Investigations into Metric Phase Transition Dynamics as the Origin of the Higgs Resonance and Quark Confinement. On the Coupling of Spacetime Elasticity and Particle Masses: A Non-Perturbative Approach to the Weak Interaction

Abstract. This paper investigates a theoretical framework that interprets the masses of elementary particles not as coupling constants to an external field, but as eigenstates of a variable spacetime metric. The central element is the lapse function N, acting as a scalar time-density, and the introduction of a non-linear metric stiffness ξ. It is shown that the rest mass of a particle is obtained as the volume integral over the deformation work stored in the metric field. The W-boson at 80.4 GeV is interpreted as the energetic threshold at which the spacetime metric departs from its linear elasticity, corresponding to the proportionality limit. At 125 GeV, the Higgs resonance is identified as the yield point where a metric phase transition and a dissipative rearrangement of the local time-density occur. The top quark at 173 GeV represents the ultimate strength or point of work hardening before the metric transitions into a state that no longer permits fermionic soliton solutions. The sequence MW→MH→Mtop thus maps a complete mechanical stress-strain curve of the vacuum. Quark confinement is derived as a consequence of the metric boundary conditions where a divergent gradient ∇N→∞ at the baryon radius creates a gradient wall, leading to geometric total reflection. Conversely, the homogeneity of the field N inside the baryon bubble provides a geometric basis for asymptotic freedom. The weak interaction is parameterised through the Fermi constant GF, which is identified as being proportional to the inverse stiffness of the spacetime barrier. The neutrino is modeled as a propagating topological node and a chiral-geometric torsion wave in the shift vector βi, which explains its half-integer spin and its identity as a pure Dirac fermion. Consequently, the theory strictly prohibits neutrinoless double beta decay 0νββ.