MINIMAL SO(10) SPLITS SUPERSYMMETRY* Ilja Doršner Institut “Jožef Stefan”, Ljubljana September 11, 2008 *Borut Bajc, I.D. and Miha Nemevšek, arXiv:0809.1069.

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

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; …

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

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.

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

MSSM: GAUGE COUPLING UNIFICATION 1(MZ) = 0.016949 ± 0.000005 2(MZ) = 0.033816 ± 0.000027 3(MZ) = 0.1176 ± 0.0020

MSGUT: GAUGE COUPLING UNIFICATION* ? *B. Bajc et al, hep-ph/0402122; C. S. Aulakh and S. K. Garg, hep-ph/0512224; S. Bertolini, T. Schwetz and M. Malinsky, hep-ph/0605006; …

FERMION MASSES IN MINIMAL SO(10)* OUR CONVENTION: *B. Bajc, A. Melfo, G. Senjanovic and F. Vissani, hep-ph/0511352.

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

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

FERMION MASSES IN MINIMAL SO(10)* *B. Bajc, A. Melfo, G. Senjanovic and F. Vissani, hep-ph/0511352.

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

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/0607208 by I. D, P. P. Pérez and G. Rodrigo.

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

LOW SCALE SUSY AND ν MASS

FITTING PROCEDURE

IMPORTANT FINDINGS : ― :

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/0405159; G. F. Giudice and A. Romanino, hep-ph/0406088.

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/0406068; B. Dutta et al, 0712.1206 [hep-ph].

FIT RESULTS

PROTON DECAY SIGNATURES* ALL RELEVANT PHASES ARE DETERMINED FROM THE FIT! ALL RELEVANT MASSES ARE FOUND FROM UNIFICATION! *P. Filevies Perez, hep-ph/0403286.

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 .