 Highest-weight weak-isospin selection in kaon decay

Suppose a transition operator obeys $[I_3,H]=H/2$ and $[I_{+},H]=0$, and acts on the lower component of an isospin-half kaon. Its output has third component zero, and $I_{+}^{2}H|K⟩=H{I}_{+}^2|K⟩=0$. This excludes an isospin-two output. A spinless parent decaying to two spinless pions has zero relative orbital angular momentum, so Bose-Einstein statistics excludes the antisymmetric isospin-one sector. The output is therefore the two-isovector singlet. In the equal-mass isospin limit, charged and neutral two-pion decay widths have ratio two, including the identical-particle counting.