# Isospin and Energy

I would to know if there is a correlation between isospin and energy. Consider for example the $\eta$ meson ($I =0$) and the pions($I=1$). The $\eta$ turns out to be much heavier then the pions ($m_\pi \approx 150 \mbox{MeV}$,$m_\eta\approx 550\mbox{MeV}$).

A counterexample is the $\Lambda_b$ ($I=0$) and the $\Sigma_b$ ($I=1$) baryons. Here the $\Sigma_b$, the higher isospin state, has a larger mass.

Are there any known trends between isospin and energy?

• Search for Gell-mann-Okubo Mass Formula – suresh Feb 12 '14 at 14:48

Consider the $\eta$ and $\pi$'s. The pions, having a symmetric isospin, must have a symmetric spin. The triplet state is less energetic than the singlet. This makes the pions lighter. A similar arguement can be made for the baryons.