SUSY GUT Model Building Stuart Raby SUSY 2008

SUSY GUT Model Building Stuart Raby SUSY 2008 Seoul, S. Korea June 20, 2008 Title of talk 1

Outline Evolution of SUSY GUTs § 4 dimensional SUSY GUTs § 5 dimensional orbifold GUTs § String orbifolds orbifold GUTs § Conclusions Title of talk 2

Outline § 4 dimensional SUSY GUTs § 5 dimensional orbifold GUTs § String orbifolds orbifold GUTs § Conclusions Title of talk 3

The Goal of Beyond SM physics Reduce # fundamental parameters 18 parameters in Standard Model 13 charged fermion masses & mi + 3 gauge couplings + 2 W & Higgs mass 27 including neutrino masses & mixing 28 including QCD q parameter 29 including GN Title of talk 4

Supersymmetric Grand Unified Theories § Charge quantization & Families § Unification of gauge couplings § Yukawa unification § Neutrino masses via See-Saw scale ~ MG Title of talk 5

Grand Unification - SO( 10 ) GUT Georgi Fritszch & Minkowski spinor repsn. of SO( 10 ) tensor product of 5 spin ½ w/even no. - signs Title of talk 6

Gauge coupling unification Dimopoulos, Raby & Wilczek PRD 24, 1681 (1981) LEP data !! Amaldi, de Boer & Furstenau, PLB 260, 447 (1991 Title of talk 7

e 3 Title of talk 8

G. C. Unif. & Proton decay A( p K+ n ) ~ C C x loop factor MT Minimal SUSY SU(5) e 3 ~ (3 a. G/5 p) ln (MT/ MG) MT ~ 1014 Ge. V Proton decays toooo fast !! Title of talk 9

G. C. Unif. & Proton decay 4 D e 3 ~ (3 a. G/5 p) ln (MTeff / MG) + e 3 (GUT B. S. ) Threshold corrections due to Higgs doublet-triplet splitting (positive) & GUT breaking sector (negative) Dermisek et al. , Babu et al. , Altarelli et al. Title of talk 10

Quark & Lepton masses and mixing Hierarchical Flavor symmetry breaking Title of talk 11

Fermion mass hierarchy FCNC Non-abelian family symmetry Suppresses flavor violation Title of talk 12

Fermion Masses in SO(10) l 16 10 16 top, bottom, tau, nt Yukawa unification “Minimal” SO(10) Model Aulakh, Babu, Bajc, Chen, Mahanthappa, Mohapatra, Senjanovic, … Renormalizable ! - large rep’s & few predictio Title of talk 13

“Minimal” SO(10) Model II Albright, Anderson, Babu, Barr, Barbieri, Berezhia Blazek, Carena, Dermisek, Dimopoulos, Hall, Pat Raby, Romanino, Rossi, Starkman, Wagner, Wilc Wiesenfeldt, Willenbrock Small rep’s, effective higher dimension op’s Many predictions !! Possible UV completion to strings !! Title of talk 14

SO(10) x [ D 3 x U(1) family sym. ] Yukawa Unification for 3 rd Family 7 real para’s + 4 phases + 3 real Majorana Neutrino masses Dermisek & Raby hep-ph/0507045 Title of talk 15

Effective higher dimension operators Title of talk 16

Global c 2 analysis 24 parameters at GUT scale compared to SM - 27 parameters CMSSM - 32 parameters Title of talk 17

Global c 2 analysis – good fits to § charged fermion masses & mixing angle § neutrino masses & mixing angles § naturally satisfies Lepton Flavor Violation and electron electric dipole moment bou Dermisek, Harada & Ra hep-ph/0606055 § fits WMAP dark matter Dermisek, Raby, Roszkowski & Ruiz de Au hep-ph/0304101 & hep-ph/050723 Title of talk 18

Requires soft SUSY breaking para’s Blazek, Dermisek & Raby PRL 88 (2002); Phys. Rev. D 65, 115004 (2002) Auto et al. , JHEP 06, 023 (2003) Tobe and Wells, Nucl. Phys. B 663, 123 (2003) Baer et al. , JHEP 0803, 056 (2008) Title of talk 19

Dermisek, Harada & Raby, hep-ph/0606055 Title of talk 20

Title of talk 0. 68 (0. 03) 21

NOT in c 2 fit Title of talk 22

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Recent analysis of DR Model “Challenging SO(10) SUSY GUTs with fami symmetries through FCNC processes” Albrecht, Altmannshofer, Buras, Guadagnoli, & Straub ar. Xiv: 0707. 3954 [hep-ph] Altmannshofer, Guadagnoli, Raby & Straub ar. Xiv: 0801. 4363 [hep-ph] Find good fits to quark, charged lepton & neutrino masses and mixing angles & test flavor violation in b physics some tension between b s g & b s l+ l- m 16 ~ 10 Te. V Title of talk 24

What is the tension ? b s g Title of talk 25

3 rd family only with Altmannshofer, Guadagnoli, Raby & Straub ar. Xiv: 0801. 4363 [hep- Title of talk ph] 26

MSO 10 SM & Large tan( b ) § Fits WMAP § Predicts light Higgs with mass of order 120 Ge. V § Predicts lighter 3 rd and heavy 1 st & 2 nd gen. squarks and sleptons (inverted scalar mass hier. ) § LFV bounds satisfied § Enhances Br[ Bs m+ m- ] § Suppresses Br( B t n ) & D MBs + l- tension ! B X g , X l s s § MSO 10 SM : Beautiful symmetry Title of talk 27

Virtues of SUSY GUTs § MZ << MGUT “Natural” § Explains charge quantization § Predicts gauge coupling unification § Predicts SUSY particles at LHC § Predicts proton decay § Predicts Yukawa coupling unification § w/Family symmetry Fermion mass hierarc § Neutrino masses and mixing via See-Saw § LSP - Dark Matter candidate § Baryogenesis via leptogenesis Title of talk 28

Problems of SUSY GUTs § GUT symmetry breaking § Higgs doublet-triplet splitting Missing partner mechanism SU(5) Missing VEV mechanism SO(10) Title of talk 29

Outline § 4 dimensional SUSY GUTs § 5 dimensional orbifold GUTs § String orbifolds orbifold GUTs § Conclusions Title of talk 30

Orbifold GUTs in 5 or 6 dimensions GUT symmetry breaking Doublet-Triplet splitting Kawamura; Hall & Nomura; Contino, Pilo, Rattazzi & Trincherini; Altarelli, Feruglio & Masina; Dermisek & Mafi; H. D. Kim & Raby; Asaka, Buchmuller & Covi; Lee; Hebecker & March-Russell H. D. Kim, Raby & Schradin JHEP 0505: 036 (2005) Title of talk 31

Hall & Nomura SU(5) GUT on M x S 1/(Z 2 x GUT symmetry breaking Suppress b-t Yukawa. Higgs D-T splitting proton decay unification via orbifold BCs 1 st & 2 nd families in bulk Brane states Bulk states Title of talk 32

G. C. Unif. & Proton decay > 4 D 5 D Orbifold GUT KK modes 0 p. R Mc ~ 1/p. R < MG < M* Title of talk Dienes et al. , Hall & Nomura Kim & S. R. , Feruglio et al. 33

G. C. Unif. & Proton decay > 4 D Dim 6 amp. ~ 1 / Mc 2 Enhanced !! 5 D Orbifold GUT Mc 0 R Brane Mc ~ 1/R < MG < M* Title of talk 34

G. C. Unif. & Proton decay > 4 D Dim 6 amp. ~ 1 / Mc 2 Suppressed !! 5 D Orbifold GUT Mc 0 R Bul k Mc ~ 1/R < MG < M* Title of talk 35

Orbifold GUTs in 5 or 6 dimensions : § GUT breaking via Orbifold “Parity” § Higgs doublet - triplet splitting via Orbifold “P” § NO proton decay via Dim 5 operators due to R symmetry § Proton decay via Dim 6 operators can be suppressed, BUT typically enhanced (model dependent) § Matter localization determines Yukawas Title of talk 36

Outline § 4 dimensional SUSY GUTs § 5 dimensional orbifold GUTs § String orbifolds orbifold GUTs § Conclusions Title of talk 37

UV completion Orbifold GUTs in 5 or 6 dimensions Derived from heterotic string in 10 D Kobayashi, Raby & Zhang; Forste, Nilles, Vaudrevange & Wingerter; Buchmuller, Hamaguchi, Lebedev & Ratz; JE Kim, JH Kim & Kyae; Buchmuller, Ludeling & Schmidt Title of talk 38

Road to the MSSM with R-parity Lebedev et al. – 0708. 2691[hep-th] Find 15 models from orbifold compactificatio of E(8)x. E(8) heterotic string ü MSSM spectrum at low energy ü Exact R parity ü Light Higgs ü Non-trivial charged fermion masses ü Neutrino masses via See-Saw Title of talk 39

Compactify E(8)x. E(8) heterotic string on (T 2)3/(Z 3 x Z 2) + Wilson lines [ A 2, A 3 ] Local SO(10) GUT Title of talk 40

D 4 family symmetry geometry string selection rule singlets doublet Title of talk 41

For detailed list of all discrete non-abelian symmetries from orbifold compactification of the heterotic string, see Kobayashi, Nilles, Ploeger, SR & Ratz hep-ph/0611020 For D 4 phenomenology, see Ko, Kobayashi, Park & SR ar. Xiv: 0704. 2807 Title of talk 42

Compactify E(8)x. E(8) heterotic string on (T 2)3/(Z 3) + A 3 only ( R 5 >> ls ) SU(6) orbifold GUT BULK After Z 2 SU(5) brane Z’ 2 = Z 2 + A 2 SU(4)x. SU(2) brane Title of talk 43

Bulk states Gauge – Higgs unification ! 3 rd family Tree level coupling Title of talk 44

“Benchmark” model 1 - Spectrum Title of talk 45

Yukawa couplings Effective higher dimension operators !! Neutrino masses via See-Saw !! Title of talk 46

Gauge coupling unification Dundee, SR & Wingerter ar. Xiv: 0805. 4186 Title of talk 47

Proton decay - Dim. 6 operators Excluded region Title of talk observable ! 48

Conclusions Evolution of SUSY GUT Model Building Bottom up § 4 D SUSY GUT + family symmetry test predictions via global analysis § Lift to 5 D ( or 6 D ) orbifold GUT Top down § Derive from heterotic string, M or F theory includes Gravity !! Title of talk 49