The Standard Model Lagrangian from the Cohesion Unified Field Theory

The Standard Model Lagrangian LSM = Lgauge+Lfermion+LHiggs+LYukawa is assembled
here from the results of the preceding papers in this series. Each sector has a geometric
origin in the Cohesion Unified Field Theory recursion field. The gauge sector (Lgauge) is
the energy density of the torsion phase connection fields derived in the gauge structure
paper. The fermion sector (Lfermion) is the gauge-covariant Dirac equation from the
Dirac and gauge structure papers. The Higgs sector (LHiggs) is the new contribution
of this paper: the Higgs field is identified as the phase separation order parameter
of the recursion medium, Φ ∝ ∆R(Dst) = R(Dst) − R0. The Mexican hat potential
V (Φ) = −µ
2
|Φ|
2 + λ|Φ|
4
is the energy of the recursion medium as a function of its
departure from electroweak phase equilibrium. The Yukawa sector (LYukawa) couples the
fermion torsion interval structure to the phase separation order parameter, generating
fermion masses. The hierarchy problem — why the Higgs mass is not driven to the
Planck scale by radiative corrections — dissolves in the Cohesion UFT: the Higgs field
is not a fundamental scalar but the phase separation of the recursion medium, and µ
2
is
the geometric curvature of R(Dst) at the electroweak density threshold, not a parameter
subject to radiative corrections. The Standard Model provides the precise quantitative
description of all particle physics; the Cohesion UFT provides the geometric substrate
from which the Lagrangian structure emerges.