1. MINIMAL SO(10) SPLITS SUPERSYMMETRY*
Ilja Doršner
Institut “Jožef Stefan”, Ljubljana
September 11, 2008
*Borut Bajc, I.D. and Miha Nemevšek, arXiv:

2. OUTLINE THE MINIMAL SO(10) MODEL: MAIN FEATURES
LOW SCALE SUPERSYMMETRY (SUSY) AND ν MASS
SPLIT SUSY AND ν MASS
EXPERIMENTAL SIGNATURES
CONCLUSIONS

3. MINIMAL SUSY SO(10) ― MSG(rand)U(nified)T(heory)*
REPRESENTATIONS:
SUPERPOTENTIAL:
(Important for fermion masses.)
(Important for unification.)
*T. E. Clark, T. K. Kuo and N. Nakagawa, Phys. Lett. B 115 (1982) 26; K. S. Babu and R. N. Mohapatra, Phys. Rev. Lett. 70 (1993) 2845; C. S. Aulakh, B. Bajc, A. Melfo, G. Senjanovic and F. Vissani, Phys. Lett. B 588 (2004) 196; …

4. PARAMETERS: (WY) 22 (17) vs. 15 3 + 12 3 up quark masses
3 down quark masses
3 charged lepton masses
3 (2) neutral lepton masses
3 CKM angles + 1 CKM phase
3 (2) PMNS angles + 3 PMNS (0) phases
22 (17)
vs. 15

5. PARAMETERS: (WH) CONDITIONS*: … RELEVANT PARAMETERS*: tan β , MSUSY
, MSUSY
RGEs: gauge coupling constants
RGEs: Yukawa couplings
*C. S. Aulakh, B. Bajc, A. Melfo, G. Senjanovic and F. Vissani, Phys. Lett. B 588 (2004) 196.

6. UNIFICATION IN MINIMAL SO(10)
MSSM
MSGUT
MGUT ≈ 2 × 1016 GeV
102 GeV
MSUSY
MGUT (≡ M(X,Y))

7. MSSM: GAUGE COUPLING UNIFICATION
1(MZ) = ±
2(MZ) = ±
3(MZ) = ±

8. MSGUT: GAUGE COUPLING UNIFICATION*?
*B. Bajc et al, hep-ph/ ; C. S. Aulakh and S. K. Garg, hep-ph/ ; S. Bertolini, T. Schwetz and M. Malinsky, hep-ph/ ; …

9. FERMION MASSES IN MINIMAL SO(10)*
OUR CONVENTION:
*B. Bajc, A. Melfo, G. Senjanovic and F. Vissani, hep-ph/

10. TYPE I SEESAW    ‹ΨD› ‹ΨD› vR ν (1,1,0) ν spin 1/2 2 ‹ΨD› 2/( ) vR
(Mn)ij νi νj ≡
spin 0 νi νj

11. TYPE II SEESAW vL 
(1,3,1) νi νj
( )ij vL νi νj

12. FERMION MASSES IN MINIMAL SO(10)*
*B. Bajc, A. Melfo, G. Senjanovic and F. Vissani, hep-ph/

13. TYPE II CONTRIBUTION TO ν MASS
b–τ UNIFICATION
PROTON DECAY (d = 6)
UPPER BOUND ON ν MASS FROM PROTON STABILITY!

14. b AND τ MASSES IN GeV UNITS AT MGUT
b–τ UNIFICATION
b AND τ MASSES IN GeV UNITS AT MGUT mb mt
MSUSY = 1 TeV
mb-mτ ≈ 0.25 × 109 eV
FII (mb-mτ )
(mν)33 ≈ 0.05 eV
tan (MZ )
THE MZ DATA ARE FROM hep-ph/ by I. D, P. P. Pérez and G. Rodrigo.

15. PROTON DECAY (d = 6)
THEORY (p → π0 e+):
EXPERIMENT:

16. LOW SCALE SUSY AND ν MASS

17. FITTING PROCEDURE

20. IMPORTANT FINDINGS : ― :

21. SPLIT SUSY* AND ν MASS RELEVANT STEPS:
i) We maximize FII in order to have a viable neutrino scale.
This fixes x, m (MGUT), α, α, λ and η.
ii) We check whether unification takes place by solving three equations for the running of gauge couplings for three unknowns ― gGUT, Mf and M½.
iii) We run masses of quarks and charged leptons and the CKM parameters to MGUT for a given tanβ and perform numerical fit that also includes fitting of neutrino mass ratio m2/m3 as well as solar and atmospheric angles.
*N. Arkani-Hamed and S. Dimopoulos, hep-ph/ ; G. F. Giudice and A. Romanino, hep-ph/

22. MGUT (≡ M(X,Y)) MGUT (≡ M(X,Y)) Mf MSUSY M½ 102 GeV 102 GeV low SUSY
split SUSY
MSGUT
MSGUT
MGUT (≡ M(X,Y))
MGUT (≡ M(X,Y))
d=5 proton decay scale* Mf
MSUSY M½
102 GeV
102 GeV
*T. Fukuyama et al, hep-ph/ ; B. Dutta et al, [hep-ph].

23. FIT RESULTS

25. PROTON DECAY SIGNATURES*
ALL RELEVANT PHASES ARE DETERMINED FROM THE FIT!
ALL RELEVANT MASSES ARE FOUND FROM UNIFICATION!
*P. Filevies Perez, hep-ph/

26. CONCLUSIONS
Our results indicate that the minimal SO(10) with low scale SUSY fails to accommodate relevant neutrino mass scale.
Split SUSY case not only generates viable ν scale but allows for consistent description of all known masses and mixing parameters in a particular region of parameter space.
The model yields interesting signatures for the next generation of proton decay experiments and observable sPMNS13 .