Private view of the present status of GUT 　 II

GUT2012@YITP March. 15-17 2012

Takeshi Fukuyama (Ritsumeikan University)

In collaboration with N.Okada, S.Meljanac, A.Ilakovac, T.Kikuchi et.al.

• This talk is maily based on the following works but considered from the different view points.

• arXiv:1104.1736 [hep-ph] • Phys.Rev.D78:015005,2008.

e-Print: arXiv:0808.3598 [hep-ph] • Phys.Rev.D78:115011,2008.

e-Print: arXiv:0808.3598 [hep-ph] • JCAP 0809:024,2008.

e-Print: arXiv:0806.4626 [hep-ph] • Phys.Rev.D78:015005,2008.

e-Print: arXiv:0803.1758 [hep-ph] • AIP Conf.Proc.1015:3-21,2008.

e-Print: arXiv:0806.1987 [hep-ph]

What is GUT ?

• Unification of coupling constant　　 Pati-Salam ?• Unification of matter　　 Pati-Salam , SU(5) ?

　　 SO(10)

　　 E_6 ？

Why is minimal SO(10) GUT comprehensive ?

• Babu-Mohapatra, Mohapatra, Dutta, Mimura, Bajic-Senjanovic et.al., Bertolini-Schwetz-Malinsky, Babu, Aulakh, …..

• Pati-Salam (1974), Georgi-Glashow (1974), Fritzsch-Minkowski (1975)

• Mohapatra-Sakita 、 Nath-Syed, He-Meljanac• Raby, Babu-Barr, Albright,….

Many vacua (SM singlets)

• (1234)

• (5678+5690+7890)

• (1256+1278+1290+3456+3478+3490)

• (13579)

D-flatness

• (24680)

Bertolini-Schwetz-Malinsky

Many solutions to the problem

• Add 120-plet Higgs

• Add 45-plet Higgs,

• Add type I, II…. Seesaw

• Flipped SU(5), SO(10),…

• GUT->MSSM by one step

Nelson-Seiberg’s No-Go th.(See Ratz et.al. 2011)

Under the conditions

(i) Superpotential is generic, and

(ii) low energy theory can be described by a supersymmetric Wess-Zumino model,

(a) R symmetry is necessary for SUSY breaking, and

(b) spontaneous R symmetry breaking is sufficient for SUSY breaking.

SUSY breaking mechanism

• Gravity mediation• Gauge mediation 4D• Anomaly mediation• Gaugino mediation Extra D• Hybrid mediation etc.

Then why do we need extra dimensions ?

U(1)_R 　 transformation

(a) (b) (c)

Metastable vacuum

Why No-Go

No-Go leads us to

• Break SU(5) and/or higher ranked SO(10),

E_6 gauge stmmetries by any method other than Higgs mechanism

Break Pati-Salam and lower ranked symmetry by Higgs mechanism

Our Setup

　 SO(10) 　 inv 　　　　　　　　　　　 PS 　inv

　　　　　　　　　　　　　　　　　　　 vev　 of (10,1,3)

　　 Standard

　　　　　　　　ｙ＝０　　　　　　　　　　　ｙ＝ pi/2　

　 SO(10) brane PS brane

Gauge coupling unification

R-symmetric superpotential 　Hybrid Inflation model

• Shifted and Smooth hybrid Inflation model　　　　　　　　（ Lazarides, Inflationay 　

Cosmology,

Jeannerot-Khalil-Lazarides-Shafi)

Cosmological parameters

• Power spectrum of the primordial curvature perturbation,

from WMAP

(a) The spectral index as a function of T_rh.

The dashed lines correspond to the WMAP 5-year data

(b) The number of e-folds versus v_PS.

(c) The tensor to scalar ratio versus v_PS.

(Jeannerot et.al.)

Thank you