# Why $SU(3)$ and not $U(3)$?

Is there a good reason not to pick $U(3)$ as the colour group? Is there any experiment or intrinsic reason that would ruled out $U(3)$ as colour group instead?

• Other Phys.SE questions about the precise form of the standard model gauge group: physics.stackexchange.com/q/105816/2451 , physics.stackexchange.com/q/116831/2451 Jun 13 '14 at 19:13
• $U(3)$ has 9 generators, you would thus get an extra massless gauge boson (resembling very much an extra photon) on top of the eight gluons. Jun 13 '14 at 20:13

Suppose that $\text{U}(3)$ was the gauge group. We can decompose this as $$\text{U}(3)=\text{U}(1)\times\text{SU}(3),$$
which implies that in addition to the $\text{SU}(3)$ that has eight generators corresponding to eight gluons, there would be an additional generator for $\text{U}(1)$. The latter in principle corresponds to an additional gauge boson, but a theory of the strong interactions containing such a particle is inconsistent with experiment.