Evidence for Duality Constraints inΔ→π+Δ(1236)Decays

Partial-wave analysis of ${\pi }^{+}+p\to {\pi }^0+{\Delta }^{++}$ at 1820-2090 MeV c.m. energy shows that this reaction is dominated by the $F_{37}\mathrm{}\left(1950\right)\mathrm{}$ resonance decaying to $\Delta \mathrm{}\left(1236\right)\mathrm{}$ with $s$-channel helicity $\frac{3}{2}$. The analysis also gives evidence for $F_{35}\mathrm{}\left(1890\right)\mathrm{}\to \pi +\Delta$ via $F$ wave. The coupling of $F_{37}$ to helicity-$\frac{3}{2}$ states, and the unexpected dominance of $F$- over $P$-wave decay for $F_{35}\mathrm{}\left(1890\right)\mathrm{}$, can both be interpreted as arising from the constraints of $s-t$ channel duality.