IndisputableMonolith.StandardModel.ElectroweakMassBridge
The ElectroweakMassBridge module supplies the W and Z boson mass formulas together with weak mixing angle identities that connect the Higgs vacuum expectation value to electroweak observables in the Recognition Science setting. Researchers tracing the Standard Model low-energy limit would reference these when verifying consistency with collider data. The module contains only definitions and direct algebraic consequences with no non-trivial proofs.
claim$m_W^2 = g^2 v^2 / 4$, $m_Z^2 = (g^2 + g'^2) v^2 / 4$, $\\,\cos^2\theta_W = g^2 / (g^2 + g'^2)$, together with the ordering $m_W^2 \le m_Z^2$ and the identity $\cos^2\theta_W + \sin^2\theta_W = 1$.
background
This module operates inside the Standard Model section of the Recognition Science framework. It imports the RS time quantum from Constants and the effective scalar coordinate construction from HiggsEFTBridge, whose doc-comment states the chain RS cost geometry to effective scalar coordinate to canonical Higgs EFT. The module introduces the electroweak mass expressions that follow once the vacuum expectation value v is obtained from the dimensionless RS coordinate ε = h/v after symmetry breaking.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the electroweak mass bridge required by the Higgs EFT Low-Energy Limit master certificate and the Longitudinal Vector-Boson Scattering analysis. It completes the mass step in the chain from RS cost geometry through the Higgs EFT to the W and Z masses, enabling the high-energy unitarity cancellation checks described in the downstream documentation.
scope and limits
- Does not derive the gauge couplings g and g' from RS primitives.
- Does not include radiative corrections or running of parameters.
- Does not address fermion masses or Yukawa couplings.
- Does not treat the origin of the Higgs potential itself.
used by (3)
depends on (2)
declarations in this module (19)
-
def
mW_sq -
def
mZ_sq -
def
mW -
def
mZ -
theorem
mW_sq_nonneg -
theorem
mZ_sq_nonneg -
theorem
mW_sq_le_mZ_sq -
theorem
mW_sq_lt_mZ_sq_of_gp_pos -
theorem
mW_over_mZ_sq -
def
cos_sq_thetaW_SM -
def
sin_sq_thetaW_SM -
theorem
cos_sq_plus_sin_sq_thetaW -
theorem
mW_over_mZ_sq_eq_cos_sq -
theorem
cos_sq_thetaW_in_unit_interval -
theorem
mZ_sq_ge_mW_sq -
theorem
mW_over_mZ_eq_cos_thetaW -
structure
ElectroweakMassBridgeCert -
def
electroweakMassBridgeCert -
theorem
electroweakMassBridgeCert_inhabited