Implications of asymptotic safety in two minimal <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>Z</mml:mi> </mml:math> -prime models

We consider the implications of asymptotic safety on two U(1) gauge extensions of the standard model that are minimal in the sense that anomaly cancellation only requires the presence of right-handed neutrinos. We study the UV fixed points of the gauge couplings taking into account kinetic mixing between hypercharge and the new U(1) gauge field. We consider the possibility that the top-bottom mass splitting originates from the effect of differing gauge charges on the nontrivial fixed-point values of their respective Yukawa couplings and assess the impact of the extended gauge symmetry on the viability of this picture.