
• It highlights the importance of inverse phase transitions in early universe cosmology, a scenario previously less explored for baryogenesis.
• The model is testable at current and future colliders (LHC, Muon Collider) and offers a distinct prediction for the Higgs diphoton signal strength, providing a clear path for experimental verification.
• It addresses critical theoretical pitfalls often overlooked in previous bubble-assisted leptogenesis studies, specifically the dominance of annihilation over decay and the necessity of active sphalerons.