# Mesons and Young Tableaux

I need some help conecting Young Tableaux with actual particles.
I think I have some feel for using Young Tableaux for instance: a baryon in SU(3) where the states are u,d,s can be represented by $\square \bigotimes \square \bigotimes \square$ which gives some tableaux which I can arrive at fine. (I don't know how to latex that in so I'll just leave it at that)

Now my question is what about mesons? Here the tableuaux is $\square \bigotimes$ (A two box column) for the conjugate. What I am confused about is when I consider a box, I think of a particle. How then can an antiparticle have two boxes in SU(3) and the overall tableaux have three boxes. One a mixed state with 8 dimensionality, and a antisymmetric diagram with 3 boxes.

How can one tell then that these diagrams are truly 2 particle diagrams for a meson rather than say a baryon in an anti or mixed symmetric state? How would one assign the 8 mixed states to the actual particle states explicitly might help?

I have a feeling it has to be related to the idea when considering mesons, we have to think of color and not quarks as the degrees of freedom? However, it still seems like that would need two boxes. So I am at a loss...

• I have no idea why you say "When I consider a box, I think of a particle". Young tableaux are a purely abstract graphic notation for representations of $\mathrm{SU}(N)$ and related groups, so I do not understand what you are trying to ask for - it is just a fact of Young tableaux that the anti-fundamental representation of $\mathrm{SU}(3)$ is drawn as a 2-box column. Commented Jan 26, 2016 at 20:24
• What I am trying to ultimately figure out is given SU(3) $\bigotimes$ SU(3)_bar for a meson, how to assign the 3 x 3 (nine) states to the 8 + 1 states and why. I am very confused by group theory and what we actually mean by representations. I have spent a long time trying to grasp it to no great success. So maybe a source for a beginner trying to learn group theory would be helpful to point out as well. I have tried wiki and few other sites, but they have me confused. I'll post a side question regarding that. Commented Jan 27, 2016 at 15:34