Stabilizing the Higgs potential with a Z${}^{\prime }$

Abstract

Current data point toward metastability of the electroweak vacuum within the Standard Model. We study the possibility of stabilizing the Higgs potential in U(1) extensions thereof. A generic Z${}^{\prime }$ boson improves stability of the scalar potential in two ways: it increases the Higgs self--coupling, due to a positive contribution to the beta--function of the latter, and it decreases the top quark Yukawa coupling, which again has a stabilizing effect. We determine the range of U(1) charges which leads to a stable electroweak vacuum. In certain classes of models, such stabilization is possible even if the Z${}^{\prime }$ does not couple to the Higgs and is due entirely to the reduction of the top Yukawa coupling. We also study the effect of the kinetic mixing between the extra U(1) and hypercharge gauge fields.

14 pages, 7 figures; a typo in Delta V fixed, references added

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