# Tag Info

28

Two particles forming an $SU(2)$ doublet means that they transform into each other under an $SU(2)$ transformation. For example a proton and neutron (which form such a doublet) transform as, \left( \begin{array}{c} p \\ n \end{array} \right) \xrightarrow{SU(2)} \exp \left( - \frac{ i }{ 2} \theta_a \sigma_a \right) \left( \begin{array}{...

12

You probably know that the electrons in atoms occupy a series of energy levels, the $1s$, $2s$, $2p$, etc orbitals. Although the structure of nuclei is complicated, basically the same idea applies to nuclei as well as atoms. This happens because you can't put more than one fermion into the same quantum state. The electrons in atoms are fermions, and so are ...

11

The isospin is different. $I=0$ for the $\Lambda^0$ and $I=1$ for the $\Sigma^{0}$. This makes the $\Lambda^0$ an isospin singlet state but the $\Sigma^0$ is part of an isospin triplet. There are quite few other examples e.g. compare a proton (uud with $I=1/2$) with a $\Delta^{+}$ (uud with $I=3/2$).

10

Symmetry and statistics. The quarks being fermions dictate a fully antisymmetric wavefunction of the three constituents of the baryon. The color wavefunction is antisymmetric, so the combined spin&flavor wavefunction must be symmetric. The spin 1/2 combination (SU(3) octet) is of mixed symmetry and so is the flavor symmetry of the baryon octet you ...

10

Both SU(3) flavor and SU(2) isospin are approximate symmetries of the Standard Model at low energies. Consider physics below the proton mass, where we can talk about the pions and kaons that are the avatars of these symmetries. At energies this low, it doesn't make sense to talk about the heavy quarks (charm, bottom, top), so we're left with the light quarks:...

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By isospin I assume you mean weak isospin which is an exact gauge symmetry of the standard model. There is another thing called flavour isospin which is an approximate global symmetry of the strong interaction. Also, this is a long reply because I've included background and example that you may or may not need. If I am not explaining things well enough for ...

4

First at all - if I understood right - the existence of antiquarks is hypothetical. Your understanding is entirely incorrect. Anti-quarks are a work-a-day reality in the particle physics world. The annihilation of quarks and anti-quarks to form lepton pairs (i.e. Drell-Yan scattering) is not merely regularly observed, it is used a physics tool to probe the ...

4

The 3 pions can be considered as 3 states of the same particle, the isospin being used to label the 3 states. Since pions are bosons, the total wave function must be symmetric (Pauli principle). The total wave function is the (tensorial) product of space-wave function, spin wave-function and isospin wave-function. Spin wave-function is symmetric since pions ...

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