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“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