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I have seen stated that for unflavoured quarks, the relation between baryon number, electric charge and third component of isospin can be written as $Q= B/2 + I_3$. However, I have also seen this relation being used for rho mesons. My question then is, in which cases is this relation true? When is it not?

I can already see that for the pions, the rho mesons and the nucleons it holds true. However, it won't hold true for example for flavoured hadrons. Is this the only rule to it? Is there a way to complete it so as to make it more general?

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The general form of this equation is: $$Q=I_3+\frac{1}{2}Y$$ where $Y$ is the hypercharge, defined as: $$Y=B'+C+S+T+B$$ (The sum of the baryon number and the flavour numbers associated to charm, strange, top and bottom quarks).

The formula you gave was used before the discovery of the charm, top or bottom quark.

Your formula and its generalization are both called the Gell-Mann - Nishijima formula

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  • $\begingroup$ One might object that it is not immediately obvious how to apply the formula to a particle with no well defined flavor quantum numbers, e.g. a $K_L$... $\endgroup$
    – pppqqq
    Commented Dec 26, 2018 at 13:46

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