# How to calculate U-spin for baryons

I am trying to calculate U-spin for sigma baryons. I don't know why U-spin for $\Sigma^{+}$ and $\Sigma^{-}$ and $\Sigma^{*+}$ is 1/2, but for $\Sigma^{*-}$ is 3/2?

I know that $\Sigma^{+}$ and $\Sigma^{-}$ are octet, and $\Sigma^{*+}$ and $\Sigma^{*-}$ are decuplet, but I don't understand their U-spins.

So, behold!, in the baryon octet, the $\Sigma^-$ is part of a U-doublet, the $\Sigma^0$ mixing with the $\Lambda^0$ to provide the center of a U-triplet, and the $\Sigma^+$ of a doublet.
In the decuplet, the $\Sigma^{*+}$ is in a doublet, the $\Sigma^{*0}$ a triplet, and the $\Sigma^{*-}$ a quartet. These are exactly the values u=1/2 and 3/2 you are puzzled by, above. Two pictures are worth a thousand words.
The underlying reason is the asymmetry of the triangular decuplet weight diagram. The top apex of the increasing-V decuplet triangle is the $\Delta^{++}$, so, as you jack up the V-spin, you transition from a U-quartet ultimately to a U-singlet in it.