⚛️ phenomenology

The flavour of SU(15) composite quarks and leptons

This paper proposes an $SU(15)_p$ composite model where Standard Model particles emerge as bound states, demonstrating that a specific flavor structure with two spurions can simultaneously reproduce all quark and lepton masses and the CKM matrix while predicting that electron electric dipole moments and neutral kaon mixing provide the most stringent constraints on the compositeness scale, potentially reaching up to $10^6$ TeV.

Original authors: Benoît Assi, Ryan Plestid, Amartya Sengupta, Jure Zupan

Published 2026-08-04

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CC BY 4.0

Original authors: Benoît Assi, Ryan Plestid, Amartya Sengupta, Jure Zupan

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, intricate LEGO set. For decades, scientists have been building models of reality using the smallest bricks they can find: particles like electrons and quarks. The Standard Model is the current instruction manual, treating these particles as fundamental, unbreakable dots. But what if they aren't dots at all? What if, deep down, they are tiny, complex structures made of even smaller, invisible pieces? This is the realm of "composite models," a wild idea where the familiar particles we know are actually bound states of hypothetical "preons," held together by a mysterious, super-strong force that only kicks in at incredibly high energies.

The big question is: if these tiny LEGO bricks exist, why do we see the specific patterns of mass and mixing that we do? Why is an electron so light while a top quark is heavy? Why do particles change flavors (like a muon turning into an electron) in very specific, rare ways? Usually, if you build a model with new, tiny bricks, you accidentally create a mess of "flavor violations"—particles swapping identities too often, which we don't see in real life. This creates a tightrope walk for physicists: they need a model that explains the heavy and light particles and keeps the flavor-swapping under control, all while hiding the new bricks from our current microscopes.

This paper dives into a specific, bold proposal where the Standard Model's particles emerge from a theory called SU(15). Think of this theory as a massive, 15-dimensional dance floor where "preons" are the dancers. The authors, Benoît Assi and colleagues, investigate how this dance floor produces the three generations of quarks and leptons we see, and how it generates the specific "flavor" patterns (the masses and mixings) without breaking the rules of the universe. They find that by introducing two special "conductor" fields (scalars) that break the symmetry of the dance, the model can naturally reproduce the observed masses of all quarks and charged leptons, as well as the CKM matrix (the rulebook for how quarks mix).

However, the story doesn't end with a perfect fit. The paper suggests that while this model works beautifully for mass, it makes very specific predictions about how often particles should break the rules and swap flavors. The authors run a detailed numerical simulation to see if their "benchmark" version of the model holds up against real-world data. They find that the model is surprisingly predictive: the same mechanisms that give particles their mass also dictate how often they should decay or mix. The results suggest that the scale at which these preons exist (the "compositeness scale," $\Lambda_{pre}$ ) must be incredibly high—around $10^4$ to $10^5$ TeV—to avoid contradicting current experiments.

Crucially, the paper argues that the most sensitive way to test this theory isn't necessarily by smashing particles together in a collider (which would need to be impossibly powerful), but by looking for extremely rare events. The authors calculate that the electron's electric dipole moment (a measure of how "lopsided" its charge distribution is) and the mixing of neutral kaons ( $K^0-\bar{K}^0$ ) are the "smoking guns." In their benchmark scenario, these observables constrain the preon scale to be around $10^4$ TeV. Interestingly, they predict that future experiments measuring the electron's dipole moment could push this sensitivity up to $10^6$ TeV, potentially seeing the effects of these preons even before we can directly observe proton decay. The paper concludes that while the model is consistent with current data, it is tightly constrained, and the next generation of precision experiments will be the ultimate judge of whether these hidden preons are real or just a beautiful mathematical mirage.

Technical Summary: The Flavour of SU(15) Composite Quarks and Leptons

Problem Statement
While the Standard Model (SM) successfully describes elementary particles, the possibility that quarks and leptons are composite bound states of more fundamental "preons" remains a compelling theoretical avenue. A significant challenge in preon models has been generating light fermionic composite states consistent with experimental data, particularly regarding the observed hierarchies of fermion masses and the structure of the Cabibbo-Kobayashi-Maskawa (CKM) mixing matrix. Previous work by the authors and collaborators proposed an SU(15) $_p$ confining chiral gauge theory where the SM quarks, leptons, and Higgs emerge as composite bound states. However, the detailed flavour structure of this model—specifically how it generates realistic Yukawa couplings and CKM mixing while satisfying low-energy flavour constraints—remained largely unexplored. This paper addresses the gap between the model's high-scale dynamics and its low-energy phenomenological predictions.

Methodology
The authors analyze the SU(15) $_p$ preon model, which contains 19 fundamental chiral fermions and one conjugate symmetric fermion, confined at a scale $\Lambda_{\text{pre}}$ . The model possesses a global SU(4) $_F$ flavour symmetry acting on four singlet preons, which is spontaneously broken to SU(3) $_F$ to yield three generations. To generate realistic flavour structures, the model introduces two scalar fields, $A$ and $A'$ , transforming in the conjugate antisymmetric (105) and symmetric (120) representations of SU(15) $_p$ , respectively.

The methodology involves:

Effective Operator Construction: Deriving the SM Yukawa couplings for quarks and charged leptons by integrating out the scalar fields $A$ and $A'$ at the confinement scale. This involves matching preon-level operators to prebaryon-level effective operators using large- $N$ ( $N=15$ ) power counting and Dimensional Analysis (NDA).
Flavour Spurion Analysis: Treating the Yukawa couplings of the scalars to the singlet preons ( $\lambda$ and $\lambda'$ ) as flavour spurions. The authors impose a hierarchical Froggatt-Nielsen-like texture on these spurions, controlled by a small parameter $\kappa \sim 0.15$ , to seed the observed mass hierarchies.
Numerical Benchmarking: Performing a numerical minimization to fit the non-perturbative coefficients (matrix elements) and spurion parameters to the observed six quark masses, three charged lepton masses, and the CKM matrix. The fit assumes $O(1)$ non-perturbative coefficients and explores the impact of "right-handed isospin" ( $SU(2)_I$ ) symmetry breaking.
Phenomenological Constraints: Calculating the Wilson coefficients for various flavour-changing neutral current (FCNC) processes, including dipole operators, semi-leptonic and leptonic four-fermion operators, and neutral meson mixing. These are compared against current experimental bounds (e.g., proton decay, EDMs, $K^0-\bar{K}^0$ mixing, $\mu \to e\gamma$ ) to determine the lower bounds on the compositeness scale $\Lambda_{\text{pre}}$ .

Key Contributions

Yukawa Generation Mechanism: The paper demonstrates that the quark and charged lepton Yukawa matrices arise from a combination of tree-level scalar exchanges and one-loop box diagrams. Crucially, it identifies that a "right-handed isospin" symmetry ( $SU(2)_I$ ) naturally aligns up- and down-type Yukawas, predicting a trivial CKM matrix unless this symmetry is broken. The authors show that spontaneous breaking via composite scalar vacuum expectation values (vevs) is the primary mechanism required to generate a realistic CKM matrix.
Lepton Sector Distinction: Unlike the quark sector, the lepton Yukawa couplings are found to be $1/N$ suppressed due to a mismatch in preon species between charged leptons and the composite Higgs. The model requires "non-local" contributions mediated by light composite scalar bound states (di-prebaryons) to generate the correct lepton mass hierarchy, particularly for the tau lepton.
Benchmark Fit: The authors provide a specific benchmark fit where $O(1)$ non-perturbative coefficients reproduce all SM fermion masses and the CKM matrix. This fit reveals that the model requires only mild fine-tuning (cancellations of order a few) in the first-generation sector to match the small up-quark mass and specific CKM elements, while heavier generations are naturally reproduced.
Flavour Constraints on $\Lambda_{\text{pre}}$ : The study systematically evaluates the reach of various flavour observables on the compositeness scale. It establishes that while proton decay sets a baseline bound in the range of $\Lambda_{\text{pre}} \sim 10^4$ – $10^6$ TeV (depending on vector-like quark masses and Wilson coefficients), precision flavour physics offers competitive and complementary sensitivity.

Results

Mass Hierarchies: The hierarchical texture of the spurions $\lambda$ and $\lambda'$ successfully generates the observed mass hierarchies. The up-type quark masses scale roughly as $\kappa^4, \kappa^2, 1$ , while down-type quarks and charged leptons follow similar patterns, with the top-bottom mass splitting driven primarily by the ratio of Higgs vevs ( $\tan \beta \approx 23$ ).
CKM Matrix: The misalignment between the up and down Yukawa matrices, induced by the breaking of $SU(2)_I$ via composite scalar vevs, generates a non-trivial CKM matrix consistent with experimental data.
Sensitivity to $\Lambda_{\text{pre}}$ :
- Strongest Constraints: In the benchmark scenario, the electron Electric Dipole Moment (e-EDM) and the CP-violating parameter $\epsilon_K$ in $K^0-\bar{K}^0$ mixing provide the strongest constraints, reaching sensitivities of $\Lambda_{\text{pre}} \sim 9.5 \times 10^3$ TeV and $\sim 8.5 \times 10^3$ TeV, respectively.
- Future Projections: The projected sensitivity of future e-EDM experiments ( $d_e \sim 10^{-34}$ e cm) could extend the reach to $\Lambda_{\text{pre}} \sim 2 \times 10^6$ TeV, surpassing the projected reach of Hyper-Kamiokande for proton decay.
- Complementary Probes: Processes such as $\mu \to e\gamma$ , $D^0-\bar{D}^0$ mixing, and $B_d-\bar{B}_d$ mixing provide complementary reach in the $10^2$ – $10^3$ TeV range.
- Anarchic vs. Benchmark: Under a flavour-anarchic prior (assuming $O(1)$ flavour-violating coefficients), the e-EDM sensitivity is significantly higher ( $\sim 1.3 \times 10^6$ TeV). However, the specific hierarchical structure of the benchmark fit suppresses many off-diagonal couplings, reducing the sensitivity of some observables (like $\mu \to e\gamma$ ) but maintaining the e-EDM and $\epsilon_K$ as the most powerful probes within the benchmark scenario.

Significance
The paper claims that flavour physics serves as a highly competitive and complementary probe to proton decay searches for testing the SU(15) preon model. The tight correlation between the generation of SM fermion masses and the mediation of flavour-violating processes makes the model predictive. The authors emphasize that the electron EDM and neutral kaon mixing are currently the most sensitive low-energy probes of the compositeness scale in this framework. Furthermore, the study highlights that the model can accommodate the observed flavour structure with $O(1)$ non-perturbative coefficients, suggesting that the required dynamics are natural within the large- $N$ expansion. The work establishes a concrete link between the high-scale dynamics of chiral gauge theories and precision flavour observables, demonstrating that future improvements in EDM and meson mixing measurements could probe scales beyond the reach of direct collider searches or even future proton decay experiments.

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