= Delta baryon pion branching ratios
{c}
{title2=$\Gamma(\Delta^+\to p\pi^0):\Gamma(\Delta^+\to n\pi^+)=2:1$}
Couple the nucleon <isospin> $1/2$ to the <pion> isospin $1$. The highest state $|3/2,3/2\rangle=|p\pi^+\rangle$ is normalized. One application of the total <isospin> lowering operator gives $|3/2,1/2\rangle=\sqrt{2/3}|p\pi^0\rangle+\sqrt{1/3}|n\pi^+\rangle$. For a common <isospin-invariant two-body decay amplitude>, the partial <decay rates> relative to the $\Delta^{++}$ channel are $2/3$ and $1/3$. The lowest state gives $\Delta^-\to n\pi^-$. Exact relations assume isospin-degenerate masses and common kinematic factors; electromagnetic and quark-mass differences cause corrections.
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