Exploring Leptogenesis in the Era of First Order Electroweak Phase Transition

This paper proposes a novel low-scale leptogenesis mechanism enabled by a first-order electroweak phase transition, which keeps sphalerons active below the standard decoupling temperature to convert lepton asymmetry into baryon asymmetry even for right-handed neutrinos with masses as low as 35 GeV, offering potential detection signatures through stochastic gravitational waves and accelerator experiments.

The Gist

The Big Mystery: Why is there something rather than nothing?

Imagine the Big Bang as a giant cosmic explosion that created the universe. According to our best theories, this explosion should have created equal amounts of matter (the stuff we are made of) and antimatter (its evil twin). When matter and antimatter meet, they annihilate each other instantly, turning into pure energy.

If the universe had created equal amounts, they would have all cancelled each other out, leaving a universe filled only with light and no stars, planets, or people. But here we are. There is a tiny bit more matter than antimatter. This leftover matter is everything we see. The big question in physics is: How did that tiny extra bit of matter survive?

The Usual Story: The "Heavy" Neutrino

For decades, physicists have had a favorite theory called Leptogenesis.

• The Characters: Imagine the universe is a busy kitchen. The "chefs" are heavy, invisible particles called Right-Handed Neutrinos (RHNs).
• The Recipe: These chefs are supposed to be very heavy (like a giant boulder). They decay (break apart) into lighter particles, creating a slight imbalance between matter and antimatter.
• The Problem: In the standard story, these chefs need to be so heavy (trillions of times heavier than a proton) that we can never build a machine big enough to find them. It's like trying to find a specific grain of sand on a beach the size of the solar system.

The New Twist: The "Light" Chef and the Freezing Universe

This paper proposes a clever workaround. What if those "chefs" (the neutrinos) aren't giant boulders, but actually lightweight (about the size of a bowling ball, or even lighter)?

If they are light, we could find them in current particle accelerators. But there's a catch: In the standard story, the universe cools down too fast. There is a "magic temperature" (about 131.7 GeV) where the universe undergoes a phase change. Below this temperature, the mechanism that turns the "lepton" imbalance into "baryon" (matter) imbalance shuts off.

If the universe cools below this temperature before the light chefs can do their job, the asymmetry is lost. It's like trying to bake a cake, but the oven turns off before the batter sets.

The Solution: The "Bubble" Universe

The authors suggest a different way the universe cooled down. Instead of a smooth, gradual cooling (like water slowly turning to ice), they propose the universe underwent a First-Order Phase Transition.

The Analogy: Boiling Water vs. Supercooled Water

• Standard View (Smooth Crossover): Imagine water freezing. It slowly gets colder, and ice crystals form gradually everywhere.
• This Paper's View (First-Order): Imagine supercooled water in a freezer. It stays liquid even though it's below freezing. Suddenly, a single ice crystal forms (a bubble). This bubble grows rapidly, swallowing the liquid water until the whole container is frozen.

In this scenario, the universe stays in a "hot, symmetric" state (liquid water) even after it drops below the standard "magic temperature."

1. The Delay: Because the universe is trapped in this "supercooled" state, the "magic switch" that turns off the matter-making process stays ON.
2. The Chef Works: The lightweight neutrinos (chefs) have time to break apart and create the matter/antimatter imbalance while the universe is still "hot" enough for the process to work, even though the temperature is lower than we thought possible.
3. The Freeze: Eventually, the bubbles of "broken" phase (ice) expand and fill the universe. Once the bubbles form, the switch turns off, but by then, the extra matter has already been saved.

Why This is a Big Deal

1. We Can Find Them: Because the neutrinos can be much lighter (as low as 35 GeV, which is lighter than the Higgs boson!), we might be able to detect them in current or upcoming particle colliders (like the Large Hadron Collider or future machines). We don't need a machine the size of the galaxy anymore.
2. Low Reheating Temperature: This theory works even if the universe was "reheated" (heated up after the Big Bang) to a very low temperature. Other theories require the universe to be super hot to work; this one works in a "cooler" universe.
3. Listening to the Past: When those "bubbles" of the new phase collided and expanded, they would have created ripples in space-time called Gravitational Waves. The paper predicts that future detectors (like LISA) might be able to "hear" these ripples, giving us a direct sound recording of the universe's first moments.
4. Testing the Theory: The theory suggests that the Higgs boson (the particle that gives mass to others) interacts with itself slightly differently than we thought. Future experiments at the High-Luminosity LHC could measure this "self-coupling" and confirm if this bubble theory is true.

Summary

The paper says: "We think the universe didn't cool down smoothly. Instead, it froze like supercooled water, forming bubbles. This delay allowed light, detectable neutrinos to create the extra matter that makes us exist. We can test this by looking for these light neutrinos in particle colliders, listening for gravitational waves from the 'bubbles,' and measuring how the Higgs boson behaves."

It turns a problem that seemed impossible (finding heavy neutrinos) into an exciting opportunity to find light ones and hear the echoes of the universe's birth.

Technical Summary

1. Problem Statement

The generation of the Baryon Asymmetry of the Universe (BAU) via thermal leptogenesis typically requires the decay of heavy Right-Handed Neutrinos (RHNs). In standard scenarios, this process faces two major constraints:

1. The Davidson-Ibarra Bound: For hierarchical RHNs, the mass $M_N$ must be $\gtrsim 10^9$ GeV to generate sufficient CP asymmetry. While resonant enhancement allows for lower masses (near the Electroweak scale, $\sim 160$ GeV), further lowering the mass scale is problematic.
2. Sphaleron Decoupling: In the Standard Model (SM), the electroweak phase transition (EWPT) is a smooth crossover. Consequently, sphaleron processes (which convert lepton asymmetry to baryon asymmetry) decouple at a critical temperature $T_{sp}^{SM} \approx 131.7$ GeV. Below this temperature, the conversion is suppressed.
3. The Reheating Temperature ($T_{RH}$) Limit: If the Universe's reheating temperature after inflation is below $T_{sp}^{SM}$ (which is theoretically possible, with lower bounds as low as a few MeV), standard leptogenesis fails because the Universe never reaches the temperature required for sphaleron activity.

The Core Question: Is it possible to realize successful low-scale leptogenesis (with $M_N < T_{sp}^{SM}$) even if the Universe's maximum temperature (reheating temperature) is below 131.7 GeV?

2. Methodology

The authors propose a novel mechanism relying on a Strongly First-Order Electroweak Phase Transition (FOEWPT) rather than the SM's smooth crossover.

• Model Extension: They extend the SM Higgs potential by adding a non-renormalizable dimension-6 operator:
  $$V_{tree}(\phi) = -\frac{\mu_h^2}{2}\phi^2 + \frac{\lambda_h}{4}\phi^4 + \frac{1}{8}\frac{\phi^6}{\Lambda^2}$$
  where $\Lambda$ is the cutoff scale. This modification allows for a first-order phase transition.
• Thermal Analysis: They compute the effective thermal potential $V_{eff}(\phi, T)$ including one-loop finite temperature corrections and daisy resummation. They utilize the CosmoTransition package and the FindBounce package to calculate the bubble nucleation rate.
• Nucleation Temperature ($T_n$): The key parameter is $T_n$, the temperature at which bubbles of the broken phase nucleate efficiently (defined by the condition that the number of bubbles per horizon volume $N_b \approx 1$). In a FOEWPT, $T_n$ can be significantly lower than the critical temperature $T_c$ and, crucially, lower than the SM sphaleron decoupling temperature ($T_{sp}^{SM}$).
• Leptogenesis Dynamics:
  • They assume the Universe remains in the false vacuum (symmetric phase, $\langle H \rangle = 0$) down to $T_n$.
  • In this symmetric phase, sphalerons remain active and in equilibrium even at temperatures well below 131.7 GeV.
  • RHNs with masses $T_n < M_N < T_{sp}^{SM}$ decay out of equilibrium, generating a lepton asymmetry.
  • This asymmetry is converted to baryon asymmetry by active sphalerons before the bubbles expand and the true vacuum (where sphalerons are suppressed) takes over.
• Numerical Simulation: They solve the Boltzmann equations for RHN abundance ($Y_N$) and $B-L$ asymmetry ($Y_{B-L}$) using the Casas-Ibarra parametrization for the neutrino Yukawa couplings.

3. Key Contributions

• Lowering the Sphaleron Decoupling Temperature: The paper demonstrates that in a FOEWPT scenario, the effective sphaleron decoupling temperature is determined by the bubble nucleation temperature $T_n$, not the SM value of 131.7 GeV.
• Feasibility of Sub-EW Scale Leptogenesis: They show that successful leptogenesis is possible with RHN masses as low as 35 GeV, provided $T_n$ is sufficiently low (down to $\sim 34$ GeV).
• Low Reheating Temperature Compatibility: Unlike other low-scale scenarios (e.g., Higgs decay or oscillation leptogenesis) which require $T_{RH} > T_{sp}^{SM}$, this framework works even if the Universe's reheating temperature is below 131.7 GeV.
• Model Independence: While they use a dimension-6 operator as a case study, the mechanism relies on the general property of FOEWPT where $T_n < T_{sp}^{SM}$, making the proposal applicable to various new physics frameworks.

4. Results

• Parameter Space for FOEWPT:
  • The cutoff scale $\Lambda$ must be in the range $571.6 \text{ GeV} \lesssim \Lambda \lesssim 810 \text{ GeV}$.
  • This corresponds to a nucleation temperature range of $33.8 \text{ GeV} \lesssim T_n \lesssim 119 \text{ GeV}$.
  • The lower bound on $\Lambda$ is set by the requirement for successful bubble nucleation ($N_b \geq 1$), and the upper bound by the requirement for a strong first-order transition (barrier height).
• Leptogenesis Success:
  • For RHN masses in the range $M_N \in [35, 100]$ GeV, the correct BAU can be reproduced.
  • This requires quasi-degenerate RHNs with a mass splitting $\Delta M \in [3.16 \times 10^{-11}, 1.07 \times 10^{-7}]$ GeV and specific active-sterile mixing angles.
  • The required Yukawa couplings are in the range $|Y_\nu| \sim 10^{-8} - 10^{-6}$.
• Experimental Signatures:
  • Triple Higgs Coupling ($\lambda_3$): The dimension-6 operator modifies the triple Higgs coupling. The predicted deviation $\Delta \lambda_3$ falls within the sensitivity reach of the High-Luminosity LHC (HL-LHC), particularly for $\Lambda \gtrsim 625$ GeV.
  • Gravitational Waves (GWs): The strong first-order phase transition generates a stochastic gravitational wave background via sound waves and turbulence. The signal peaks in the frequency range detectable by future observatories like LISA, BBO, DECIGO, and Einstein Telescope.

5. Significance

This work offers a unique solution to the "low-scale leptogenesis" problem by decoupling the sphaleron decoupling temperature from the standard crossover value.

• Testability: It brings the seesaw scale down to the Electroweak scale (and even below the Higgs mass), making RHNs potentially detectable at current and future colliders (FCC-ee, CEPC, ILC).
• Cosmological Consistency: It resolves the tension between low reheating temperatures (allowed by Big Bang Nucleosynthesis constraints) and the need for high temperatures to generate baryon asymmetry.
• Multi-Messenger Probe: The scenario provides a rare opportunity to cross-verify the origin of matter (leptogenesis) through three distinct channels: collider searches for RHNs, precision measurements of Higgs self-couplings, and gravitational wave astronomy.

In summary, the paper establishes that a strongly first-order electroweak phase transition creates a "window of opportunity" where sphalerons remain active at very low temperatures, enabling the generation of the universe's matter-antimatter asymmetry by relatively light neutrinos, even in a low-temperature cosmological history.