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Suppose that $U(3)$ was the gauge group. We can decompose this as $U(3)=U(1)\times SU(3)$, which implies that in addition to the $SU(3)$ that has eight generators corresponding to eight gluons, there would be an additional generator for $U(1)$.

Would that generator behave like a photon? (no self interaction and no color)

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  • $\begingroup$ Probably yes, but there is an adendum, the coupling would be the strong coupling, and thus, it would couple to electric neutral particles $\endgroup$
    – Hydro Guy
    Jun 13 '14 at 21:31
  • $\begingroup$ It would behave indeed very much like a photon, being the $U(1)$ abelian. $\endgroup$
    – TwoBs
    Jun 13 '14 at 21:35
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    $\begingroup$ Related Phys.SE question by OP: physics.stackexchange.com/q/119190/2451 $\endgroup$
    – Qmechanic
    Jun 13 '14 at 21:36
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    $\begingroup$ @user23873 the coupling could be small and different than those of the gluons. Moreover, even allowing them to be the same at some scale, the running is totally different: one becomes bigger towards the IR whereas feh other becomes smaller in the IR $\endgroup$
    – TwoBs
    Jun 13 '14 at 21:37

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