Charge assignments in multiple-$U\left(1\right)\mathrm{}$ gauge theories

We discuss the choice of gauge field basis in multiple-$U\left(1\right)\mathrm{}$ gauge theories. We find that there is a preferred basis, specified by the charge orthogonality condition, in which the $U\left(1\right)\mathrm{}$ gauge fields do not mix under one-loop renormalization group running.