Hidden Fine Tuning In The Quark Sector Of Little Higgs Models

In Little Higgs models a collective symmetry prevents the higgs from acquiring a quadratically divergent mass at one loop. We have previously shown that the couplings in the Littlest Higgs model introduced to give the top quark a mass do not naturally respect the collective symmetry. We extend our previous work showing that the problem is generic: it arises from the fact that the would be collective symmetry of any one top quark mass term is broken by gauge interactions.