The is an isospin-1 triplet, , ,

PHYSICS · Subjective · Fermi University Physics · Quantum Mechanics · Particle Physics & Quantum Fields · Symmetry, groups and the quark model

Symmetry and Flavour, Ch Isospin as a group: SU(2), Clebsch-Gordan ratios and G-parity

Problem

The

\Sigma(1385)

is an isospin-1 triplet,

\Sigma^{*+}

\Sigma^{*0}

\Sigma^{*-}

, and can decay to

\Sigma\pi

, where the

\Sigma

(isospin-1:

\Sigma^+,\Sigma^0,\Sigma^-

) and the pion (isospin-1) are each isospin-1 multiplets. Restrict attention to the

\Sigma\pi

decays of

\Sigma^{*+}

alone (ignoring the dominant

\Lambda\pi

channel, since

\Lambda

is an isosinglet and carries no isospin information). Using the

SU(2)

Clebsch-Gordan coefficients for coupling two isospin-1 multiplets to total isospin 1, predict the ratio

\Gamma(\Sigma^{*+}\to\Sigma^+\pi^0)/\Gamma(\Sigma^{*+}\to\Sigma^0\pi^+)