Dynamical Origin of the Higgs Mechanism via Discrete Lattice Spinor Condensation and Nonperturbative Gap Equations

The microscopic origin of the Higgs mechanism in the Standard Model remains a fundamental theoretical challenge. We propose a nonperturbative lattice framework in which the Higgs field emerges dynamically as a collective excitation of chiral spinor condensates, rather than as a fundamental scalar degree of freedom. By utilizing the overlap Dirac operator, we preserve exact lattice chiral symmetry through the Ginsparg-Wilson relation, allowing for a consistent formulation of fermion condensation on the lattice. Through the Hubbard-Stratonovich transformation, we derive an effective action in which a nonvanishing vacuum expectation value is dynamically generated in the strong-coupling regime, leading to the emergence of a Mexican-hat potential structure without assuming an elementary tachyonic mass term. Our results suggest that the electroweak scale may emerge from the collective dynamics of lattice fermions, offering a dynamical interpretation of the mass hierarchy.