⚛️ phenomenology

Low Primordial Helium as a Probe of Non-Unitary Neutrino Mixing

This paper proposes that the low primordial helium mass fraction reported by the EMPRESS collaboration can be explained by non-unitary neutrino mixing, a feature of seesaw extensions to the Standard Model, which enhances neutron-to-proton conversion rates and aligns theoretical predictions with observational data while remaining consistent with current experimental constraints.

Original authors: Shu-Yuan Guo, Jia-Qi Li

Published 2026-10-22

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CC BY 4.0

Original authors: Shu-Yuan Guo, Jia-Qi Li

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

In the first few minutes after the Big Bang, the universe was a seething, dense soup of energy and particles. As it expanded and cooled, this primordial plasma began to forge the first atomic nuclei, a process known as Big Bang nucleosynthesis. During this brief window, protons and neutrons combined to create the lightest elements: hydrogen, helium, and a trace of deuterium. The amount of helium produced is not a random number; it is a precise cosmic fingerprint. It depends on how fast the universe was expanding at that moment, how many types of light particles were zipping around, and how quickly neutrons could transform into protons before the process froze out. Because the laws of physics that governed this era are so well understood, scientists can calculate exactly how much helium should exist today. If the actual amount we measure in the oldest, most pristine parts of the universe differs from that prediction, it is a powerful signal that our understanding of the early universe is incomplete.

Recently, a team of astronomers known as the EMPRESS collaboration reported a measurement that has sent ripples through the field. By analyzing the light from twenty-nine newly observed galaxies, many of which are extremely poor in heavy elements, they determined that the primordial mass fraction of helium is 0.2402. This value is slightly lower than the standard prediction of 0.2470. While the difference seems small, it is statistically significant enough to suggest that something in our standard model of cosmology might be missing. The standard model assumes that the three known types of neutrinos—ghostly particles that rarely interact with matter—behave in a perfectly predictable way. However, the discrepancy in helium abundance hints that these particles might be acting in a more complex manner than previously thought.

A new study by physicists Shu-Yuan Guo and Jia-Qi Li from Yantai University proposes a specific explanation for this low helium count. They suggest that the three known neutrinos are not entirely isolated from a hidden, heavier set of particles. In the standard view, the mixing of these three neutrino types is "unitary," meaning the probabilities of them transforming into one another add up perfectly to one, like a complete set of puzzle pieces. The researchers explore a scenario where this rule is slightly broken, a condition called non-unitary mixing. This happens in many theoretical extensions of the Standard Model of particle physics, where heavy, invisible particles interact with the light neutrinos we can detect, subtly altering their behavior.

The mechanism by which this affects the early universe is direct and physical. In the hot, dense environment of the Big Bang, neutrons and protons were constantly swapping identities through weak nuclear interactions. The rate of this swapping was governed by a fundamental constant of nature, often called the Fermi constant, which dictates the strength of these weak forces. In a standard universe, the strength of this force is the same whether it is measured in the decay of a muon or in the decay of a neutron. However, if the neutrino mixing is non-unitary, the effective strength of the force during neutron decay becomes slightly stronger than in muon decay. This enhancement speeds up the conversion of neutrons into protons. Because neutrons are the building blocks of helium, having fewer of them available when the nuclear fusion begins means less helium is created. The result is a universe with a lower helium abundance, exactly matching the lower value observed by EMPRESS.

To test this idea, the authors performed a full numerical simulation of the Big Bang, incorporating this modified mixing and the resulting change in the weak interaction strength. They combined their calculations with the latest measurements of helium and deuterium, as well as data on the density of ordinary matter in the universe. The results were striking. The simulation showed that a small deviation from perfect mixing, specifically a parameter value of 0.982, could perfectly reproduce the low helium abundance observed by EMPRESS. Crucially, this solution did not require changing other fundamental cosmological parameters, such as the number of light particle species or the density of matter, which had to be adjusted in other proposed explanations to fit the data.

The study also checked whether this proposed deviation was physically possible. The required level of non-unitarity is very small, but it is large enough to be detectable. The authors compared their finding against existing constraints from terrestrial neutrino experiments, which have placed strict limits on how much the mixing can deviate from the standard model. They found that their best-fit value sits just inside the allowed range, meaning it is consistent with all current laboratory data. This makes the non-unitary mixing scenario a viable and elegant solution to the helium puzzle. It suggests that the universe's lightest elements are not just a record of the Big Bang, but also a sensitive probe of the hidden, heavy particles that may exist beyond our current detection capabilities.

While other explanations for the low helium count have been proposed, such as a different number of relativistic species or an imbalance in the number of neutrinos versus antineutrinos, those models require shifting the standard cosmological parameters away from their well-established values. The non-unitary mixing model, by contrast, keeps the standard cosmological picture intact while attributing the anomaly to a subtle, yet fundamental, property of neutrino physics. The authors emphasize that this is not a definitive proof, but a strong indication that the data can be explained without abandoning the standard cosmological framework. As future experiments refine the measurements of primordial helium and deuterium, and as terrestrial neutrino detectors become more sensitive, this specific deviation from unitarity will be put to the test. If confirmed, it would open a new window into the physics of the very first moments of our universe.

Technical Summary: Low Primordial Helium as a Probe of Non-Unitary Neutrino Mixing

Problem Statement
The paper addresses a recent tension in Big Bang Nucleosynthesis (BBN) cosmology. The EMPRESS collaboration reported a primordial helium mass fraction of $Y_P = 0.2402 \pm 0.0040$ , which lies more than $1\sigma$ below the standard $\Lambda$ CDM prediction of $Y_P \approx 0.2470$ . When combined with deuterium abundance ( $D/H$ ) and Planck baryon density constraints, this low $Y_P$ implies a $\sim 2\sigma$ tension with the standard effective number of relativistic species ( $N_{\text{eff}} = 3.044$ ) or suggests a non-zero electron-neutrino degeneracy ( $\xi_e$ ). While previous explanations have invoked modified expansion rates ( $N_{\text{eff}}$ ), lepton asymmetry, or exotic physics (e.g., early dark energy), this work investigates whether the discrepancy can be resolved by non-unitary neutrino mixing, a generic feature of seesaw extensions to the Standard Model (SM).

Methodology
The authors employ a theoretical framework where the three-neutrino mixing matrix is non-unitary due to mixing with heavy sterile states. This non-unitarity is parameterized by a matrix $N = \alpha U_{\text{PMNS}}$ , where $\alpha$ is a lower-triangular matrix. The key mechanism identified is the mismatch between the Fermi constant measured in muon decay ( $G_\mu^F$ ) and the effective Fermi constant governing beta decay ( $G_\beta^F$ ).

Theoretical Formalism: The paper derives that non-unitarity leads to $G_\beta^F = G_\mu^F / \sqrt{(NN^\dagger)_{22}}$ . Since $(NN^\dagger)_{22} \leq 1$ , it follows that $G_\beta^F \geq G_\mu^F$ . This enhancement increases the neutron-to-proton conversion rates ( $n \leftrightarrow p$ ), reducing the neutron abundance at freeze-out and consequently lowering the predicted $Y_P$ .
Numerical Implementation: The authors utilize the PRyMordial code to perform full numerical BBN calculations. They self-consistently implement two effects of non-unitarity:
- The direct modification of weak interaction rates via $G_\beta^F$ .
- The indirect modification of neutrino decoupling and $N_{\text{eff}}$ via non-standard neutral-current interactions.
Statistical Analysis: A $\chi^2$ analysis is performed using the EMPRESS 2025 $Y_P$ measurement, the deuterium abundance ( $D/H$ ), and the Planck baryon density prior. The analysis compares the non-unitary scenario (varying $\alpha_{22}$ ) against standard interpretations that vary $N_{\text{eff}}$ and/or the lepton asymmetry parameter $\xi_e$ .

Key Contributions and Results

Mechanism Identification: The paper demonstrates that a small deviation from unitarity, specifically $\alpha_{22} < 1$ , enhances the beta-decay rate sufficiently to lower $Y_P$ without requiring a change in the expansion rate ( $N_{\text{eff}}$ ) or lepton asymmetry.
Quantitative Fit: The full numerical calculation yields a best-fit point at $\alpha_{22} = 0.982$ and $\eta_{10} = 6.07$ . At this point, the standard cosmological parameters ( $N_{\text{eff}} = 3.044$ , $\xi_e = 0$ ) remain fully consistent with the data.
Comparison with Alternatives:
- In the standard scenario ( $\alpha_{22}=1$ ), fitting the low $Y_P$ requires $N_{\text{eff}} \approx 2.54$ (a significant deviation from 3.044) or a non-zero lepton asymmetry $\xi_e \approx 0.05$ .
- The non-unitary scenario reproduces the low $Y_P$ while keeping $N_{\text{eff}}$ and $\xi_e$ at their standard values.
Experimental Consistency: The required deviation ( $\alpha_{22} = 0.982$ ) lies just inside the current $3\sigma$ constraint derived from neutrino oscillation data ( $\alpha_{22} > 0.98$ ). The authors note that while CKM unitarity tests might suggest a tighter bound ( $\alpha_{22} > 0.999$ ), they adopt the more conservative oscillation-based limit to avoid assuming the absence of new physics in the quark sector.
Subdominant Effects: The paper confirms that the indirect effect of non-unitarity on $N_{\text{eff}}$ is negligible (changing $N_{\text{eff}}$ by less than $6 \times 10^{-3}$ over the relevant range), meaning the primary driver of the $Y_P$ reduction is the direct modification of the weak interaction rates.

Significance
The paper claims that non-unitary neutrino mixing provides a "viable explanation" for the EMPRESS low helium measurement. Its primary significance lies in offering a solution that does not require modifying the standard cosmological parameters ( $N_{\text{eff}}$ , $\eta$ , $\xi_e$ ) or invoking exotic cosmological models. Instead, it attributes the anomaly to a single, well-motivated particle physics parameter ( $\alpha_{22}$ ) inherent in seesaw extensions of the Standard Model. The authors conclude that improved determinations of $Y_P$ and $D/H$ , alongside future terrestrial neutrino experiments, will be crucial for testing this specific non-unitary scenario.

Technical Summary: Low Primordial Helium as a Probe of Non-Unitary Neutrino Mixing

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