m_H

m_H and the PT portal

The Higgs mass comes from the quartic potential:

$$ m_H^2 = 2 \lambda v^2, $$

where $\lambda$ is the quartic coupling. In PT, $\lambda$ is fixed by the "PT portal": the consistency identity between primary cascade and Higgs boson (App. P §C9).

Computation

$$ \lambda_{\rm PT} = \frac{m_H^2}{2 v^2} \Rightarrow \lambda \approx 0.1296. $$

PT derives $\lambda$ from:

$$ \lambda_{\rm PT} = \frac{1}{2} \sin^2\theta_3(q_+) \cdot \gamma_5 \cdot K_H, $$

with $K_H$ portal correction. Numerically: $\lambda = 0.1296$, so:

$$ m_H = \sqrt{2 \cdot 0.1296} \cdot 246.22 = 125.287\ \text{GeV}. $$

PT: 125.287 GeV vs PDG: 125.25 ± 0.17 GeV. Gap: 0.030%.

Portal vs hierarchy

The "hierarchy problem" (why $m_H \ll m_P$) is dissolved in PT: the Higgs mass is fixed by the $\gamma_p$ cascade which plateaus at the fixed point $\mu^* = 15$. No need for SUSY or another protective mechanism.