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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?

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    $\begingroup$ Search for Gell-mann-Okubo Mass Formula $\endgroup$ – suresh Feb 12 '14 at 14:48
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The energy differences are not due to the isospin which has little direct impact on the energy. Instead the energy difference is due to the spin-spin interaction. However, having a different isospin state impacts that allowed spin states. For the mesons, which are bosons, the states must be symmetric. On the other hand, the baryons, which are fermions, the states must be antisymmetric.

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.

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