⚛️ phenomenology

Cogenesis of baryon and lepton number asymmetries matching the EMPRESS Data

This paper proposes a supersymmetric $U(1)_{B-L}$ extension of the Standard Model where the decay of a dominant $B-L$ Higgs field simultaneously generates the observed baryon asymmetry and a large electron neutrino asymmetry consistent with EMPRESS data through resonant leptogenesis, while also predicting a detectable gravitational wave background from cosmic strings.

Original authors: Kyu Jung Bae, Arghyajit Datta, Rinku Maji, Wan-Il Park

Published 2026-07-07

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CC BY 4.0

Original authors: Kyu Jung Bae, Arghyajit Datta, Rinku Maji, Wan-Il Park

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe as a giant, cosmic kitchen. For a long time, physicists have been trying to figure out two very specific recipes:

The "Matter" Recipe: Why is the universe made of matter (us, stars, planets) and not antimatter? We know there is a tiny bit more matter than antimatter, but we don't know exactly how that happened.
The "Neutrino" Recipe: A new measurement (called EMPRESS) suggests that there is a huge, previously unseen imbalance in the "electron neutrinos" (ghostly particles that barely interact with anything).

The problem is that standard recipes for making matter usually mess up the neutrino recipe, and vice versa. It's like trying to bake a cake that is perfectly sweet but also perfectly salty; usually, you can't get both right with the same batter.

This paper proposes a clever new way to bake both cakes at once using a "Supersymmetric U(1)B-L" model. Here is how they do it, using simple analogies:

1. The "Flaton" is the Master Chef

The authors introduce a special, heavy, invisible particle called a flaton (let's call it the "Master Chef").

The Setup: In the early universe, this Chef was stuck in a "holding pattern" (a flat potential) while the universe was expanding. This caused a brief period of "thermal inflation," like the dough rising slowly in a warm kitchen.
The Big Event: Eventually, the Chef decided to "cook" (decay). But here is the trick: the Chef didn't cook everything at once.

2. The Two-Stage Cooking Process

The paper suggests the Chef cooked in two distinct batches, which solves the puzzle of getting the right amounts of matter and neutrinos.

Batch 1: The "Early" Cook (Making Matter)
A tiny, small portion of the Chef's energy decayed just before the universe cooled down to a critical temperature (the Electroweak Phase Transition).
- The Analogy: Imagine the Chef drops a few crumbs into a hot pan. These crumbs turn into heavy particles (Right-Handed Neutrinos) that immediately break apart.
- The Result: Because this happened while the universe was still "hot" enough, a special process called a sphaleron (think of it as a cosmic mixer) could turn these particles into the tiny amount of Baryon Asymmetry (matter) we see today.
Batch 2: The "Late" Cook (Making Neutrinos)
The rest of the Chef (the vast majority of the energy) waited a long time to decay, long after the universe had cooled down and the "cosmic mixer" (sphaleron) had turned off.
- The Analogy: The Chef drops the rest of the ingredients into a cold pan. The heavy particles form and break apart, but because the "mixer" is off, they cannot turn into matter. Instead, they create a massive pile of Lepton Asymmetry (specifically electron neutrinos).
- The Result: This explains the huge neutrino imbalance hinted at by the EMPRESS data without accidentally creating too much matter.

3. The "Magic Cancellation" (The Secret Sauce)

There is a catch. Usually, if you make a lot of neutrinos, you also make a lot of matter (or the wrong kind of matter). The authors found a way to fix this using a concept called Resonant Leptogenesis.

The Analogy: Imagine you have three flavors of ice cream: Vanilla, Chocolate, and Strawberry.
- The "Late Cook" makes a huge amount of Vanilla (positive electron neutrinos).
- However, it also makes a tiny bit of Chocolate and Strawberry that are negative (opposite charge).
- When you mix them all together, the Chocolate and Strawberry cancel each other out almost perfectly, leaving you with a huge amount of Vanilla but a very small total amount of "flavor" left over.
Why this matters: The universe only cares about the total flavor left over to make matter. Because the flavors canceled out so well, the total "leftover" was tiny, which is exactly what we need for the matter in the universe. But the specific "Vanilla" (electron neutrinos) remained huge, matching the EMPRESS data.

4. The Cosmic Strings and the "Sound" of the Universe

The paper also predicts that when the "Master Chef" (the symmetry) broke, it created Cosmic Strings.

The Analogy: Imagine cracking an eggshell; sometimes you get a long, thin crack that runs across the whole shell. These are cosmic strings—long, thin defects in the fabric of space-time.
The Sound: As these strings wiggle and snap, they create ripples in space-time called Gravitational Waves. The authors calculate that these waves might be loud enough to be heard by future "ears" (detectors like DECIGO or LISA) in the future. It's like listening to the echo of the Chef's kitchen from billions of years ago.

Summary of the Claims

The Solution: A single mechanism (the decay of a scalar field) can explain both the tiny amount of matter and the huge amount of electron neutrinos.
The Conditions: This only works if the universe broke a specific symmetry at a very high energy scale (around $10^{10}$ GeV) and if the light neutrinos follow a "Normal Hierarchy" (a specific ordering of their masses).
The Prediction: This scenario creates a specific "hum" (gravitational waves) that future experiments might detect.

In short, the paper claims that by having a "lazy" Chef who cooks in two stages and uses a "canceling" trick with flavors, we can explain the universe's matter and neutrino puzzles simultaneously, while also leaving a sound signature for us to find later.

Technical Summary: Cogenesis of Baryon and Lepton Number Asymmetries Matching the EMPRESS Data

Problem Statement
The paper addresses two concurrent cosmological puzzles: the observed tiny baryon asymmetry of the Universe ( $Y_B^{obs} \approx 8.73 \times 10^{-11}$ ) and the recent EMPRESS data (2022 and 2025) which hints at a large positive electron neutrino asymmetry ( $Y_{\nu_e}^{BBN} \simeq +O(10^{-4} - 10^{-3})$ ). Standard leptogenesis scenarios face a significant challenge in explaining these simultaneously. Typically, a positive baryon asymmetry requires a positive $B-L$ asymmetry (implying a negative total lepton asymmetry, $Y_L < 0$ ). However, if the same mechanism generates the lepton asymmetry, standard flavor dynamics often predict a negative electron neutrino asymmetry ( $Y_{\nu_e} < 0$ ) to satisfy $Y_L < 0$ , contradicting the EMPRESS preference for $Y_{\nu_e} > 0$ . Furthermore, generating a large $Y_{\nu_e}$ without overproducing $Y_B$ usually requires the leptogenesis to occur after the electroweak phase transition (EWPT), yet a single source must also account for the observed $Y_B$ which is generated via sphalerons active only above the EWPT.

Methodology and Model Framework
The authors propose a supersymmetric $U(1)_{B-L}$ extension of the Standard Model. The core mechanism relies on a specific cosmic history involving thermal inflation driven by a flaton field ( $\phi$ ), which is the $D$ -flat direction of the $U(1)_{B-L}$ Higgs fields ( $\Phi_1, \Phi_2$ ).

Cosmic History: The universe undergoes a thermal inflation phase where the flaton $\phi$ is held near the origin. Upon decay, the flaton dominates the energy density (early matter domination) before decaying into heavy right-handed neutrinos (RHNs).
Dual-Stage Leptogenesis: The decay of the flaton $\phi$ $ϕ$ occurs over a prolonged period.
- Early Decay (Pre-EWPT): A small fraction of the flaton condensate decays into RHNs before the sphaleron processes freeze out at $T_{sp} \sim 137$ GeV. These RHNs decay promptly, generating a lepton asymmetry that is partially converted into the observed baryon asymmetry via sphalerons.
- Late Decay (Post-EWPT): The majority of the flaton condensate decays well after the EWPT. The resulting RHNs decay to produce a large lepton asymmetry. Since sphalerons are inactive, this asymmetry is preserved as a lepton number asymmetry, specifically manifesting as a large electron neutrino asymmetry.
Flavor Dynamics and Resonance: The model utilizes resonant leptogenesis with quasi-degenerate RHNs ( $M_1 \approx M_2$ ). The CP asymmetry is resonantly enhanced. Crucially, the authors employ the Casas-Ibarra parametrization with a specific complex angle $\theta$ in the $R$ -matrix. This allows for a scenario where the CP asymmetry in the electron flavor ( $\epsilon_{e}$ ) is positive and large, while the asymmetries in muon and tau flavors ( $\epsilon_{\mu}, \epsilon_{\tau}$ ) are negative and partially cancel the total lepton asymmetry.
Suppression Mechanisms: The baryon asymmetry is naturally suppressed relative to the lepton asymmetry by two factors:
- The dilution factor from the entropy production during the reheating of the flaton condensate.
- The cancellation among different lepton flavor CP asymmetries, ensuring the total $B-L$ asymmetry remains small enough to yield the correct $Y_B$ without violating the large $Y_{\nu_e}$ requirement.

Key Contributions and Results

Simultaneous Explanation: The paper demonstrates that a single source (the decay of the $B-L$ Higgs condensate) can generate both the observed $Y_B$ and the large positive $Y_{\nu_e}$ favored by EMPRESS data.
Sign Resolution: The authors show that it is possible to have $Y_B > 0$ and $Y_{\nu_e} > 0$ simultaneously. This is achieved by tuning the neutrino mixing parameters such that the total CP asymmetry ( $\sum \epsilon_i$ ) is negative (yielding $Y_L < 0 \to Y_B > 0$ ), while the electron-specific CP asymmetry ( $\epsilon_e$ ) is positive.
Parameter Space Constraints:
- The symmetry breaking scale is constrained to $v_\phi \sim 10^{10}$ GeV.
- The reheating temperature is found to be $T_R \sim 8$ GeV (well below the EWPT).
- The RHN mass is set to $M \sim 200$ GeV with a mass splitting $\delta M \sim 10^{-13}$ GeV to satisfy resonance conditions.
- The analysis indicates that the Normal Hierarchy (NH) of light neutrino masses is required to achieve the correct signs for both asymmetries. The Inverted Hierarchy (IH) scenario failed to produce the necessary parameter space for this specific sign configuration.
Gravitational Waves: The spontaneous breaking of $U(1)_{B-L}$ generates topologically stable, strong type-I cosmic strings. The authors calculate the stochastic gravitational wave background (GW) from this string network. They find that for $v_\phi \gtrsim 10^{10.3}$ GeV, the GW spectrum falls within the sensitivity ranges of future detectors such as LISA, DECIGO, ultimate DECIGO, BBO, and $\mu$ Ares.
Phase Transition GW: The paper also considers GWs from a first-order phase transition (bubble collisions) but concludes that the resulting signal ( $\Omega_{GW} h^2 \sim 10^{-19}$ ) is too weak to be detected by proposed experiments like SKA.

Significance and Claims
The authors claim that their work offers a "simple scenario" that resolves the tension between the EMPRESS data and standard baryogenesis expectations without requiring multiple independent sources for baryon and lepton asymmetries. The significance lies in:

Unification: Linking the origin of the baryon asymmetry and the large electron neutrino asymmetry to a single scalar condensate decay.
Flavor Tuning: Demonstrating that flavor-dependent CP violation can naturally lead to a positive electron neutrino asymmetry even when the total lepton asymmetry is negative.
Testability: Proposing that the model's validity can be tested via the detection of gravitational waves from cosmic strings in the frequency bands of future space-based interferometers (specifically for $v_\phi \sim 10^{10} - 10^{11}$ GeV).
Normal Hierarchy Preference: Highlighting a close connection between the positivity of the observed asymmetries and the normal mass hierarchy of light neutrinos.

The paper concludes that while some level of tuning is required (specifically in the complex angle $\theta$ and mass splitting $\delta M$ ), the framework is theoretically consistent with current observational constraints and offers a distinct signature for future gravitational wave astronomy.