|V_ts|

|V_ts| — top to strange

$|V_{ts}| \approx 0.039$, larger than $|V_{td}|$ by ~5× — the t → s transition crosses only one generation.

By CKM unitarity:

$$ |V_{ts}| \approx |V_{cb}|. $$

Computation

PT value: - $|V_{cb}| = 0.040\,75$ - correction: $|V_{ts}| = -|V_{cb}| + |V_{us}| \cdot |V_{ub}| \cdot e^{i\delta_{\rm CP}}$

$$ |V_{ts}| \approx 0.040\,75 - 0.22421 \cdot 0.003814 \cdot \cos(\delta_{\rm CP}) = 0.038\,811. $$

PT: 0.038 811 vs PDG: 0.0388 ± 0.0011. Gap: 0.029%.

Consequence: b → s

Rare $b \to s\gamma$ and $b \to s\ell\ell$ decays (LHCb) are governed by $|V_{tb} V_{ts}^*|^2$. PT precision enables fine predictions for the P'_5 tension observed at LHCb (cf. PT_BRIDGE article).