Tension between gauge coupling unification, the Higgs boson mass, and a gauge-breaking origin of the supersymmetricμ-term

Abstract

We investigate the possibility of generating the µ-term in the MSSM by the condensation of a field that is a singlet under the SM gauge group but charged under an additional family-independent U (1)X gauge symmetry. We attempt to do so while preserving the gauge coupling unification of the MSSM. For this, we find that SM non-singlet exotics must be present in the spectrum. We also prove that the pure U (1)X anomalies can always be solved with rationally charged fields, but that a large number of SM singlets are often required. For U (1)X charges that are consistent with an embedding of the MSSM in SU (5) or SO (10), we show that the U (1)X charges of the MSSM states can always be expressed as a linear combination of abelian subgroups of E6. However, the SM exotics do not appear to have a straightforward embedding into GUT multiplets. We conclude from this study that if this approach to the µ-term is correct, as experiment can probe, it will necessarily complicate the standard picture of supersymmetric grand unification.

Discovering chiral Higgsinos at the CERN LHC

“…In [3], though, the electroweak exotics have the same quantum numbers as the Higgs doublets, while in [4] the potential of the singlets is not fully explored, there are singlets that are vectorlike under Uð1Þ 0 , and an R-parity is imposed.…”

“…where Q, U c , D c , L, E c are the supersymmetric standard 1 Similar charge assignments are considered in [3,4]. model (SSM) chiral superfields for the standard model fermions.…”

Supersymmetric D-term Twin Higgs

“…Such models were considered in the context of non-twinned SUSY in refs. [32][33][34][35][36][37][38][39][40][41]. The non-decoupling D-term potential can be written as…”

Testing aU(1)solution to theμproblem

“…Also, the U (1) 3 and the U (1) -gravitational anomalies must be cancelled. Almost without fail, this leads to additional SM singlets (often with irrational U (1) charges) [7]. The model building can rapidly become baroque.…”

“…This induces new conditions to avoid mixed-anomalies between the U (1) and the SM symmetry groups. It is challenging to satisfy these conditions while simultaneously maintaining gauge coupling unification and avoiding introducing new "µ-like" terms for exotic matter [7,8]. We briefly discuss this tension, along with other model building challenges before settling on a choice for the charges of our U (1) .…”