MINIMAL SO (10) SPLITS SUPERSYMMETRY*
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Transcript of MINIMAL SO (10) SPLITS SUPERSYMMETRY*
MINIMAL SO(10) SPLITS SUPERSYMMETRY*
Ilja DoršnerInstitut “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)*
SUPERPOTENTIAL:
REPRESENTATIONS:
*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; …
(Important for fermion masses.)
(Important for unification.)
PARAMETERS: (WY)
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) 15vs.
CONDITIONS*: …
RELEVANT PARAMETERS*:
tan β
0, 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.
PARAMETERS: (WH)
MSSM MSGUT
MGUT ≈ 2 × 1016 GeV
102 GeV
MSUSY
MGUT (≡ M(X,Y))
102 GeV
MSUSY
UNIFICATION IN MINIMAL SO(10)
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.
vR 2 ‹ΨD› 2/( )
vR
TYPE I SEESAW
ν ν
νi νj
(1,1,0)
spin 1/2
spin 0(Mn)ij νi νj ≡
‹ΨD› ‹ΨD›
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!
tan (MZ )
THE MZ DATA ARE FROM hep-ph/0607208 by I. D, P. P. Pérez and G. Rodrigo.
b AND τ MASSES IN GeV UNITS AT MGUT
mb
m
MSUSY = 1 TeV
b–τ UNIFICATION
mb-mτ ≈ 0.25 × 109 eV
(mν)33 ≈ 0.05 eV
FII (mb-mτ )
PROTON DECAY (d = 6)THEORY (p → π0 e+):
EXPERIMENT:
LOW SCALE SUSY AND ν MASS
FITTING PROCEDURE
: ―
IMPORTANT FINDINGS
:
SPLIT SUSY* AND ν MASS
i) We maximize FII in order to have a viable neutrino scale.This fixes x, m (MGUT), α, α, λ and η.
RELEVANT STEPS:
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))
102 GeVM½
MSGUT
MGUT (≡ M(X,Y))
102 GeV
MSUSY
MSGUT
Mf
d=5 proton decay scale*
*T. Fukuyama et al, hep-ph/0406068; B. Dutta et al, 0712.1206 [hep-ph].
low SUSY split SUSY
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 sPMNS
13 .