A Simplified Scheme for GUT-inspired Theories with Multiple Abelian Factors

Grand Unified Theories often involve additional Abelian group factors apart from the standard model hypercharge, that generally lead to loop-induced mixing gauge kinetic terms. In this letter, we show that at the one-loop level this effect can be avoided in many cases by a suitable choice of basis in group space and present a general scheme for the construction of this basis. In supersymmetric theories however, a residual mixing in the soft SUSY breaking gaugino mass terms may appear. We generalize the renormalization group equations for the gaugino mass terms to account for this effect. In a further calculation we also present the necessary adjustments in the renormalization group equations of the trilinear soft breaking couplings and the soft breaking scalar mass squares.