Nonlinear Supersymmet-ric Higgs bosons

Sun Kun Oh (Konkuk Univ)

APCTP2010 LHC Physics Workshop at Korea10-12, August, 2010, Konkuk Univer-

sity

Flow 1. Introduction2. Nonlinear models

◦Nonlinear SM --1990◦Nonlinear SU(5) --2000◦Nonlinear MSSM --2010

3. Summary

1. Introduction Nonlinear realization of super-

symmetry.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 trans-formations 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 nonlin-ear realization is that no supersymmet-ric 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. Nacht-mann, 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 mass-less.

In the limit of flat space, where the supergravity multiplet decou-ples from the ordinary matter, the fermionic spectrum in the nonlinear realization is the same as these in the standard model.

The manifestation of supersym-metry in the nonlinear models may occur in the Higgs sector.

The linear supersymmetric mod-els need extended Higgs sectors.

Likewise, the nonlinear realiza-tion of the supersymmetry re-quires an extention of the Higgs sector.

This seems to be a common as-pect of both linear and nonlinear realizations.

The minimal version of the non-linear supersymmetric standard models has the same Higgs sec-tor as the linear next-to-the min-imal supersymmetric standard model (NMSSM).

Both of the two models need two Higgs doublets and one Higgs singlet.

The minimal version of the non-linear supersymmetric SU(5) models is the same as the linear minimal supersymmetric stan-dard model (MSSM).

The Higgs sectors of both of them is dtermined by two Higgs doublets in the low energy limit.

Nonlinear modelsNonlinear SMNonlinear SU(5)Nonlinear MSSMThese models differ in gauge

symmetry. Higgs sectors are essentially dif -

ferent 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.

Dudas et al.

Dudas et al.

3. Electroweak phase transitionGenerally, 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 investi-gated previously.

First-order EWPT

Second-order EWPT

Strength of first-order EWPT2 2 2

1 1 2 2( ) { ( ) ( )} { ( ) ( )} { ( ) ( )}C A C B C A C B C A C B CdT v T v T v T v T x T x T= - + - + -

A B

(1) Strong

(2) Weak

( ) 1C

C

dTT >

( ) 1C

C

dTT <

163.164cT =300T =

100T = 0T =

500T =

T=500 T=300 =163.164

T=100

T=0

cT

1v

V

Strong first-order EWPT

Seon Hee Kim-KPS (2005.10.22)

4. Summary The nonlinear realization of super-

symmetry is a legitimate option and a possible alternative for the linear realizations of supersymmetry if no supersymmetric particles be dis-covered at the future experiments such as the LHC.

The Higgs sectors of nonlinear models might be tested and distin-guished from each other at the LHC.

The Higgs phenomenology of the nonlinear supersymmetric mod-els show interesting predictions, such as very low-mass neutral Higgs scalar boson.

Electroweak phase transitions and CP violations of various non-linear models are of importance as well as of interest.