# How to determine SU(3) multiplicity in beta function

1. Jun 20, 2013

### lonewolf219

Hello,

I was given this formula to find the beta values for U(1) SU(2) and SU(3). I am having trouble with SU(3).

$\frac{11}{3}$(3)-$\frac{2}{3}$(F$_{L}$)-$\frac{2}{3}$(F$_{R}$)

I don't know what the two fermion terms are... I know they will only be the quarks. I am trying to multiply by 3 twice, but it doesn't seem to be the right answer. The up$_{R}$ is multiplied by 3 and again by 3 for RGB and generations? Same for down$_{R}$? And then the pair of Q$_{L}$ has what multiplicity? It's the multiplicity that is confusing me, I think... any help would be appreciated!

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