= Cabibbo-angle extraction from semileptonic decay rates
{c}
{title2=$\tan^2\theta_C=(B_s/\tau_s)(\tau_d/B_d)(\Delta_d/\Delta_s)^5$}
If two <semileptonic decays> differ by $s\to u$ versus $d\to u$, an equal-hadronic-strength approximation and a fifth-power <phase space> ansatz give $r_s=K\sin^2\theta_C\,\Delta_s^5$ and $r_d=K\cos^2\theta_C\,\Delta_d^5$. Their partial decay rates are $r_i=B_i/\tau_i$, where $B_i$ is the appropriate <branching fraction> and $\tau_i$ the total <mean lifetime>. Taking the ratio gives the displayed expression. Different hadronic <hadronic form factors>, finite <Electron> <mass> and recoil corrections prevent this simplified extraction from being an exact determination.
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