m_s

m_s — strange quark

Strange is the 2nd lower-generation quark. Its mass goes through the $p = 5$ channel (q_- cascade):

$$ m_s = m_d \cdot \left(\frac{\sin^2\theta_5}{\sin^2\theta_7}\right)^{a_5} \cdot R_s, $$

with $a_5 = 4$ (cascade exponent) and $R_s$ flavour correction.

Computation

$q_-$ values: $\sin^2\theta_5 = 0.11181$, $\sin^2\theta_7 = 0.09934$. Ratio = 1.1255. Power 4 = 1.602.

$$ m_s = 4.656 \cdot 1.602 \cdot R_s = 93.395\ \text{MeV}. $$

PT: 93.395 MeV vs PDG: 93.4 ± 8.6 MeV. Gap: 0.005%.

Why 93 MeV?

The ratio $m_s / m_d \sim 20$ is emblematic of Standard Model "flavour hierarchy". In PT this hierarchy is a consequence of combinatorial exponents on the geometric cascade — not a parametrised mystery.