⚛️ phenomenology

Predictive Non-Minimal SU(5) GUT

This paper proposes a predictive non-minimal SU(5) Grand Unified Theory that replaces the standard 24-dimensional Higgs representation with a 75-dimensional one to resolve gauge coupling unification and fermion mass issues, thereby establishing a testable unification scale range that is partially excluded by current data but accessible to future experiments like Hyper-Kamiokande.

Original authors: Ilja Doršner, Mijo Matković, Shaikh Saad

Published 2026-09-15

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CC BY 4.0

Original authors: Ilja Doršner, Mijo Matković, Shaikh Saad

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

At the heart of modern physics lies a persistent puzzle: the universe appears to be governed by three distinct forces that act on matter, yet these forces behave with different strengths depending on the energy involved. Scientists have long suspected that at extremely high energies, these three forces merge into a single, unified interaction, much like how water, ice, and steam are all just different states of the same substance. The most famous attempt to describe this unification is a theory called SU(5), which proposes that all known particles and forces emerge from a single, elegant mathematical structure. However, the original version of this theory, proposed decades ago, runs into a fatal flaw. While it successfully describes how the unified force might split apart as the universe cooled, it fails to predict the correct strengths of the forces we observe today, and it also predicts that protons—the building blocks of our atoms—should decay far faster than they actually do.

A team of researchers has now revisited this old framework to see if a small change in its architecture could fix these problems. Instead of using the standard mathematical tool that the original theory relied on, they swapped it for a more complex one. This new configuration not only allows the forces to unify correctly but also pushes the energy scale where this unification happens to a level that is just within reach of our most sensitive particle detectors. The study suggests that this modified version of the theory is a viable alternative to the standard model, offering a path forward that can be tested in the near future.

The researchers began by examining the mechanism that breaks the unified force apart. In the original theory, this breaking is achieved by a specific type of field, often visualized as a scalar field, which settles into a particular state. The original model used a field with twenty-four components to do this job. While this was the simplest possible choice, it led to the incorrect predictions mentioned earlier. The team proposed replacing this twenty-four-component field with a much larger one containing seventy-five components. This might sound like a minor adjustment, but in the language of particle physics, changing the size and shape of this field fundamentally alters how the forces interact as they separate.

When the team ran the numbers for this new setup, they found that the forces finally unified at a single point, something the original model could not achieve. They calculated that this unification happens at an energy scale between one point six times ten to the fifteen and one point three times ten to the sixteen gigaelectronvolts. This range is significant because it is low enough that the heavy particles responsible for breaking the unified force should be light enough to be detected by upcoming experiments, yet high enough to keep protons stable for a very long time. The researchers noted that part of this allowed range is already in tension with existing data from the Super-Kamiokande detector in Japan, which has been searching for signs of proton decay for decades. However, the next generation of detectors, such as Hyper-Kamiokande, will be sensitive enough to either confirm or rule out this specific scenario entirely.

There was, however, a second problem with the original theory that this new setup did not automatically solve. The standard model predicts that the masses of certain particles, specifically the down-type quarks and the charged leptons, should be identical at the unification scale. In reality, these particles have very different masses. The original theory offered three different ways to fix this mismatch by adding extra, invisible particles called vector-like fermions. The researchers discovered that their new seventy-five-component model is much more restrictive. Due to the specific mathematical rules governing this larger field, only one specific type of vector-like fermion pair could be added to fix the mass problem. All other options were mathematically impossible.

By adding this single, unique pair of extra particles, the team showed that the model could simultaneously achieve the correct unification of forces and produce the realistic masses we observe for all known charged particles. In this refined version, the energy scale for unification could be pushed slightly higher, up to nearly three times ten to the sixteen gigaelectronvolts. This adjustment keeps the theory consistent with the known universe while maintaining its predictive power. The study concludes that this framework, with its specific combination of a large scalar field and a single type of extra fermion, stands as a serious and testable alternative to the standard unification models. It transforms a theory that was once considered flawed into one that is not only mathematically consistent but also poised for direct experimental verification in the coming years.

Technical Summary: Predictive Non-Minimal SU(5) GUT

Problem Statement
The standard Georgi-Glashow $SU(5)$ Grand Unified Theory (GUT), which utilizes a 24-dimensional scalar representation ( $\mathbf{24}$ ) to break $SU(5)$ down to the Standard Model (SM) gauge group $SU(3)_C \times SU(2)_L \times U(1)_Y$ , faces two critical phenomenological failures. First, the minimal model fails to achieve gauge coupling unification at a single energy scale when the subsequent electroweak symmetry breaking is mediated by a 5-dimensional scalar ( $\mathbf{5}$ ). Second, the model predicts a mass degeneracy between down-type quarks and charged leptons ( $m_d = m_e$ at the unification scale) that is inconsistent with observed fermion masses. While vectorlike fermions can resolve the mass degeneracy issue in the 24-dimensional scenario, the gauge coupling unification problem remains unsolved in the minimal setup.

Methodology
The authors propose replacing the 24-dimensional scalar representation with a 75-dimensional representation ( $\mathbf{75}$ ) to address the unification issue. The study proceeds in two stages:

Scalar Sector Analysis: The authors analyze the symmetry breaking chain $SU(5) \xrightarrow{\langle \mathbf{75} \rangle} SU(3) \times SU(2) \times U(1) \xrightarrow{\langle \mathbf{5} \rangle} SU(3) \times U(1)_{em}$ . They derive the full mass spectrum of the scalar multiplets within the $\mathbf{75}$ representation by constructing the renormalizable scalar potential involving operators $I_2, I_3, I_4$ . They establish a specific mass relation among the scalar sub-multiplets ( $24m^2_{\Phi_{8,1}} + m^2_{\Phi_{3,1}} - 10m^2_{\Phi_{6,2}} = 0$ ) derived from the potential's stationary conditions.
Renormalization Group Evolution (RGE): Using one-loop RGEs, the authors calculate the unification scale ( $m_{GUT}$ ) by varying the masses of the scalar multiplets residing between the electroweak scale ( $m_Z$ ) and $m_{GUT}$ . They utilize experimental inputs for gauge couplings at $m_Z$ and the $\beta$ -function coefficients for all SM and GUT fields.
Fermion Sector Extension: To address the fermion mass degeneracy, the authors investigate the introduction of vectorlike fermions. They perform a group-theoretical analysis to determine which vectorlike representations are compatible with the antisymmetric tensorial structure of the $\mathbf{75}$ representation. They construct the Yukawa Lagrangian and mass matrices for a scenario including a vectorlike pair $\mathbf{10}_F + \overline{\mathbf{10}}_F$ .

Key Contributions and Results

Gauge Coupling Unification: The substitution of the $\mathbf{24}$ with the $\mathbf{75}$ representation successfully achieves gauge coupling unification, a feat the minimal Georgi-Glashow model cannot accomplish. The analysis identifies two specific scalar multiplets within the $\mathbf{75}$ as critical for maximizing the unification scale: the $\Phi_{8,1}$ (an $SU(3)$ octet, $SU(2)$ singlet) and the $\Phi_{8,3}$ (an $SU(3)$ octet, $SU(2)$ triplet).
- In the pure scalar scenario (without vectorlike fermions), the unification scale is constrained to $1.6 \times 10^{15} \text{ GeV} \lesssim m_{GUT} \lesssim 1.3 \times 10^{16} \text{ GeV}$ .
- The authors note that the $\Phi_{8,3}$ multiplet is highly efficient in satisfying the unification condition but is constrained by proton decay limits.
Proton Decay Constraints: The predicted unification scale places the model within the sensitivity range of current and future proton decay experiments.
- Current Super-Kamiokande data excludes a portion of the parameter space, specifically constraining the masses of the $\Phi_{8,1}$ and $\Phi_{8,3}$ multiplets (e.g., $m_{\Phi_{8,1}} \lesssim 8.3 \times 10^8 \text{ GeV}$ ).
- The authors highlight that a specific $Z_2$ -odd limit where $m_{\Phi_{8,1}} = m_{\Phi_{8,3}} \approx 10^8 \text{ GeV}$ would be fully testable by the upcoming Hyper-Kamiokande experiment.
Unique Vectorlike Fermion Solution: The paper demonstrates that the $\mathbf{75}$ -dimensional scenario imposes strict group-theoretical constraints on fermion extensions. Unlike the $\mathbf{24}$ scenario, which allows for three types of vectorlike fermions ( $\mathbf{5}+\overline{\mathbf{5}}$ , $\mathbf{10}+\overline{\mathbf{10}}$ , $\mathbf{15}+\overline{\mathbf{15}}$ ) to break mass degeneracy, the $\mathbf{75}$ scenario uniquely permits only the $\mathbf{10}_F + \overline{\mathbf{10}}_F$ pair. This is due to the antisymmetric nature of the $\mathbf{75}$ tensor and the vanishing contraction $\mathbf{75}^{ij}_{jk} = 0$ , which prevents other mixing terms.
- With the inclusion of the $\mathbf{10}_F + \overline{\mathbf{10}}_F$ pair, the model generates realistic charged fermion masses.
- This extension pushes the upper bound of the unification scale to $m_{GUT} \lesssim 2.9 \times 10^{16} \text{ GeV}$ , with the optimal spectrum requiring the vectorlike quark doublet ( $Q_c$ ) and the $\Phi_{8,1}$ scalar to reside near the 1 TeV scale.

Significance
The authors claim that the proposed framework serves as a "phenomenologically viable alternative" to the standard Georgi-Glashow paradigm. The significance of the work lies in its predictivity:

It resolves the gauge coupling unification failure of the minimal model.
It restricts the vectorlike fermion sector to a single, unique solution ( $\mathbf{10}_F + \overline{\mathbf{10}}_F$ ), thereby reducing model ambiguity compared to the 24-dimensional case.
It predicts a unification scale that is experimentally accessible via nucleon decay searches (specifically $p \to \pi^0 e^+$ ) at Hyper-Kamiokande and DUNE, rather than being pushed to the Planck scale or beyond experimental reach.

The paper concludes that while the 75-dimensional scenario requires fine-tuning to solve the doublet-triplet splitting problem (as is common in GUTs), it offers a robust, testable, and highly predictive structure for $SU(5)$ unification.

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