Delta baryon

The Delta baryon ground multiplet is a short-lived baryon resonance family with isospin $3/2$ and spin-parity $3/2^{+}$. Its four charge states have ordinary valence contents $uuu$, $uud$, $udd$ and $ddd$, with charges $+2,+1,0,-1$ in elementary-charge units.

The familiar Delta-plus baryon and the proton share valence flavor content but differ in their spin coupling and mass. Strong decay into a nucleon and a pion gives the Delta resonance a broad decay width. In scattering, a resonance appears through an energy-dependent amplitude and cross section, not as an indefinitely stable additional constituent of every atomic nucleus.^[ref]

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.