higgsGaugeCoupling
plain-language theorem explainer
The definition supplies the electroweak gauge coupling as twice the square of the vector boson mass divided by the vacuum expectation value. A physicist modeling spontaneous symmetry breaking in Recognition Science cites this when connecting J-cost minima to W and Z masses. It is realized as a direct algebraic expression with no lemmas or hypotheses.
Claim. The gauge coupling induced by the Higgs mechanism equals $2 m_V^2 / v$, where $m_V$ is the mass of the massive vector boson and $v$ is the vacuum expectation value of the Higgs field.
background
In Recognition Science the electroweak symmetry breaking is obtained when the J-cost functional develops a minimum at nonzero vacuum expectation value. J-cost is the cost of a recognition event, equivalently the derived cost of the comparator of a multiplicative recognizer on positive ratios. The vacuum expectation value $v$ is the point that minimizes this cost, breaking SU(2)_L × U(1)_Y to U(1)_EM while the photon remains massless.
proof idea
The definition is a direct algebraic expression implementing the relation between vector boson mass and vacuum expectation value. No lemmas are invoked; the expression follows immediately from the arithmetic operations on the two real arguments.
why it matters
This definition supplies the explicit link between the J-cost minimum and the electroweak vector boson masses inside the Standard Model sector. It supports the module's derivation of W and Z masses from the Higgs vacuum expectation value, consistent with the phi-ladder and eight-tick octave structure. The accompanying summary flags the possible phi-related hierarchy as an open question under investigation.
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