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December 1

Why is isospin separated in Gell-Mann–Nishijima?

In the Gell-Mann–Nishijima formula, isospin is separated out: $Q=I_{3}+{\frac {1}{2}}(B+S+C+B^{\prime }+T)$ .

Wouldn't it be simpler to write it as: $Q={\frac {1}{2}}(B+U+D+S+C+B^{\prime }+T)$ (where U is Upness and D is Downness).

In fact, why does isospin exist at all? Shouldn't we just talk about Up/Down same as the other quark flavors?

Ariel. (talk) 18:43, 1 December 2019 (UTC)[reply]

You're looking back at some of the history that led to the quark model. At the time, there was just a "particle zoo" with some observed patterns but no unifying model. The Gell-Mann–Nishijima formula is one of the stepping-stones that got us to the quark model and to electroweak unification. The term inside the parentheses gets labeled "hypercharge", and these two terms later lead to weak isospin and weak hypercharge, which have a more fundamental role in the standard model. The original up-down isospin can still be practically useful because there's an approximate symmetry between up and down quarks, which have very similar mass. --Amble (talk) 20:21, 2 December 2019 (UTC)[reply]