Baryon Asymmetry of the Universe from Preon Confinement and Supersymmetry Breaking

Abstract: We propose a mechanism for generating the baryon asymmetry of the universe (BAU) within a supersymmetric preon model based on $U(1)\times SU(3)$ internal symmetry. Integrating out massive preons at the confinement scale $Λ<em>{cr} \sim 10<sup>{14}$ GeV induces a Chern-Simons (CS) term in the effective gauge action via the Callan-Harvey anomaly inflow mechanism, deriving rather than assuming the topological structure required for the model. The confinement transition, at which supersymmetry breaks intrinsically through the differential condensation of fermionic and bosonic preon composites, provides the necessary departure from thermal equilibrium. The time-varying CS coefficient sources a net topological charge, which the anomaly equation converts directly into baryon number. Electroweak sphalerons are out of equilibrium at $Λ</em>{cr}$, protecting the asymmetry from immediate washout. Matching the observed baryon-to-entropy ratio $η\sim 8.7\times 10<sup>{-10}$ constrains the fermion/boson condensation asymmetry to $ε\simeq 0.022$, a value consistent with a one-loop origin. This mechanism is structural rather than statistical, and the electroweak phase transition plays no role.

• The paper proposes baryogenesis at a preon confinement scale of about 10^14 GeV, where supersymmetry-breaking condensation generates a Chern-Simons term through anomaly inflow and converts topological charge into baryon number.
• The mechanism reproduces the observed baryon-to-entropy ratio of approximately 8.7 × 10^-10 when the fermion–boson condensation asymmetry is ε ≈ 0.022, consistent within order of magnitude with a loop-generated mass splitting.
• The scenario makes electroweak baryogenesis unnecessary but still requires solutions to intermediate-temperature sphaleron washout, an explicit triangle-diagram calculation, and a first-principles model of preon confinement.

Overview

The paper proposes a baryogenesis mechanism operating at the preon confinement scale $\Lambda_{cr} \sim 10^{14}$ GeV within a supersymmetric preon model with $U(1) \times SU(3)$ internal symmetry (2603.15694). Rather than relying on the electroweak phase transition, the mechanism derives a Chern-Simons (CS) term in the effective $U(1)$ gauge action via the Callan-Harvey anomaly inflow mechanism when massive charged preons are integrated out. The time variation of the CS coefficient during a SUSY-breaking confinement transition sources topological charge, which the anomaly equation converts into baryon number. Matching the observed baryon-to-entropy ratio $\eta \simeq 8.7 \times 10^{-10}$ fixes the model's single free parameter, the fermion/boson condensation asymmetry, to $\epsilon \simeq 0.022$.

The preon model and intrinsic SUSY breaking

The model contains two fundamental fermionic preons, $\psi_0 \sim (0, \mathbf{3})$ and $\psi_1 \sim (1/3, \mathbf{1})$, with anomaly cancellation requiring the completion $\tilde\psi_0 \sim (0, \bar{\mathbf{3}})$ and $\psi_{-1} \sim (-1/3, \mathbf{1})$. Above $\Lambda_{cr}$ the preons are free; below, SM quarks, leptons, and their superpartners emerge as three-body composites. Supersymmetry breaks intrinsically at confinement: because fermionic and bosonic composites condense at different rates, superpartner masses are set by a different dynamical scale than SM masses.

At tree level, the Yukawa-type preon interaction potential yields degenerate fermionic and bosonic binding energies ($U(1) \times SU(3)$0), so the mass splitting is genuinely loop-generated:

$U(1) \times SU(3)$1

For $U(1) \times SU(3)$2 this gives $U(1) \times SU(3)$3, within a factor of four of the observationally required $U(1) \times SU(3)$4. The author presents this as consistent with a one-loop origin without fine-tuning, though the estimate is admittedly crude and depends on the unspecified confinement dynamics.

Induced Chern-Simons term

The technical core of the paper is a one-loop computation of the three-point function of the $U(1) \times SU(3)$5 gauge field from integrating out the massive charged preons $U(1) \times SU(3)$6 and $U(1) \times SU(3)$7. The triangle diagram with a closed fermion loop produces a Levi-Civita tensor structure via the $U(1) \times SU(3)$8 trace identity, and the scalar integral evaluates to a mass-independent result:

$U(1) \times SU(3)$9

This is the standard non-decoupling behavior of anomaly inflow: the induced CS coefficient $U(1)$0 is topological and insensitive to the magnitude of the preon mass, making the mechanism stable against radiative corrections to $U(1)$1. In thermal equilibrium the contributions of $U(1)$2 and $U(1)$3 cancel exactly, so no asymmetry is generated — the departure from equilibrium is supplied by the differential condensation during the SUSY-breaking transition, which accumulates

$U(1)$4

with a factor of 3 for preon generations. A notable claim is that this CS term is derived rather than assumed, in contrast to the author's earlier work in the same framework, which relied on a statistical fluctuation of the CS background — a mechanism vulnerable to the objection that the observed asymmetry is a local accident of our Hubble patch. The present mechanism is structural and universal across Hubble patches.

Baryon number generation and the observed asymmetry

The anomaly equation $U(1)$5 with $U(1)$6 gives $U(1)$7. The confinement transition is argued to be first-order: the massive gauge field of Maxwell-Chern-Simons QED generates a cubic term in the finite-temperature effective potential via Coleman-Weinberg, driving bubble nucleation. The paper concedes that the non-relativistic approximation underlying the preon potential is marginal at $U(1)$8 and that a fully relativistic treatment is deferred.

Washout protection at the generation epoch follows from the rate comparison $U(1)$9 GeV versus $\eta \simeq 8.7 \times 10^{-10}$0 GeV at $\eta \simeq 8.7 \times 10^{-10}$1, so electroweak sphalerons are out of equilibrium at confinement. The baryon-to-entropy ratio evaluates to

$\eta \simeq 8.7 \times 10^{-10}$2

which, matched to the observed $\eta \simeq 8.7 \times 10^{-10}$3, yields $\eta \simeq 8.7 \times 10^{-10}$4. The paper emphasizes that the smallness of $\eta \simeq 8.7 \times 10^{-10}$5 is not due to a small $\eta \simeq 8.7 \times 10^{-10}$6 alone but to the combined suppression from $\eta \simeq 8.7 \times 10^{-10}$7, $\eta \simeq 8.7 \times 10^{-10}$8, and the preon charge factor $\eta \simeq 8.7 \times 10^{-10}$9.

The electroweak phase transition as spectator

The paper argues that the electroweak phase transition plays no generative role: the asymmetry is imprinted on the composite spectrum at $\epsilon \simeq 0.022$0, eleven orders of magnitude in temperature above electroweak symmetry breaking. This makes the mechanism independent of the Higgs mass, the order of the EWPT, and LHC constraints on electroweak-scale BSM physics. The author also notes that fixing $\epsilon \simeq 0.022$1 constrains the preon gauge coupling $\epsilon \simeq 0.022$2 at $\epsilon \simeq 0.022$3, which in turn determines soft SUSY-breaking parameters and potentially predicts superpartner masses.

Limitations and open problems

The paper is candid about three unresolved issues. First, the intermediate-scale washout problem: sphalerons re-enter equilibrium for $\epsilon \simeq 0.022$4 GeV, and if the generated asymmetry carries $\epsilon \simeq 0.022$5, the standard argument would erase it. The paper offers an "emergent symmetry" mitigation — $\epsilon \simeq 0.022$6, $\epsilon \simeq 0.022$7, and even $\epsilon \simeq 0.022$8 are emergent composite-level structures in this framework, so sphalerons act only on a spectrum that already carries the asymmetry — but explicitly concedes that a rigorous demonstration requires a complete treatment of emergent $\epsilon \simeq 0.022$9 dynamics not currently available. Two conservative fallbacks are proposed: nonzero $\psi_0 \sim (0, \mathbf{3})$0 from the $\psi_0 \sim (0, \mathbf{3})$1 extension, and dynamical freezing in the condensed phase of the first-order transition. Second, the triangle-diagram coefficient has not been evaluated explicitly within the $\psi_0 \sim (0, \mathbf{3})$2 framework; an explicit FeynCalc computation is planned for a companion paper. Third, the confinement force itself remains unspecified (hypercolor, four-fermion interaction, or $\psi_0 \sim (0, \mathbf{3})$3-based), so $\psi_0 \sim (0, \mathbf{3})$4 is currently fitted observationally rather than derived; only if computed from first principles does the result become a genuine prediction.

Conclusion

The paper constructs a high-scale baryogenesis scenario in which the three Sakharov conditions are satisfied by three independent features of preon dynamics: $\psi_0 \sim (0, \mathbf{3})$5 violation from the anomaly equation acting on a derived CS term, CP violation from the condensation asymmetry $\psi_0 \sim (0, \mathbf{3})$6, and non-equilibrium from the intrinsically SUSY-breaking confinement transition. Its principal quantitative result is $\psi_0 \sim (0, \mathbf{3})$7, consistent with a one-loop origin, and its principal structural claim is that the mechanism is derived rather than assumed and operates uniformly across Hubble patches. The framework's viability ultimately rests on resolving the emergent-gauge-symmetry washout question and specifying the confinement dynamics, both of which the author identifies as the immediate program for future work.