Leptogenesis and neutrino mass with one right-handed neutrino and Higgs inflaton

This paper proposes a minimal model utilizing a single right-handed neutrino and a second Higgs doublet that drives inflation via non-minimal gravity coupling to simultaneously explain the baryon asymmetry through Affleck-Dine leptogenesis and neutrino masses, while remaining consistent with cosmological data and offering detectable prospects for future experiments.

The Gist

The Big Picture: Solving Three Cosmic Mysteries with Two New Pieces

Imagine the universe as a giant, complex puzzle. Scientists have been trying to fit the pieces together for decades, but three specific pieces are missing or don't quite fit:

1. The "Why is there something rather than nothing?" problem: Why is the universe made of matter (us, stars, planets) instead of being an empty void? There should have been equal amounts of matter and antimatter, which would have cancelled each other out.
2. The "Ghostly Neutrino" problem: We know tiny particles called neutrinos exist and have mass, but the Standard Model of physics (our rulebook for how particles work) says they should be weightless.
3. The "Big Bang Aftermath" problem: The universe expanded incredibly fast right after the Big Bang (a phase called Inflation). We know this happened, but we don't know what drove it.

The Paper's Solution:
This team of physicists proposes a "minimalist" solution. Instead of inventing a whole new zoo of exotic particles, they suggest adding just two new ingredients to the universe's recipe:

1. One "Right-Handed Neutrino" (RHN): A heavy, invisible cousin to the neutrinos we know.
2. A "Second Higgs": A second version of the famous Higgs boson (the particle that gives mass to others).

Here is the magic trick: This second Higgs does double duty. It acts as the "engine" that drove the rapid expansion of the early universe (Inflation), and it also acts as the "mixer" that created the imbalance between matter and antimatter.

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The Story of the Universe: A Three-Act Play

Act 1: The Great Expansion (Inflation)

Imagine the early universe as a tiny, cramped balloon. Suddenly, it needs to blow up to the size of a beach ball in a split second.

• The Old Idea: Usually, scientists think a mysterious, invisible "inflaton" field pushes the balloon.
• This Paper's Idea: The "Second Higgs" is the inflaton. It's like a spring-loaded piston inside the balloon. When it activates, it pushes the universe to expand rapidly.
• The Twist: This Higgs doesn't just push; it has a special "tilt" in its energy field. As the universe expands, this tilt starts to spin, like a top.

Act 2: The Great Imbalance (Leptogenesis)

Now, the universe has expanded, but it's still a soup of particles. We need to create more matter than antimatter.

• The Analogy: Imagine a giant dance floor (the universe) where dancers (particles) are spinning. Usually, they spin in perfect pairs: one clockwise, one counter-clockwise. If they stop, they cancel out.
• The Mechanism (Affleck-Dine): Because of that "tilt" in the Second Higgs, the dance floor starts to spin unevenly. The "Second Higgs" field acts like a giant conductor, telling the particles to lean slightly more to one side.
• The Result: This creates a slight excess of "leptons" (a family of particles including electrons and neutrinos). Later, through a cosmic traffic cop called the Sphaleron, this lepton excess gets converted into a baryon excess (protons and neutrons).
• The Outcome: This tiny imbalance is why we exist today. If the spin had been perfect, we would have been a universe of pure energy with no stars or people.

Act 3: The Ghostly Mass (Neutrinos)

Finally, we need to explain why neutrinos have mass.

• The Setup: We have our heavy "Right-Handed Neutrino" (the cousin) and our "Second Higgs."
• The Trick: The paper suggests a two-step process to give mass to the light neutrinos we detect:
  1. The Direct Hit: The heavy cousin interacts with the normal Higgs to give one neutrino a tiny mass (like a direct handshake).
  2. The Loop: The other neutrinos get their mass through a "loop" involving the Second Higgs and the heavy cousin. It's like a relay race where the baton (mass) is passed through a complicated circuit.
• The Result: This explains the observed "mixing" of neutrinos (how they change flavors) and their tiny masses without needing a massive, untestable energy scale.

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Why This is a Big Deal (The "Minimalist" Advantage)

In physics, there is a rule of thumb: The simpler, the better.

• The Problem with Other Theories: Many theories trying to solve these problems require three or more heavy neutrinos and complex, hidden symmetries. This makes the math messy and the predictions hard to test.
• The Paper's Win: By using only one heavy neutrino and one extra Higgs, the model is incredibly tight. It's like building a house with only two types of bricks instead of twenty.
• The Catch: Because the model is so simple, it leaves very little room for error. The numbers have to be just right.

The "Goldilocks" Zone and Future Tests

The authors ran their numbers against the latest data from space telescopes (like Planck and the new ACT data).

• The Good News: The model works! It fits the data for the cosmic microwave background (the afterglow of the Big Bang) and the observed amount of matter in the universe.
• The Bad News: The "ACT 2025" data is very strict. It rules out most of the possible settings, leaving only a tiny "Goldilocks zone" where the model works.
• The Exciting Part: Because the particles involved are predicted to be relatively light (around the TeV scale, which is within reach of our current particle accelerators like the Large Hadron Collider), we might actually be able to find them soon.
  • The "Smoking Gun": If we see a specific type of radioactive decay (where a muon turns into an electron and a photon, $\mu \to e\gamma$) in future experiments like MEG II, it would be a direct confirmation that this specific "Second Higgs" and "Heavy Neutrino" exist.

Summary in One Sentence

This paper proposes that the universe was inflated, filled with matter, and gave neutrinos their mass using a "two-for-one" deal: a second Higgs boson that acted as both the cosmic engine and the matter-maker, paired with a single heavy neutrino, creating a simple, testable, and elegant explanation for our existence.

Technical Summary

1. Problem Statement

The paper addresses three major open questions in particle physics and cosmology simultaneously:

1. Baryon Asymmetry of the Universe (BAU): The observed matter-antimatter asymmetry.
2. Neutrino Mass and Mixing: The origin of non-zero neutrino masses, which the Standard Model (SM) cannot explain.
3. Cosmic Inflation: The mechanism driving the rapid expansion of the early universe, solving the horizon and flatness problems.

The Challenge:

• Canonical Leptogenesis: Typically requires at least two heavy right-handed neutrinos (RHNs) to generate sufficient CP violation and explain neutrino data. This usually pushes the mass scale to $M_1 \gtrsim 10^9$ GeV (Davidson-Ibarra bound), making it inaccessible to terrestrial experiments.
• Inflation: Often requires a separate scalar field (inflaton) beyond the SM Higgs.
• Minimality: The authors aim to construct a minimal framework that explains all three phenomena using the fewest possible Beyond Standard Model (BSM) fields, specifically avoiding the need for multiple RHNs or a separate inflaton.

2. Methodology and Model Setup

The authors propose a novel, minimal extension of the Standard Model involving only two new fields:

1. One Gauge Singlet Right-Handed Neutrino ($N$): A single RHN.
2. A Second Higgs Doublet ($\eta$): An inert doublet that also serves as the inflaton.

Key Features of the Model:

• Scalar Potential & Symmetry: The model utilizes a $Z_2$ symmetry where $\eta$ and $N$ are odd, and SM fields are even. This prevents $\eta$ from acquiring a vacuum expectation value (VEV) at tree level, keeping the SM Higgs sector in the "alignment limit."
• Neutrino Mass Generation (Hybrid Seesaw):
  • Type-I Seesaw: The SM Higgs ($\Phi$) couples to $N$ via Yukawa coupling $y_\alpha$, generating a mass for one active neutrino at tree level: $(m_\nu^I)_{\alpha\beta} \propto y_\alpha y_\beta v^2 / M_N$.
  • Radiative (Scotogenic) Seesaw: The inert doublet $\eta$ couples to $N$ via Yukawa coupling $Y_\alpha$. This generates a mass for the second active neutrino at the one-loop level involving $\eta$ and $N$.
  • Result: The lightest neutrino mass is naturally zero. The combination of tree-level and loop-level contributions naturally explains the neutrino mass hierarchy (Normal or Inverted) without fine-tuning.
• Inflation (Higgs Inflation):
  • Inflation is driven by the non-minimal coupling of the scalar fields ($\Phi$ and $\eta$) to gravity: $f(|\Phi|, |\eta|) = \xi_1|\Phi|^2 + \xi_2|\eta|^2$.
  • In the large field limit, the potential reduces to the Starobinsky inflation form ($R^2$ inflation), which is consistent with current CMB data.
• Baryogenesis (Affleck-Dine Mechanism):
  • Instead of relying on the CP-violating decay of heavy RHNs (which is impossible with only one RHN), the model employs the Affleck-Dine (AD) mechanism.
  • The $U(1)_L$ (lepton number) is explicitly broken by the $\lambda_5$ term in the scalar potential: $\lambda_5 [(\Phi^\dagger \eta)^2 + h.c.]$.
  • During inflation, the complex phase of the $\eta$ field (the AD field) evolves, generating a lepton asymmetry ($n_L$). This asymmetry is later converted into baryon asymmetry via electroweak sphalerons.

3. Key Contributions

• Minimal Field Content: Demonstrates that one RHN and one additional Higgs doublet are sufficient to explain BAU, neutrino masses, and inflation. This is a significant reduction in model complexity compared to standard resonant leptogenesis or multi-inflaton scenarios.
• Unified Dynamics: The same field ($\eta$) acts as the inflaton and the source of lepton asymmetry (via the AD mechanism), while the single RHN facilitates both neutrino mass generation and the decay required for reheating.
• Reheating Dynamics: The authors perform a detailed analysis of the reheating phase, accounting for a transition between different equations of state (from matter-like to radiation-like) due to the specific shape of the potential. This allows for lower reheating temperatures ($T_{RH}$) compared to standard single-field Starobinsky models.
• Constraint Analysis: The model is rigorously tested against:
  • CMB Data: PLANCK 2018 and the newer ACT 2025 (Atacama Cosmology Telescope) data.
  • Neutrino Oscillation Data: Mass squared differences and mixing angles.
  • Lepton Flavor Violation (LFV): Constraints from $\mu \to e\gamma$ (MEG II).
  • Isocurvature Perturbations: Constraints on the initial phase of the AD field.

4. Results

• Parameter Space Constraints:
  • ACT 2025 vs. PLANCK 2018: While PLANCK 2018 allows a large parameter space, the ACT 2025 data significantly restricts the allowed region, disfavoring most of the parameter space and leaving only a small, viable window.
  • Mass Scale: The preferred mass spectrum for the BSM particles (specifically the inert Higgs mass $m_\eta$ and RHN mass $M_N$) lies around the TeV scale. This makes the model potentially testable at future terrestrial colliders.
  • Reheating Temperature: The model accommodates lower reheating temperatures ($T_{RH} \sim 10^2 - 10^4$ GeV) compared to standard Starobinsky inflation, which is crucial for satisfying the constraints from neutrino masses and washout processes.
• Leptogenesis Viability:
  • Successful baryogenesis is achieved via the AD mechanism. The generated lepton asymmetry depends on the coupling $\lambda_5$, the initial phase $\theta_i$, and the reheating temperature.
  • The model avoids strong washout effects (which would erase the asymmetry) by carefully tuning the Yukawa couplings and mass splittings.
• Neutrino Masses: The model predicts a vanishingly small mass for the lightest active neutrino ($m_{\nu_1} \approx 0$). This keeps the effective neutrino mass ($m_{\beta\beta}$) below the sensitivity of current experiments like KATRIN but potentially testable by future neutrinoless double beta decay experiments.
• Flavor Violation: The parameter space is constrained by MEG II limits on $\mu \to e\gamma$. The authors show that the allowed region lies just below current limits but within the reach of future sensitivities (MEG II and PRISM/PRIME).

5. Significance

• Theoretical Economy: The paper provides a compelling example of "minimalism" in BSM physics, showing that complex cosmological phenomena can be explained with a very small extension of the SM.
• Testability: By pushing the BSM mass scale down to the TeV range, the model moves away from the "unobservable" GUT scale ($10^9$ GeV) typical of canonical leptogenesis. This opens the door for direct detection of the inert Higgs and RHNs at colliders like the LHC or future machines.
• Cosmological Consistency: The work highlights the tension between different cosmological datasets (PLANCK vs. ACT). The fact that the model survives the stricter ACT 2025 constraints in a specific, small region makes it a robust candidate for future verification.
• Future Probes: The model makes distinct predictions for:
  • Neutrinoless Double Beta Decay: Specifically for normal ordering, it predicts a rate that could be falsified by upcoming experiments.
  • Lepton Flavor Violation: The $\mu \to e\gamma$ rate is close to current experimental limits, offering a near-future test.
  • CMB Isocurvature: The model predicts specific isocurvature perturbations that could be probed by next-generation CMB experiments.

In conclusion, this paper presents a highly predictive, minimal framework that unifies inflation, neutrino mass generation, and baryogenesis, with a parameter space that is tightly constrained by the latest cosmological data but remains accessible to terrestrial experiments.