Electroweak Breaking and the mu problem in Supergravity Models with an Additional U(1)

TL;DR

This work studies electroweak symmetry breaking in supersymmetric models extended by a non-anomalous U(1)' and a standard-model singlet S, which generates an effective μ term via μ_s = h_s s/√2 when S develops a vacuum expectation value. It identifies two phenomenologically viable routes to small Z–Z' mixing and TeV-scale Z' masses: a large trilinear coupling scenario where A dominates the potential and a large-scenario where the singlet drives the breaking with s ≫ v; both lead to distinct Higgs- and neutralino/chargino-spectrum patterns. Using one-loop renormalization group equations, the authors relate electroweak-scale soft parameters to string-scale boundary conditions and show that universal soft terms at the string scale generally fail to produce viable low-energy configurations without exotics, whereas nonuniversal boundary conditions or the presence of exotics can realize the desired vacua. The results highlight the model’s testable collider implications, including light Z' bosons and altered Higgs/neutralino sectors, and demonstrate how string-inspired boundary conditions influence electroweak breaking in U(1)' extensions.

Abstract

We consider electroweak symmetry breaking in supersymmetric models with an extra non-anomalous U(1)' gauge symmetry and an extra standard-model singlet scalar S. For appropriate charges the U(1)' forbids an elementary mu term, but an effective mu is generated by the VEV of S, leading to a natural solution to the mu problem. There are a variety of scenarios leading to acceptably small Z-Z' mixing and other phenomenological consequences, all of which involve some but not excessive fine tuning. One class, driven by a large trilinear soft supersymmetry breaking term, implies small mixing, a light Z' (e.g., 200 GeV), and an electroweak phase transition that may be first order at tree level. In another class, with m_S^2 < 0 (radiative breaking), the typical scale of dimensional parameters, including M_{Z'} and the effective mu, is O(1 TeV), but the electroweak scale is smaller due to cancellations. We relate the soft supersymmetry breaking parameters at the electroweak scale to those at the string scale, choosing Yukawa couplings as determined within a class of string models. We find that one does not obtain either scenario for universal soft supersymmetry breaking mass parameters at the string scale and no exotic multiplets contributing to the renormalization group equations. However, either scenario is possible when the assumption of universal soft breaking is relaxed. Radiative breaking can also be generated by exotics, which are expected in most string models.

Figures (11)

• Figure 1: (a): $c_{A}$ dependence of the dimensionless field VEVs for the hybrid minimum. (b): $c_{A}$ dependence of various dimensionless quantities for the hybrid minimum.
• Figure 2: $c_{A}$ dependence of the Higgs masses for the hybrid minimum.
• Figure 3: (a) $c_{A}$ dependence of the dimensionless VEVs, and (b) various dimensionless quantities for the pure trilinear coupling minimum.
• Figure 4: (a): $c_{A}$ dependence of the Higgs masses for the pure $c_{A}$ minimum. (b): Variation of the potential with $f_{1}$ for the parameter values in (\ref{['posmass']}) and different values of $c_{A}$ from 2 to 5 in steps of 0.5.
• Figure 5: Variation of the chargino masses (a) and the neutralino masses (b) with the $SU(2)_{L}$ gaugino mass $M_{2}$ in the large $c_{A}$ minimum.