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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
