Nonlinear Supersymmetric Higgs bosons Sun Kun Oh (Konkuk Univ) APCTP 2010 LHC Physics Workshop at Korea 10-12, August, 2010, Konkuk University

Flow 1. Introduction 2. Nonlinear models ◦ Nonlinear SM ◦ Nonlinear SU(5) ◦ Nonlinear MSSM Summary

1. Introduction Nonlinear realization of supersymmetry. The supersymmetry may as well be realized nonlinearly as linearly. Most of the supersymmetric models, such as MSSM or NMSSM, are linear models, in the sense that the supersymmetric transformations are linear.

Samuel and Wess developed some decades ago the formalism for extending the standard model to a supersymmetric theory in a nonlinear way. ◦ S. Samuel and J. Wess, Nucl. Phys. B221 (1983) 153; Nucl. Phys. B226 (1983) 289; Nucl. Phys. B233 (1984) 488.

A characteristic property of the nonlinear realization is that no supersymmetric partners are required. In global nonlinear supersymmetric models, the only additional field to be introduced is the Akulov-Volkov field, which is in fact a Goldstino field. ◦ O. Nachtmann and M. Wirbel, Z. Phys. C23 (1984) 85; Z. Phys. C23 (1984) 199; J. P. Ma, O. Nachtmann, and M. Wirbel, Z. Phys. C30 (1986) 407; O. Nachtmann and T. Schucker, Z. Phys. C39 (1986) 291.

The massless physical Goldstino, which has not been observed experimentally, can be avoided if one turns to the curved space, to supergravity. The massless gravitino absorbs the Goldstino via super Higgs mechanism and becomes massive in supergravity. Thus, the Goldstino can be gauged away. Meanwhile, the graviton remains massless.

In the limit of flat space, where the supergravity multiplet decouples from the ordinary matter, the fermionic spectrum in the nonlinear realization is the same as these in the standard model. The manifestation of supersymmetry in the nonlinear models may occur in the Higgs sector.

The linear supersymmetric models need extended Higgs sectors. Likewise, the nonlinear realization of the supersymmetry requires an extention of the Higgs sector. This seems to be a common aspect of both linear and nonlinear realizations.

The minimal version of the nonlinear supersymmetric standard models has the same Higgs sector as the linear next-to- the minimal supersymmetric standard model (NMSSM). Both of the two models need two Higgs doublets and one Higgs singlet.

The minimal version of the nonlinear supersymmetric SU(5) models is the same as the linear minimal supersymmetric standard model (MSSM). The Higgs sectors of both of them is dtermined by two Higgs doublets in the low energy limit.

Nonlinear models Nonlinear SM Nonlinear SU(5) Nonlinear MSSM These models differ in gauge symmetry. Higgs sectors are essentially different between them.

Nonliear SM (1996)

Nonlinear SM (1999)

Nonlinear SU(5) (1999)

Nonlinear SU(5) (2004)

Nonlinear SU(5) 2004)

Nonlinear SU(5) (2006)

Nonlinear SM (2006)

Nonlinear MSSM (2010)

Dudas et al.

3. Electroweak phase transition Generally, first-order EWPT and second- order EWPT have typical structures in the Higgs potential of both linear and non-linear models. Linear models have been investigated previously.

First-order EWPT

Second-order EWPT

Strength of first-order EWPT A B (1) Strong (2) Weak

T=500T=300 = T=100 T=0

Strong first-order EWPT Seon Hee Kim-KPS ( )

4. Summary The nonlinear realization of supersymmetry is a legitimate option and a possible alternative for the linear realizations of supersymmetry if no supersymmetric particles be discovered at the future experiments such as the LHC. The Higgs sectors of nonlinear models might be tested and distinguished from each other at the LHC.

The Higgs phenomenology of the nonlinear supersymmetric models show interesting predictions, such as very low- mass neutral Higgs scalar boson. Electroweak phase transitions and CP violations of various nonlinear models are of importance as well as of interest.