Leptoquarks and the Emergence of the Standard Model Gauge Group in a Self-Consistent Preon Model

TL;DR

This paper demonstrates that in a preon model, both leptoquarks and the Standard Model gauge group naturally emerge as predictions, with specific properties and implications for proton decay and composite structures.

Contribution

It introduces a self-consistent preon model where gauge groups and leptoquarks are emergent, not assumed, and develops the vertical bootstrap principle for organizing composite states.

Findings

Leptoquarks with specific charges emerge as structural predictions.

Proton decay via leptoquarks is highly suppressed, consistent with experimental bounds.

The Standard Model gauge group arises as a low-energy emergent symmetry.

Abstract

We show that in a self-consistent preon model, where Standard Model quarks and leptons are three-body composites confined at a metacolor scale Lambda_cr ~ 10^14 GeV, both leptoquarks and the Standard Model gauge group SU(3)_c x SU(2)_L x U(1)_Y emerge as structural predictions rather than inputs. Combining the preon content of a quark with that of a lepton gives exactly four distinct six-body bosonic leptoquark composites per generation, with electric charges Q = +2/3, -1/3, -1/3, -4/3 and a universal B-L = -2/3 fixed by the preon charge assignments. Their mass is of order Lambda_cr rather than of order the SM fermion masses, because the dynamical near-cancellation that produces light fermion masses is specific to three-body fermionic composites and does not extend to six-body bosonic ones. The fractional B-L = -2/3 forbids proton decay via single leptoquark exchange, requiring a dimension-12 operator and giving tau(p -> e+ pi0) ~ 10^58 years, consistent with the experimental bound > 2.4 x 10^34 years. It is shown that the SM gauge group emerges as a low-energy symmetry consistent with the Planck-scale boundary condition, and leptoquarks are required -- not merely permitted -- by the matching. The anomaly-matching argument extends to a tower of 3n-body composites, each level imposing consistency conditions on the next; we call this the vertical bootstrap and advance it as the organizing principle of the preon program.