Abstract

We propose a lattice structure and space group symmetry, Pmmm (No. 47), for the QCD condensate ground state, whose Wyckoff positions are occupied by the four light quarks and antiquarks u, d, u~, d~. These serve as the fundamental building blocks of both the condensate lattice ground state and the baryonic and leptonic particle excitations embedded within it as topological defects of the nominal Wyckoff occupation, offering a more structured alternative to the QCD instanton liquid picture. Building on Bloch quark wave solutions of a tight-binding Hamiltonian defined on this lattice, we propose a generalization of Einstein’s Equivalence Principle: composite particles embedded in the lattice and propagating by tunnelling cannot distinguish acceleration by gravity, the strong, weak, or electromagnetic forces, or curvature of the lattice itself, arising from local variation in unit cell shape. We derive an eight-by-eight tight-binding Hamiltonian that decouples into two four-by-four blocks separating the quark and antiquark sectors. Electrons, positrons, protons, neutrons, deuterons, and α-particles are embedded in the lattice as defect-induced deviations from the nominal Wyckoff occupation, with their spin and helicity emerging structurally from this picture. We further propose that the lattice’s unit cells carry a small nonzero rest mass, whose collective gravitational effect across a galactic halo may account for the discrepancy between visible mass and rotation curves, identifying the Pmmm condensate as a dark matter candidate. Finally, we outline a mechanism near black hole horizons by which local melting of the condensate lattice followed by quark reactions that conserve the number and flavor of the quarks could yield a new route to baryon asymmetry. We propose a framework that goes several steps beyond the Standard Model by introducing a Pmmm space group unit cell for the QCD condensate ground state, built from the four light quarks and antiquarks u, d, u~, d~. We further propose that topological defects of the Pmmm condensate lattice are the geometric origin of particle excitations.

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