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Inducing the mu and the B mu Term by the Radion and the 5d Chern-Simons Term

Arthur Hebecker, John March-Russell, Robert Ziegler

TL;DR

This work examines how the MSSM μ and Bμ terms can be generated in 5d gauge-Higgs unification via the F-term of the radion, with the 5d supersymmetric Chern-Simons term providing crucial contributions to the Higgs potential. It develops a concrete program beginning with an abelian toy model, extends to a non-abelian generalization, and computes μ, Bμ, and Higgs soft masses in terms of the radion F-term $F_T$ and the chiral compensator F-term $F_ ext{varphi}$, including CS-term corrections parametrized by $c'$. An explicit SU(6) orbifold-GUT construction demonstrates how these ingredients can realize a viable high-scale SUSY-breaking pattern and reveals the importance of CS-induced effects for achieving realistic electroweak symmetry breaking after renormalization-group running. The results connect higher-dimensional gauge-GUT/string constructions to testable Higgs-sector signatures at the LHC, proposing a framework in which high-scale physics leaves observable imprints on Higgs mass patterns.

Abstract

In 5-dimensional models with gauge-Higgs unification, the F-term vacuum expectation value of the radion provides, in close analogy to the Giudice-Masiero mechanism, a natural source for the mu and B mu term. Both the leading order gauge theory lagrangian and the supersymmetric Chern-Simons term contain couplings to the radion superfield which can be used for this purpose. We analyse the basic features of this mechanism for mu term generation and provide an explicit example, based on a variation of the SU(6) gauge-Higgs unification model of Burdman and Nomura. This construction contains all the relevant features used in our generic analysis. More generally, we expect our mechanism to be relevant to many of the recently discussed orbifold GUT models derived from heterotic string theory. This provides an interesting way of testing high-scale physics via Higgs mass patterns accessible at the LHC.

Inducing the mu and the B mu Term by the Radion and the 5d Chern-Simons Term

TL;DR

This work examines how the MSSM μ and Bμ terms can be generated in 5d gauge-Higgs unification via the F-term of the radion, with the 5d supersymmetric Chern-Simons term providing crucial contributions to the Higgs potential. It develops a concrete program beginning with an abelian toy model, extends to a non-abelian generalization, and computes μ, Bμ, and Higgs soft masses in terms of the radion F-term and the chiral compensator F-term , including CS-term corrections parametrized by . An explicit SU(6) orbifold-GUT construction demonstrates how these ingredients can realize a viable high-scale SUSY-breaking pattern and reveals the importance of CS-induced effects for achieving realistic electroweak symmetry breaking after renormalization-group running. The results connect higher-dimensional gauge-GUT/string constructions to testable Higgs-sector signatures at the LHC, proposing a framework in which high-scale physics leaves observable imprints on Higgs mass patterns.

Abstract

In 5-dimensional models with gauge-Higgs unification, the F-term vacuum expectation value of the radion provides, in close analogy to the Giudice-Masiero mechanism, a natural source for the mu and B mu term. Both the leading order gauge theory lagrangian and the supersymmetric Chern-Simons term contain couplings to the radion superfield which can be used for this purpose. We analyse the basic features of this mechanism for mu term generation and provide an explicit example, based on a variation of the SU(6) gauge-Higgs unification model of Burdman and Nomura. This construction contains all the relevant features used in our generic analysis. More generally, we expect our mechanism to be relevant to many of the recently discussed orbifold GUT models derived from heterotic string theory. This provides an interesting way of testing high-scale physics via Higgs mass patterns accessible at the LHC.

Paper Structure

This paper contains 7 sections, 55 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The basic mechanism in an abelian toy model
  3. Non-abelian generalization
  4. Calculating the $\mu$ and $B\mu$ term and the Higgs-sector soft scalar masses
  5. Including the effect of the Chern-Simons term and some phenomenological consequences
  6. An explicit SU(6) orbifold-GUT model
  7. Conclusions

Figures (1)

  • Figure 1: In two different 5d limits, the 6d model described in the text goes over into the model of Burdman/Nomura or into 'Our Model'.