Delta baryon

A Delta baryon is a short-lived spin-three-halves baryon resonance.

Couple the nucleon isospin $1/2$ to the pion isospin $1$. The highest state $|3/2,3/2⟩=|p{\pi }^{+}⟩$ is normalized. One application of the total isospin lowering operator gives $|3/2,1/2⟩=\sqrt{2/3}|p{\pi }^0⟩+\sqrt{1/3}|n{\pi }^{+}⟩$. 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.

The Delta-plus baryon is the electrically charged $+1$ member of the Delta baryon multiplet.