Matter-Antimatter Asymmetry from Dirac-Majorana Flip-Flop

The gist: A novel leptogenesis scenario involving a Dirac-Majorana flip-flop proposes that lepton number violation occurs at high temperatures via a singlet scalar field acquiring a non-zero vacuum expectation value, and this transition can generate observable gravitational waves while light Dirac neutrinos generate detectable dark radiation in the CMB.

Introduction to the Problem

The visible or baryonic matter content of the present Universe is highly asymmetric, which leads to a puzzle known as the baryon asymmetry of the Universe (BAU) [1–3]. The observed BAU is quantified in terms of the baryon-to-photon number density ratio as [2] based on cosmic microwave background (CMB) measurements, which is consistent with the value extracted from big bang nucleosynthesis (BBN) observations of primordial elemental abundances [1]. While the standard model (SM) has, in principle, all the basic ingredients to satisfy the Sakharov conditions needed to dynamically generate baryon asymmetry starting from a symmetric Universe [4, 5], the quark sector CP violation falls short by almost 10 orders of magnitude [6]. In addition, the electroweak phase transition in the SM is not strongly firstorder enough to ensure adequate departure from equilibrium, necessary to produce the BAU [7]. This has led to several beyond standard model (BSM) proposals, out of which baryogenesis [8, 9] or leptogenesis [10] have been the most widely studied ones.

The Dirac-Majorana Flip-Flop Mechanism

The paper proposes a novel alternative by realizing conventional leptogenesis with LNV in a light Dirac neutrino setup by considering a flip-flop of Dirac and Majorana nature of neutrinos in the early Universe This relies on lepton number violation in the early Universe due to finite-temperature effects whereas the observations in the present Universe remain consistent with global lepton number conservation. Specifically, a singlet scalar field with non-zero lepton number acquiring a non-zero vacuum expectation value (VEV) generates Majorana masses for right-handed neutrinos (RHNs), which facilitates leptogenesis from out-of-equilibrium decay of heavy Majorana fermions. At a later epoch, the singlet scalar VEV shifts to zero, restoring lepton number symmetry, leading to purely Dirac neutrinos at low temperature.

The Two-Step Phase Transition Framework

The framework employs a toy model with two singlet scalars, phi and sigma, undergoing a two-step phase transition. The sequence of VEVs is described as (0, 0) → (0, vϕ) → (vσ, 0) across temperatures Tc1 and Tc2. At T > Tc1, the scalar field phi acquires a large VEV imparting Majorana masses to RHNs. As the Universe cools, a first-order phase transition (FOPT) occurs at Tc2 from (0, vϕ) to (vσ, 0), where sigma gains a non-zero VEV while phi's VEV returns to zero. This FOPT can lead to observable gravitational waves, with the conceptual visualization showing GWs associated with the transition.

Particle Content and Yukawa Couplings

The SM is extended by two copies of gauge singlet right-handed neutrinos νR, one Majorana dark fermion singlet χ, and a neutrinophilic Higgs doublet η. The relevant Yukawa Lagrangian involves terms such as −LY ⊃ yαiLαην˜ Ri + YijϕνcRiνRj + Yχσχcχ + h.c. At high temperatures T > Tsph ∼ 131.7 GeV, phi acquires a large VEV vϕ ≫ Tsph generating Majorana mass terms for νR, allowing the decay νR → Lη decay to generate nonzero lepton asymmetry. The presence of a neutrinophilic Higgs doublet allows for sizeable Yukawa coupling of Dirac neutrinos, assisting in leptogenesis and leading to the thermalization of the right-chiral parts, which enhances dark radiation or ∆Neff.

Observational Signatures and Constraints

The model predicts several observable consequences depending on the parameter space. A first-order VEV-restoring phase transition can lead to observable gravitational waves (GWs). Light Dirac neutrinos can generate detectable dark radiation at CMB experiments. The analysis identifies benchmark points consistent with a strong FOPT, and the right panel of Fig. 3 shows the peak amplitudes of the gravitational wave spectra generated during bubble collisions. Furthermore, precision CMB measurements can probe this scenario due to enhanced dark radiation from thermalized Dirac neutrinos. The parameter space consistent with successful leptogenesis and a two-step FOPT has complementary detection prospects in terms of CMB surveys and GW detectors.

Leptogenesis Calculation Details

The lepton asymmetry at the sphaleron decoupling epoch TSph ∼ 130 GeV gets converted into baryon asymmetry as YB ≃ asph YB−L = 1/4 YB−L. The final baryon asymmetry ηB can be analytically estimated to be ηB = asph / fϵκ, where the factor f accounts for the change in the relativistic degrees of freedom from the scale of leptogenesis until recombination and comes out to be f = 106.75. The numerical solution of Boltzmann equations shows that as Yukawa coupling y increases, washout due to inverse decay increases leading to smaller lepton asymmetry. This process is further detailed by solving Eqs. (B10) and (B11) for the evolution of comoving abundances for different values of the Dirac Yukawa coupling y. The results are shown in Fig. 5 for BP1 in Table I with fixed CP asymmetry ϵ = 0.1 but varying Dirac Yukawa coupling y.

Conclusion and Future Directions

The paper concludes by stating that the model can open up new directions in UV complete model building with additional symmetries, fields as well as related phenomenology, which are left for future works. The scenario successfully realizes conventional leptogenesis with LNV in a light Dirac neutrino setup by considering a flip-flop of Dirac and Majorana nature of neutrinos in the early Universe. The presence of a neutrinophilic Higgs doublet and two singlet scalars can have complementary detection prospects at colliders. This model offers a way to generate the observed matter-antimatter asymmetry while maintaining consistency with the absence of LNV signals at terrestrial experiments. The framework is consistent with both gravitational wave and CMB experimental signatures.

Acknowledgments

The work of D.B. and I.S. are supported by the Science and Engineering Research Board (SERB), Government of India grant CRG/2022/000603. The paper is supported by various references including [1] through [1995] and others listed in the bibliography.

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The observed matter-antimatter asymmetry can be generated dynamically via leptogenesis, where a non-zero lepton asymmetry is generated first and then gets converted into baryon asymmetry via sphalerons. Creation of non-zero lepton asymmetry typically requires lepton number violation (LNV) which, within the seesaw framework, results in the Majorana nature of light neutrinos. With no signs of LNV at terrestrial experiments, we propose a novel leptogenesis scenario where LNV occurs at high temperatures while zero-temperature physics is consistent with the pure Dirac nature of neutrinos. In a concrete model of this Dirac-Majorana flip-flop, the right chiral parts of Dirac neutrinos initially acquire a large Majorana mass in the early Universe when a singlet scalar field with two units of lepton number acquires a non-zero vacuum expectation value (VEV), thereby facilitating leptogenesis from out-of-equilibrium decay of heavy Majorana fermions. At lower temperatures, the VEV of the scalar singlet gets restored to zero to be consistent with lepton number conservation.

1. textbf Real-time Gravitational Wave Signatures from Phase Transitions in Cosmology: The improved system can simulate observable gravitational waves by calculating "GW spectra from a first-order VEV-restoring phase transition, as suggested by the paper's mention of additional detection prospects like stochastic gravitational waves (GWs)."

2. textbf Enhanced Dark Radiation Detection via CMB Analysis: The system can predict and analyze the signature of a scenario where light Dirac neutrinos are thermalized, leading to detectable dark radiation at cosmic microwave background experiments, as implied by the text discussing a sizeable Yukawa coupling of Dirac neutrinos to the neutrinophilic Higgs doublet not only assists in leptogenesis, but also leads to the thermalization of the right-chiral parts.

3. textbf Precision Parameter Space Mapping for BSM Physics: The AI can perform numerical scans over complex parameter spaces like Tn - MνR (Tn) = YνR vϕ(Tn) plane to identify regions consistent with successful leptogenesis and a two-step FOPT, directly aiding in the search for green colored points within reach of detectors like LISA, BBO, and DECIGO.

4. textbf Contextual Analysis of Neutrino Mass Mechanisms: The system can differentiate between Dirac and Majorana neutrino scenarios by analyzing the temperature evolution of vacuum expectation values, specifically tracking when the VEV of the scalar field gets restored to zero to be consistent with lepton number conservation, allowing for a more nuanced understanding of how light Dirac neutrinos can generate detectable dark radiation.

5. textbf Model Constraint Generation via Washout Term Evaluation: The AI can calculate and incorporate the washout terms for lepton asymmetry, like inverse decays and scatterings as defined in Eq. (B14), enabling it to predict the impact of these processes on the final baryon asymmetry, which is crucial for fitting model predictions with observed data.