“International Workshop on Grand Unified Theories: Current Status and Future Prospects”

Ritsumeikan University, Kusatsu, ShigaDecember 17-19, 2007

K.S. BabuOklahoma State University

K.S. Babu, J.C. Pati, Z. Tavartkiladze (2007)

Motivation/“Evidence” favoring SO(10) GUTMotivation/“Evidence” favoring SO(10) GUTDoublet-Triplet Splitting Issues:Doublet-Triplet Splitting Issues: Dimopoulos-Wilczek MechanismDimopoulos-Wilczek Mechanism Stability of VEV structureStability of VEV structure Absence of pseudo-Goldsone bosonsAbsence of pseudo-Goldsone bosons GUT threshold corrections and unificationGUT threshold corrections and unificationProton decayProton decay d=5 and d=6 proton decay rates d=5 and d=6 proton decay rates Correlation between the twoCorrelation between the twoConclusionsConclusions

Outline

Motivations/Evidence favoring SO(10)

Miraculous cancellation of anomalies

Structure of matter multiplets

Matter Unification Matter Unification in 16 of SO(10)in 16 of SO(10)

Standard Model Supersymmetry

Evolution of gauge couplings

Gauge coupling evolution in our SO(10) model

• SU(5)

• SO(10)

• E6

• E8

• …

• [SU(3)][SU(3)]33

• [SU(5)][SU(5)]22

• [SU(3)][SU(3)]44

• ……

GUT gauge groups

Matter multiplets:

Higgs:

Yukawa Couplings

Contain color triplets

Minimal SUSY SU(5) GUT

MSSM Higgs doublets have color triplet partners in GUTsMSSM Higgs doublets have color triplet partners in GUTs

must remain lightmust remain light

must have GUT scale mass to prevent rapid must have GUT scale mass to prevent rapid proton decayproton decay

Doublet-triplet splitting

Even if color triplets have GUT scale Even if color triplets have GUT scale mass, d=5 proton decay is problematicmass, d=5 proton decay is problematic

The GOODThe GOOD

(1)(1) Predicts unification of couplingsPredicts unification of couplings

(2)(2) Uses economic Higgs sectorUses economic Higgs sector

The BADThe BAD

(1)(1) Unnatural fine tuningUnnatural fine tuning

(2)(2) Large proton decay rateLarge proton decay rate

FINE-TUNED TO O(MW)

Doublet-triplet splitting in SU(5)

Realistic SO(10) model without fine-tuning

Economic Higgs system

Babu, Pati, Wilczek (1998)Barr, Raby (1997)Babu, Pati, Tavartkiladze (2007)

B-L VEV gives mass to triplets only

If 10H only couples to fermions, no d=5 proton decay

Doublets from and light

4 doublets, unification upset

Add mass term for 10’H

Dimopoulos-Wilczek mechanism

Dimopoulos, Wilczek (1981)Babu, Barr (1993)

Issues to be addressed with DW mechanism

Complete SO(10) Model

Fixing the VEVs

Doublet-Triplet Mass Matrix

Stability of doublet mass

Spectrum of doublets and triplets

Spectrum heavy states from 45

Spectrum from 10 + 10-bar

Gauge boson spectrum

Threshold corrections

Weak scale threshold

GUT scale thresholdHisano, Murayama, Yanagida (1993)Hisano, Moroi, Tobe, Yanagida (1995)

Correlation between d=5 and d=6 proton decay

Gauge coupling evolution in our SO(10) model

Gauge boson induced d=6 proton decay

Sakai, Yanagida (1982)

Weinberg (1982)

Higgsino mediated d=5 proton decay

Proton Decay in the present SO(10) model

d = 6 Proton decay

Summary and Conclusions