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Baryons are made of three quarks, in the form $\vert qqq \rangle$. If we consider just the isospin doublet $u$ and $d$, there are 8 total possibilities:

enter image description here

Now, the first 4 are respectively $\Delta^{++}, \Delta^+, \Delta^0$ and $ \Delta^-$. But what about the other 4?

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ric.san
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    Recall $|p_\uparrow\rangle= \frac{1}{\sqrt {18}} [ 2| u_\uparrow d_\downarrow u_\uparrow \rangle + 2| u_\uparrow u_\uparrow d_\downarrow \rangle +2| d_\downarrow u_\uparrow u_\uparrow \rangle - | u_\uparrow u_\downarrow d_\uparrow\rangle -| u_\uparrow d_\uparrow u_\downarrow\rangle -| u_\downarrow d_\uparrow u_\uparrow\rangle
    -| d_\uparrow u_\downarrow u_\uparrow\rangle -| d_\uparrow u_\uparrow u_\downarrow\rangle -| u_\downarrow u_\uparrow d_\uparrow\rangle ]$     – Cosmas Zachos Jul 23 '22 at 16:04
  • I'm sorry sir, what's the meaning of those arrows? – ric.san Jul 23 '22 at 16:58
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    Spin. Both iso and spin symmetries are mixed! – Cosmas Zachos Jul 23 '22 at 17:53

1 Answers1

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  1. In OP's table the first 4 rows (=the isospin quadruplet) are the $\Delta$ particles, which sit inside a spin-$3/2$ $uds$ baryon decuplet.

  2. The 4th and 3rd last rows are the proton and neutron, respectively, which form an isospin duplet, and which sit inside a spin-$1/2$ $uds$ baryon octet.

  3. The last 2 rows (=the second isospin duplet) are absent in the standard model, cf. e.g. this related Phys.SE post.

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