Primordial Dirac Leptogenesis

This paper proposes a novel mechanism for primordial Dirac leptogenesis occurring during the post-inflationary reheating phase, where an inflaton-generated asymmetry is transferred to chiral neutrinos and subsequently to baryons via sphalerons, offering a testable prediction for the effective number of relativistic species ($N_{\text{eff}}$) while naturally accommodating small neutrino Yukawa couplings.

The Gist

Imagine the early Universe right after the Big Bang as a giant, chaotic kitchen. For a long time, scientists have been puzzled by a simple question: Why is there more matter than antimatter? If the Universe started with equal amounts of both, they should have annihilated each other, leaving nothing but light. But here we are, made of matter. This paper proposes a new recipe to explain how that imbalance happened.

Here is the story of their new idea, broken down into simple steps:

1. The Missing Ingredient: A "Ghost" Particle

In the standard recipe (the Standard Model of physics), we know about particles like electrons and neutrinos. But this paper suggests there's a "ghost" version of the neutrino, called a right-handed neutrino, that doesn't interact with anything except gravity and a very weak force. Think of it as a shy guest at a party who only talks to one specific person and ignores everyone else.

Because these particles are so shy, they are "Dirac" particles (like regular matter) rather than "Majorana" particles (which would be their own antiparticles). This is important because it means the total "lepton number" (a kind of cosmic accounting for these particles) stays balanced, which is a rule this new theory wants to keep.

2. The Chef: The Inflaton

The paper introduces a character called the inflaton. Think of the inflaton as a giant, vibrating drumstick that was shaking the Universe into existence during a period called "inflation." When this drumstick stopped shaking and started to decay (break down), it was supposed to fill the kitchen with food (particles).

Usually, we think this drumstick breaks down evenly, creating equal amounts of left-handed and right-handed particles. But in this new recipe, the drumstick has a twist. Because of a specific "complex phase" (a fancy way of saying a hidden angle in the math), the drumstick breaks down slightly unevenly. It produces a tiny bit more of one type of particle than the other.

3. The Transfer: Passing the Baton

Here is the clever part of the mechanism:

• Step A (The Asymmetry): The inflaton decays into two types of "Higgs" particles (think of them as different types of flour). Because of that hidden twist, the kitchen ends up with a slight imbalance: a little more of "Flour A" than "Flour B."
• Step B (The Handoff): This imbalance in the flour is then passed on to the neutrinos. The "Flour A" turns into left-handed neutrinos, and "Flour B" turns into right-handed neutrinos. Because the flour was unbalanced, the neutrinos are now unbalanced too.
• Step C (The Magic Trick): The left-handed neutrinos are connected to the rest of the kitchen (protons and neutrons) via a mechanism called sphalerons. Think of sphalerons as a magical conveyor belt that can turn a left-handed neutrino into a proton (baryon). The right-handed neutrinos are too shy to use this belt, so they just sit there.
• The Result: The conveyor belt converts the extra left-handed neutrinos into extra protons. The right-handed neutrinos stay behind, preserving the balance sheet. The result? A Universe with more matter (protons) than antimatter.

4. The Timing is Everything

For this to work, the timing must be perfect:

• The "ghost" particles (right-handed neutrinos) must be created before the conveyor belt (sphalerons) stops working.
• The "flour" (the Higgs particles) must not get mixed up and wiped out by other reactions before they can turn into neutrinos.
• The paper shows that if the "ghost" particles are heavy enough and the interactions are just right, the imbalance survives the chaos of the early Universe and freezes into the matter we see today.

5. How Can We Test This?

The authors don't just stop at the theory; they say we can check if this is true.

• The "Extra Heat" Test: Because these shy right-handed neutrinos are light and fast, they act like extra heat in the early Universe. Scientists measure the "effective number of neutrino species" ($N_{eff}$). Currently, we expect about 3.045 types. This theory predicts there might be a tiny bit more (around 0.1 extra), which future telescopes and cosmological experiments will be able to detect.
• The Collider Test: The theory suggests the "ghost" Higgs particle isn't too heavy. It might be light enough to be created in particle colliders (like the Large Hadron Collider) in the near future.

Summary

In short, this paper suggests that the reason we exist (and not just empty light) is because a vibrating cosmic drumstick (the inflaton) broke down unevenly right after the Big Bang. This created a slight imbalance in a special type of flour, which was then passed to shy neutrino particles. These particles used a cosmic conveyor belt to turn that imbalance into the matter that makes up stars, planets, and us.

The best part? This story keeps the "lepton number" balanced (no magic creation of lepton numbers from nothing) and makes a specific prediction about extra heat in the Universe that we can test with our next generation of telescopes.

Technical Summary

Technical Summary: Primordial Dirac Leptogenesis

Problem Statement
The observed baryon asymmetry of the Universe (BAU) remains unexplained within the Standard Model (SM), as the SM's CP violation and departure from thermal equilibrium are insufficient to generate the observed magnitude. While Majorana leptogenesis is a well-established solution, it violates global lepton number ($L$) and relies on heavy right-handed Majorana neutrinos. In contrast, Dirac leptogenesis preserves global $L$, requiring neutrinos to be Dirac particles with extremely small Yukawa couplings ($y_\nu \lesssim 10^{-11}$). A primary challenge in Dirac leptogenesis is sourcing the initial chiral asymmetry between left- and right-handed neutrinos without violating $L$, particularly given the suppression of asymmetry generation by the tiny neutrino Yukawa couplings. Previous realizations often required heavy scalar doublets distinct from the SM Higgs, as the SM Higgs alone could not generate a sufficient asymmetry due to these small couplings.

Methodology and Model Construction
The authors propose a minimal realization of Dirac leptogenesis where the initial asymmetry is generated during the post-inflationary reheating phase, rather than through the decays of heavy scalars in a thermal bath. The model extends the SM with three new fields:

1. An inflaton field $\phi$.
2. An inert Higgs doublet $\hat{h}$.
3. Right-handed neutrinos $\nu_R$ (Dirac partners to SM left-handed neutrinos $\nu_L$).

All new fields are charged under a discrete $Z_2$ symmetry ($\phi \to -\phi$, $\hat{h} \to -\hat{h}$, $\nu_R \to -\nu_R$). The global lepton number is conserved, forbidding Majorana mass terms. The scalar potential includes interactions between the SM Higgs ($h$), the inert doublet ($\hat{h}$), and the inflaton ($\phi$). Crucially, the inflaton couples to the Higgs sector via a trilinear term involving a complex coupling $g_\phi$ and a quartic coupling $\lambda_5$ between the Higgs doublets.

The mechanism proceeds in three stages:

1. Generation of Scalar Asymmetry: During reheating, the oscillating inflaton decays out of equilibrium into Higgs doublets ($\phi \to h^\dagger \hat{h}$ and $\phi \to h \hat{h}^\dagger$). Interference between tree-level and absorptive loop-level amplitudes (mediated by $\lambda_5$) generates a CP-violating asymmetry in the scalar sector ($\Delta \rho_{\hat{h}} \neq 0$). This occurs while maintaining $\Delta L = 0$ globally, but creating a chiral imbalance ($L_L = -L_R \neq 0$).
2. Transfer to Neutrinos: The asymmetric inert doublet $\hat{h}$ decays into chiral neutrinos via Yukawa interactions ($\hat{h} \to \nu_L \nu_R$). Because the Yukawa couplings are tiny, the right-handed neutrinos $\nu_R$ do not thermalize and remain out of equilibrium.
3. Conversion to Baryon Asymmetry: The left-handed neutrino asymmetry ($L_L$) is partially converted into a baryon asymmetry ($B$) via electroweak sphaleron processes, which are active above the electroweak phase transition temperature ($T_{EW} \approx 160$ GeV). The right-handed neutrinos remain decoupled, preventing the washout of the asymmetry. Finally, at temperatures $T \ll T_{EW}$, left-right equilibration occurs, freezing out a non-zero final baryon asymmetry.

Key Results

• Baryon Asymmetry Yield: The authors derive an analytic expression for the baryon asymmetry yield ($Y_B$). In the "drift-and-decay" limit (where inverse decays are negligible), the yield is found to be:
  $$Y_B \simeq (1.2 \times 10^{-2}) \lambda_5 \sin(2\theta)$$
  where $\theta$ is the CP-violating phase of the inflaton coupling. Notably, the dependence on the specific inflaton potential drops out of the ratio of energy densities, making the result robust against details of the inflationary model.
• Parameter Constraints: To reproduce the observed baryon asymmetry ($Y_B^{obs} \approx 8.7 \times 10^{-11}$), the quartic coupling must satisfy $\lambda_5 \simeq 7.4 \times 10^{-9} / \sin(2\theta)$.
• Washout Avoidance: The model requires the inert doublet to decay before the electroweak phase transition ($T_d \gtrsim T_{EW}$) and for the scalar asymmetry to survive washout processes (mediated by $\lambda_5$) until decay. This imposes a lower bound on the inert doublet mass: $m_{\hat{h}} \gtrsim T_{EW}$.
• Cosmological Signatures: The presence of light, relativistic right-handed neutrinos contributes to the effective number of relativistic species, $N_{eff}$. The paper estimates a contribution $\Delta N_{eff} \sim 0.1$ for benchmark parameters ($m_{\hat{h}} = 500$ GeV, $\hat{y}_\nu = 10^{-7}$), which is within the sensitivity of upcoming cosmological observations (e.g., CMB-S4).

Significance and Claims
The paper claims to present a novel realization of Dirac leptogenesis that dynamically links inflation, reheating, and the origin of the baryon asymmetry. Unlike previous Dirac leptogenesis models that rely on heavy scalar decays in a thermal bath, this mechanism generates the primordial asymmetry directly within the scalar sector via CP-violating inflaton decays.

Key distinctions and contributions include:

• Role of the Higgs: The model identifies one of the scalar doublets with the SM Higgs, unlike the original Dirac leptogenesis setup which required two heavy, distinct doublets. The tiny neutrino Yukawa couplings suppress standard loop contributions (self-energy and vertex), making the CP-asymmetric inflaton decays the dominant source of asymmetry.
• No Strong Phase Transition Required: Unlike Higgsogenesis scenarios, this mechanism operates efficiently without requiring a strong first-order electroweak phase transition to avoid washout.
• Testability: The framework predicts a measurable deviation in $N_{eff}$ and requires the inert doublet mass to be within the reach of future collider experiments ($m_{\hat{h}} \gtrsim T_{EW}$).
• Conservation of Lepton Number: The mechanism successfully generates the BAU while strictly conserving global lepton number, offering a viable alternative to Majorana scenarios and aligning with the non-observation of neutrinoless double beta decay.

The authors conclude that this setup provides a general and testable framework for explaining the BAU, with the potential to address other open questions such as the origin of dark matter.