SupersymmetricGUTs - uni-bonn.desusy10.uni-bonn.de/data/susy10_raby.pdf · 4 dimensional SUSY GUTs...

Supersymmetric GUTs

Stuart Raby

Pre-SUSY 2010Bonn, Germany

August 21, 2010

Outline

Evolution of SUSY GUTs 4 dimensional SUSY GUTs 5 dimensional orbifold GUTs String orbifolds orbifold GUTs Conclusions

Outline

4 dimensional SUSY GUTs 5 dimensional orbifold GUTs String orbifolds orbifold GUTs Conclusions

The Goal of Beyond SM physics Reduce # fundamental parameters

18 parameters in Standard Model13 charged fermion masses & mixing

+ 3 gauge couplings+ 2 W & Higgs mass

27 including neutrino masses & mixing28 including QCD θ parameter29 including GN

Title of talk 5

Supersymmetric Grand Unified Theories MZ << MG “natural” Explains charge quantization & Families Unification of gauge couplings Yukawa coupling unification + family symmetry fermion mass hierarchy Neutrino masses via See-Saw LSP - dark matter candidate Baryogenesis via leptogenesis SUSY desert LHC probes physics at MPl SUSY GUTs “natural extension of SM”

Title of talk 6

1 1 1T , T , T

[T ,T ]

2 2 2

T SU(3)T T T 0

c T c c T cA A A A A A

c cA

A B A

A A

BC C

q q u u

il

f

d d

e

λ λ λ

ν

= = − = −

==

= =

, , , , ,c c c cuq u d l e

d eν

ν = =

1 1,2 2

0[ , ] S 2

U

( )

a a a a

c c c ca a a a

a b abc c

T q q T l l

T u T d T e TT T i T

τ τ

νε

= =

= = = ==

1 4 2, ,3 3 3

, 2 , 0U(1)

c c c c

c c c

Y

Y q q Y u u Y d d

Y l l Y e e Y ν

= = − =

= − = + =

3 2EMYQ T= +

Title of talk 7

( T )2s A A a aYD ig G igT W ig Bµ µ µ µ µ

′= ∂ + + +

* 1[ ] [ ( ) ]2gauge fermionL l i D l Tr G Gµ µν

µ µνσ− = + + − +

*2 ( )e c

ei eσ

Ψ =

The standard Dirac form of the SM can beobtained by defining 4 component Dirac field

All interactions of fermions & Higgs with gauge bosons fixed by their charges

Title of talk 8

0

0 ,u dh h

H Hh h

+

−

= =

, -

T T 01 1,2 2

A u A d

a u a u a d a d

u u d d

H H

T H H T H H

H H H HY Y

τ τ

= + =

= =

= =

1 2

ij c ij cYukawa e i j d d i j d

ij c ij c c cu i j u i j u ij i j

L l e H q d H

q u H l H Mν

λ λ

λ λ ν ν ν

− = +

+ + −

2 2| | | |gauge Higgs u d HiggsL D H D H Vµ µ− = + +

Title of talk 9

( , ) ( ) 2( ( )) ( ) ( )

( ( )), ( ) eE y e y e y F y

y x i e y e yµ µ µ αα

θ θ θ θ

θ σ θ θ θ

= + +

= − ≡

4 †

22

2

[ ( 2 [ ]) ]2

1

[ ( ) ]

. .

8

[

gauge matter i s g W B i

g gs

ij c ij cYukawa e i j d d i j d

ij c ij cu i j u i j u

YL d L exp g V gV g V L

d Tr W W h cg

L d L E H Q D H

Q U H L V H

αα

ν

θ

θ

θ λ λ

λ λ

′− = − + + +

+ + +

= +

+ +

∫

∫

∫

] .12

.c cij i j u dM V V H H h cµ +− −

Q , , , L , ,c c c cU VU D E V

D E

= =

The MSSM is obtained by defining chiral superfields

Grand Unification & Charge Quantization

c

cc

cccc

ccu uu uu uQ Q

d dd dd ed eν ν

= =

( ) ( )

c cc cc c

c

ccuu d

ee

uu d

uu dq

dd

du

d

lν

= = =

=

( ) 3 312EM L RQ B L T T= − + +

Title of talk 11

The two Higgs doublets ( ) (1,2, 2)d uH H H=

( ), ( ) SU(4) SU(2) (2)

, (4,2,1) (4,1, 2)

c c cC L R

c cc c

c c

Q q l Q q l SU

uq l

d eν

= = ⊗ ⊗

= = ⊕

Quarks & leptons fit into two irreducible reps. Pati-Salam - lepton # = 4th color

ct bQ H Q

ττ νλ λ λ λ λ λ⇒ = = = ≡

Yukawa coupling unification

Title of talk

spinor repsn.of SO( 10 )

tensor productof 5 spin ½ w/even no. + signs

GeorgiFritzsch & Minkowski

Grand Unification - SO( 10 ) GUT

Title of talk 13

Aside: SO(10) group theoryThe defining representation

{ }10 , 1, ,10

(10) : real 10 10 matrices; 1;

=

det 1

10' 1 0

i

j ji i

T

i

SO O O O O

O

=

= × = =

Infinitesimal transf.-

1 with ( ) generators with

45 parameters

T

ab ab a b a bij ab ij ij i j j i

ab ba

O ii

ω ω ω

ω ω δ δ δ δ

ω ω

= + = −

≡ Σ Σ = −

= −

Title of talk 14

Lie algebra[ , ] [ ]ab cd ab cd cd ab ad ac bc bd

ik ij jk ij jk ik bc ik bd ik ad ik acδ δ δ δΣ Σ ≡ Σ Σ − Σ Σ = Σ − Σ + Σ − Σ

or 45 45 45 ( 45 )Tij ik jl kl ij ijO O O O′ ′= =

Define spinor representation of SO(10)† 5 5

102

11 11 111

matr, { , } 2 2 2

, { , } 0 , 1 eig. 1

icesi i i j ij

i ii

i

δ

=

Γ = Γ Γ Γ = ×

Γ ≡ Γ Γ Γ = ∀ Γ = ⇒ ±∏

11[ , ] [ , ] 04

16 16

ij i j iji

Σ = Γ Γ Γ Σ =

⊕

Title of talk 15

†2 1 2 2 1 2, , 1, ,5 2 2

i iA Aα α α αα α α− −Γ + Γ Γ − Γ

= = = Define

†{ , } 0, { , }A A A Aα β α β αβδ= =†

(10)

†

{ , , , }

, 1, ,24

5 5 traceless, hermi

[ , ]2

tian mwhere atrices of SU( 5)

SO

a

A A B AB

A

C

A

C

Q X

Q A A Q Q iA f Q

αβ αβ

αβα β

αβ

λ

λ

= ∆ ∆

= =

×

=

L

† † † †

5†

1

,

12 ( )2

A A A A

X A A

αβ α β βα αβ α β βα

α αα =

∆ = = −∆ ∆ = = −∆

= − −∑

Title of talk 16

Define | 0 | | 0 0 | 0 0 A

AQ

α⟩ ≡ ⟩ ∋ ⟩ ≡⇒ ⟩ ≡

1

† † †| 0 | |, 0 |αβγδλ λαβ αβ αβ γδ∆ ⟩ = ⟩ ∆ ∆ ⟩ = ⟩10 5

(10) (5) (1) SO(6) SO(4) SU(4) (2) (2) SU(3) (2) (2) (1) (5) ' (1) ' flipped SU(5)

X

C L R

C L R B L

SO SU USU SU

SU SU USU U

−

→ ⊗→ ⊗ ≈ ⊗ ⊗→ ⊗ ⊗ ⊗→ ⊗

Title of talk SU(5) 17

spinor repsn.of SO( 10 )

tensor productof 5 spin ½ w/even no. + signs

GeorgiFritzsch & Minkowski

10

5

1

Georgi & Glashow

Grand Unification - SO( 10 ) GUT

Title of talk 18

SU(5) group theory

†(5) { | 5 5 complex matrix; 1; 1}5 5 SU U U U U detU

Uα α ββ

′

= = × = =

=

†

exp( ) where

( ) 0, 1, ,,

structure constants of

24[

SU( )]

5,

A A

A A A

A B ABC C

ABC

U iTTr T T T AT T i f T

f

ω=

= = = …=

1Choose normalization: (T T )2

f fA B ABTr δ=

Title of talk 19

( 20)

24

1 0T , 1, ,82

0 0

0 0(2) : , 21,22,231

(3

02

1 / 3 0 00 1 / 3 0 0

3 3(1) : 0 0 1 / 35 5

) :

21 / 2 0

00 1 / 2

AA

AA

Y

A

SU T A

U

YT

S

U

λ

τ −

= = … = =

− − = ≡−

1 0 00 0 0 0 0 0

1, 9, ,20 : ,0 0 0 02

1 0 0 0 00 0

0 0 0 0 0 0

12A

i

T Ai

− = …

Title of talk 20

5 , 1,2,

(3, 1, -2/3) , (1, 2, +1)

3; 4,5a

i

a i

da i

l

d l

α = = =

= =

5 , 1,2,3; 4,5

(3,1,2 / 3), (1,2, 1)

caci

c c

da i

l

d l

α

= = =

= = −

1 2 2 110 10 5 5 5 5

10 ( ) (3,1, 4 / 3)

10 (3,2,1 / 3) 10 (1 , 2

,1 )

ab abc cc

ai ai ij ij c

uq e

αβ βα α β α β= − ∝ −

≡ = −

≡ = ≡ = +

Title of talk 21

1 13 21

2 23 12

3 32 131 2 3

1 2 3

00

15 , 10 02

00

c cc

c cc

c cc

c

c

u u u ddu u u dd

u u u dde u u u e

d d d e

αβα

ν

− − = = −

− − − − − − − −

To summarize -

Title of talk 22

Gauge coupling unificationBoundary conditions

3 2 1

22

3 2 1 2 2

T '2

3, , ' 5' 3, sin

' 8

A A aG A s A a

s

G W

Yg T G g G g T W g B

g g g g g g

gg g g gg g

µ µ µ µ

θ

⊃ + +

= = =

∋ = = = = =+

at MGUT

Title of talk 23

Gauge coupling unification

Dimopoulos, Raby & Wilczek

PRD24, 1681 (1981)

LEP data !!

Amaldi, de Boer & Furstenau,

PLB260, 447 (1991)

Title of talk 24

ε3

Title of talk 25

This assumes degenerate squarks and sleptons and degenerate gauginos at GUT scale.

If, for example, then can have .

3 2 1M M M<<

3 0ε ≥

See Raby, Ratz, Schmidt-HobergarXiv:0911.4249 [hep-ph]

Title of talk 26

Proton decay - dim 6 operators

cad

cil

Title of talk 27

0p e π+→

Title of talk 28

340

4

4 5

36 2

1 10( )

10

p

G

G p

yrs Super KamiokandeBr p eM

g m

yrs Theory

τπ+

±

≥ × −→

≈

Title of talk 29

Proton decay - dim 4 operators

10 5 5 ' Q L " L Lc c c c cU D D D Eλ λ λ⊃ + +

0 0 0or ( , )p eπ π ν π π π π+ + − +→

P

Title of talk 30

2 matter parity excludes dim 4 operatorsF -F, H H→ →

2232 2 26

2 2

' 10 ' 101

G

G

g mGeVM TeVm

λ λ λ λ− − − < ≤ ⇒ <

( )

2 5

4

' pp

m

m

λ λΓ ≈

Title of talk 31

10 1010 5 Q QQ L c c c cU U D E⊃ +

Proton decay - dim 5 operators

Title of talk 32

2 21/2

2 216

( )16

( ) (LF)

t

effT

MLF

mc cA p K

M

τ µλ λπ

ν+

+∝

→ ∝

c ~ Yukawa couplingsminimize LFmaximize MT

eff

2

0 0 01 ,0

Thus for obtain

GT Deff

G T G

effG T G

M XM MM X XM M

X M M M

= ⇒ ≡ =

<< >>

( )

210 4510 (10 ).45 G

EgM B L

W X′ ′⊃ +

−

Title of talk 33

Higgs GUT breaking3 3 3

Higgs3

3 ln( )5

effG T

G

MM

απ

= + +

=

Minimal SU5 : Proton decays toooo fast !!33

( )

34

2.3 10 (92 ) at 90%

~ (1/3 - 3) 10p K

yrs ktyr CL

yrs Theoryν

τ +→> ×

×

Title of talk 34

Quark & Lepton masses and mixing

Hierarchical 3 3 ~ O(1)uq u Hλ λ

( )

P

,S Froggatt-Nielsen

Mi j u

n i j

q u H

Flavor symmetry breaking

3 3 4 4

(1) or non-Abelian SU(2), SU(3) S , , , (27), (54)U

D D A≈ ∆ ∆

Title of talk 35

Fermion mass hierarchy FCNC

Non-abelian family symmetry

Suppresses flavor violation

Title of talk 36

Fermion Masses in SO(10)λ 16 10 16 top, bottom, tau, ντ

Yukawa unification

3 2

16 16 16 16 16 16

1)

210

1

2

0 126 1

10

20

120 126 621

W ⊃ + +

+ + + +Aulakh, Babu, Bajc, Chen, Mahanthappa, Mohapatra, Senjanovic, …

“Minimal” SO(10) Model

Renormalizable ! - large rep’s & few predictions

Title of talk 37

“Minimal” SO(10) Model

2) 16 16 1 4510 10 M

6 16 W ⊃ + +

Albright, Anderson, Babu, Barr, Barbieri, Berezhiani, Blazek, Carena, Dermisek, Dimopoulos, Hall, Pati, Raby, Romanino, Rossi, Starkman, Wagner, Wilczek,Wiesenfeldt, Willenbrock

II

Possible UV completion to strings !!

Effective higher dimension operators,Small rep’s + Many predictions !!

Blazek, Dermisek & Raby PRL 88, 111804 (2002)PRD 65, 115004 (2002)

Baer & Ferrandis, PRL 87, 211803 (2001)Auto, Baer, Balazs, Belyaev, Ferrandis & Tata

JHEP 0306:023 (2003)Tobe & Wells NPB 663, 123 (2003)Dermisek, Raby, Roszkowski & Ruiz de Austri

JHEP 0304:037 (2003)JHEP 0509:029 (2005)

Baer, Kraml, Sekmen & SummyJHEP 0803:056 (2008)JHEP 0810:079 (2008)

Yukawa Unification & Soft SUSY breaking

t b ττ νλ λ λ λ λ= = = ≡Note, CANNOT predict top mass due to large SUSY threshold corrections to bottom and tau mass

So instead use Yukawa unification to predictsoft SUSY breaking masses !!

3 316 1 0 16λ

3 316 1 0 16λ

t b ττ νλ λ λ λ λ= = = ≡

0 16 10 16

16 1/2 16

2 2 TeV , <<

A m m mm few M mµ

≈ − ≈>

tan 50β ≈

MSO10SM

Fit t,b,tau requires

TM

( )2 2

2

2

10

13%2d uH H

H

m mm

m

−∆ ≡ ≈

Roughly ½ comes From RG running from

GM mτν→

20 10Varying , ,

arbitraryH

A

A m mm

∆⇒

Radiative EWSB requires

Blazek, Dermisek & Raby “Just so”

Note, this is difficult in bottom – up approach !!

Gauge coupling unification Yukawa unification Inverted scalar mass hierarchy

Bagger, Feng, Polonsky & ZhangPLB473, 264 (2000)

Suppresses flavor & CP violation Nucleon decay

MSO10SM

MSO10SM1. Extend to 3 family model in 4D

( Dermisek & Raby PLB 622, 327 (2005). )

2. Extend to orbifold GUT in 5D( HD Kim, Schradin & Raby,

JHEP 0301, 056 (2003) & JHEP 0505, 036 (2005) )

3. Extend to heterotic string in 10D compactified on Z3xZ2 orbifold( Kobayashi, Raby & Zhang,

PLB 593, 262 (2004) & NPB 704, 3 (2005))

χ2 analysis - 3rd family

11 Parameters :3

01 10/ 2 16tanG G

HM mM

A m mα ε

βµλ

∆

9 Observables ( included in χ2) :

( )EM s Z W NEW

t b b

G M M

M m m Mµ

τ

α α ρ

Dermisek, Raby, Roszkowski and Ruiz de Austri

JHEP 09 (2005) 029

Results

1. Dark Matter & WMAP2. Bs -> µ+ µ−

3. Light Higgs mass - mh4. Upper bound on mA

Lower bound on BR(Bs -> µ+ µ−)

Dark Matter & WMAP

Neutralino LSP

1 1 A f fχ χ → →

tanAb b β∝

A : broad resonance, mA arbitrary

Results - m16 & mA fixed

Green band consistent with WMAPLight Higgs mass contours

Br( Bs -> µ+ µ− )

SM : 3 x 10-9

MSSM : ~ (tan β)6 /mA4

DZero < 4.7 x 10-8 (95% CL) w/ 5.0 fb-1

“expected sensitivity”

CDF bound < 4.3 x 10-8 (95% CL) w/ 3.7 fb-1

Title of talk 49

Results - m16 & mA fixed

Constant Bs -> µ+ µ− contoursConstant χ2 contours

Light Higgs mass

|At| increases mh decreases

Carena,Quiros &Wagner ‘95

Light Higgs mass

23 g

2 2

tan tan log .

2%

t tb

b b t

b

b

M Am corrm m mm

m

α µ β λ µ βδ

δ

∝ + +

≤ −

Needed to fit data

M1/2 increases -At increases

mh decreases

mA[max] Br[ Bs -> µ+ µ− ][min]

Fermilab ??

-8

1.3 TeV

Br( )

10

A

s

m

B µ µ+ −

≤

→

≥

Summary - MSO10SM

1. Gauge & Yukawa unification2. Suppresses flavor & CP viol. & N decay3. Dark Matter consistent w/WMAP4. 114 < mh < 121 GeV5. mA < 1.3 TeV

BR(Bs -> µ+ µ−) > 10-8

Dermisek & Raby PLB 622:327 (2005).

Dermisek, Harada & Raby PRD74, 035011 (2006)

Albrecht, Altmannshofer, Buras, Guadagnoli & StraubJHEP 0710:055 (2007)

3 Family SO(10) + family symmetry

3 family SO10 SUSY Model

D3 x U(1) Family Symmetry Superpotential Yukawa couplings χ2 analysis Charged fermion masses & mixing Neutrino masses & mixing

Title of talk 57

Superpotential for charged fermion Yukawa couplings

. 3 3

3

16 1016 16 10

45 16 45 16 16

ch fermions a a

a aa a a a

W

M AM Mχ

χ

φ φχ χ

= +

+ + + +

1

2

φφ

φ

=

2

0φ

φ

=

( )45 GB L M= −

Familon VEVs assumed

Title of talk 58

Effective higher

dimension operators

Title of talk 59

SO(10) x [ D3 x U(1) family sym. ]Yukawa Unification for 3rd Family

Dermisek & Raby PLB 622:327 (2005).

7 real para’s + 4 phases

+ 3 real MajoranaNeutrino masses

Title of talk 60

( )( )

2 3 3 3

12 3 3 3

16 16 16neutrino a a

a a a

W N N

S N N S N N

λ λ= +

+ +

3 3a aS M S M= = 1616 v=

Extend to neutrino sector

Assume 3 new real para’s

Title of talk 61

12neutrino NW m VN NM Nνν ν ν= + +

sin2

vm Yν ν β=

32

32

0

33 3 1

Yυ

ε ω εξω

ε ω εω εω λεξσ εσ

′−

′= − −

( )2

2 1σω

σ=

−

2

16 2

3

0 00 0

0 0V v

λλ

λ

=

( )1 2 3NM diag M M M=

Title of talk 62

( )( )1 1T T Te N eM U m V M V m Uν ν ν

− −=

Using χ2 analysis, fit

15 charged fermion & 4 neutrino low energy observables with

11 arbitrary Yukawa & 3 Majorana mass parameters

4 & 1 d. o. f. or 5 predictions

Title of talk 63

compared to SM - 27 parametersCMSSM - 32 parameters

24 parameters at GUT scale

Global χ2 analysis

Title of talk 64

Global χ2 analysis – good fits to charged fermion masses & mixing angles neutrino masses & mixing angles naturally satisfies Lepton Flavor Violation

and electron electric dipole moment boundsDermisek, Harada & Raby

PRD74, 035011 (2006)

Title of talk 65

16

1/2

4 TeV = 300 GeV

M 200 GeV

mµ

=

=

Title of talk 66

Results for 7 < χ2 < 8

16

213

14

29

4 TeV 114 < m 129 GeV

0.010 < sin 2 0.015

1 < BR( e ) 10 < 7 2 < d ( cm) 10 < 5

h

e

m

e

ϑ

µ γ

=<

<

→ ×

×

Title of talk 67

χ2 analysis including B physics

Albrecht, Altmannshofer, Buras, Guadagnoli, & StraubJHEP 0710:055 (2007)

Find good fits to quark, charged lepton & neutrino masses and mixing angles& test flavor violation in b physics

some tension between b s γ & b s l+ l-

m16 ~ 10 TeV

Title of talk 68

( )SM SM7 t 7 7A tan sign 2C C Cχ µ β

+

∝ × ≈ −

γ

b s

t

χ − χ −

SMs 7 7favors C

BR(B

at X

)

2 l l C

σ

+ −→ ≈ +

SM SM7 7 7 7C C C Cχ +

= + ≈ −

tA 0<

What is the tension ?

Title of talk 69

7 7SMC C= −

Belle arXiv:0904.0770

However …

*B K l l+ −→

Title of talk 70

Albrecht et al.JHEP 0710:055 (2007)

7 7Required SMC C= +

Title of talk 71

MSO10SM & Large tan( β ) Fits WMAP Predicts light Higgs

with mass of order 120 – 130 GeV Predicts lighter 3rd and heavy 1st & 2nd gen.

squarks and sleptons (inverted scalar mass hier.) LFV bounds satisfied Enhances Br[ Bs µ+ µ− ] Suppresses Br( B τ ν ) & ∆ MBs B Xs γ , Xs l+ l- tension ??

LHCb

Title of talk 72

MSO10SM & Large tan( β )

predicts light gluinos ~ 300 – 500 GeV predicts light charginos and neutralinos

LHC

MSO10SM : Beautiful symmetry Many experimental tests !!

Title of talk 73

Problems of SUSY GUTs

GUT symmetry breaking Higgs doublet-triplet splitting

3 250 5050 50 75 75 H 75 75 duW M H H H X H H⊃ + + + +

Missing partner mechanism SU(5)

Missing VEV mechanism SO(10)

( ) ( )

( ) ( ) ( )

24 2

21 2

45 45 X 16 16

16 ' 45 16 16 ' 45 16' 104510 ' ' 10 '

W M F X

S S S S X

⊃ + + +

+ + + + + +

Title of talk 74

Outline

4 dimensional SUSY GUTs 5 dimensional orbifold GUTs String orbifolds orbifold GUTs Conclusions

Title of talk 75

Orbifold GUTs in 5 or 6 dimensionsGUT symmetry breakingDoublet-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 76

( )( )H H

H H

c

c

+

+

3 f10 5

amilyrd

+

Brane states

Bulk states

1st & 2nd

familiesin bulk

Hall & Nomura SU(5) GUT on M x S1/(Z2 x Z’2)

Rπ

b-τ Yukawaunification

Suppressproton decay

GUT symmetry breakingHiggs D-T splitting

via orbifold BCs

Title of talk 77

5D Orbifold GUT

G.C. Unif. & Proton decay > 4D

0 πR

Mc ~ 1/πR < MG < M*Dienes et al., Hall & Nomura,Kim & S.R., Feruglio et al.

KK modes

Title of talk 78

5D Orbifold GUT

G.C. Unif. & Proton decay > 4D

0 R

Mc ~ 1/R < MG < M*

cu} 0 π

u

cde

P

0Proton

eπγ γ

+→ +

Dim 6 amp. ~ 1 / MC2

MC

Enhanced !!u u

Brane

Title of talk 79

5D Orbifold GUT

G.C. Unif. & Proton decay > 4D

0 R

Mc ~ 1/R < MG < M*

} 0 πu

cd

P

u

0Proton

eπγ γ

+→ +

Dim 6 amp. ~ 1 / MC2

MC

Suppressed !!

u

Bulk

cU

E

Title of talk 80

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 81

Outline

4 dimensional SUSY GUTs 5 dimensional orbifold GUTs String orbifolds orbifold GUTs Conclusions

Title of talk 82

UV completion

Orbifold GUTs in 5 or 6 dimensionsDerived 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 83

Road to the MSSM with R-parityLebedev et al. – 0708.2691[hep-th]

MSSM spectrum at low energy Exact R parity Light Higgs Non-trivial charged fermion masses Neutrino masses via See-Saw

Find 15 models from orbifold compactificationof E(8)xE(8) heterotic string

Title of talk 84

Compactify E(8)xE(8) heterotic stringon (T2)3/(Z3 x Z2) + Wilson lines [ A2, A3 ]

Local SO(10) GUT

Title of talk 85

D4 family symmetry

{ }4 1 3 2

1 1 2 3 2 2

1, , ,

0 1 1 0: :

1 0 0 1

D i

f f f f

σ σ σ

σ σ

= ± ± ±

= ↔ = ↔ − −

1

2

ff

doublet 3, H , Hu df singlets

geometry string selection rule

Title of talk 86

For detailed list of all discrete non-abeliansymmetries from orbifold compactificationof the heterotic string, see

Kobayashi, Nilles, Ploeger, SR & Ratzhep-ph/0611020

For D4 phenomenology, seeKo, Kobayashi, Park & SR

arXiv:0704.2807

Title of talk 87

Compactify E(8)xE(8) heterotic stringon (T2)3/(Z3) + A3 only ( R5 >> ls )

SU(6) orbifold GUT

After Z2SU(5) brane

Z’2 = Z2 + A2SU(4)xSU(2) brane

BULK

Title of talk 88

35 24 5 5 1 H Hu d→ + + + ⊃ +

( )

( )

t20 20 10 10 Q = t

b

2 6 6 L= b

c c c

c cτ

τ

ντ

+ → + + ⊃ + +

+ → +

20 35 20 Q H tc cu⊃

Tree levelcoupling

Bulk states ( ) ( )SU 6 SU 5→

Gauge – Higgs unification !

3rd family

Title of talk 89

“Benchmark” model 1 - Spectrum

S

Title of talk 90

Yukawa couplings

Effective higher dimension operators !!

Neutrino masses via See-Saw !!

Title of talk 91

ConclusionsEvolution of SUSY GUT Model Building

Bottom up 4D SUSY GUT + family symmetry

test predictions via global analysis Lift to 5D ( or 6D ) orbifold GUT Top down Derive from heterotic string,

M or F theory includes Gravity !!

Title of talk 92

Backup Slides

93

Baer, Kraml, Sekmen and SummyJHEP 03 (2008) 056

Bottom – Up and Down and Up …

Dermisek, Raby, Roszkowski and Ruiz de Austri JHEP 09 (2005) 029

Top - Down

max( , , )min( , , )

t b

t b

f f fRf f f

τ

τ

= 2χ

( )2 2

2

2

10

13%2d uH H

H

m mm

m

−∆ ≡ ≈ BDR “Just so”

( )22 0ii X X im Q D m= +

016 10

Q U D L E | H H

1 1 -3 -3 1 5 | -2 2

m | m

U D

iX

i

c c c cV

Q

m

Baer, Kraml & SekmenarXiv:0908.0134

“DR3”( ) ( )3 1,216 16m m≤

Balazs & Dermisek JHEP 0306:024 (2003) non universal gaugino masses

Altmannshofer, Guadagnoli, Raby & StraubPLB 668, 385 (2008)

Baer, Kraml & Sekmen arXiv:0908.0134 [hep-ph] D term splitting &

Guadagnoli, Raby & Straub arXiv:0907.4709 [hep-ph]

Varying BCs at MGUT3rd Family only

t b τλ λ λ≠ =

2 2 & U Dt b H HA A m m≠ ≠

( ) ( )3 1,216 16 m m≠

Title of talk 96

Title of talk 97

Gauge coupling unificationDundee, SR & Wingerter arXiv:0805.4186

Title of talk 98

Proton decay - Dim. 6 operators

observable !Excluded region