Nucleon Decay
Stuart Raby
DUSEL 2010Rapid City, SD
October 2, 2010
Nucleon Decay
Standard Model• Baryon & Lepton number - anomalous global symmetries
• Weinberg - effective operators consistent with SM
• eg.
* * 02
1ca a
bbcu pe u ed
M
• New physics at scale M breaks B & L eg. Grand unification M = MGUT
eg. Universal large extra dims. M ~ TeV e
p e
e
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 Model
13 charged fermion masses & mixing + 3 gauge couplings + 2 W & Higgs mass27 including neutrino masses & mixing28 including QCD q parameter29 including GN
Title of talk 6
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 7
, , , , ,u
q u d l ed e
3 2EM
YQ T
0
0,u d
h hH H
h h
1 4 2: , , , 1, 2, 0
3 3 3Y
1, 1
Title of talk 8
( T )2s A A a a
YD ig G igT W ig B
* 1[ ] [ ( ) ]
2gauge fermionL l i D l Tr G G
All interactions of fermions & Higgs with gauge bosons fixed by their charges
2 2| | | |gauge Higgs u d HiggsL D H D H V
1
2
ij ijYukawa e i j d d i j d
ij iju i j u i j u ij i j
L l e H q d H
q u H l H M
Title of talk 9
( , ) ( ) 2( ( )) ( ) ( )
( ( )), ( )
eE y e y e y F y
y x i e y e y
4 †
22
2
[ ( 2 [ ]) ]2
1
[ ( )
] . .8
[
gauge matter i s g W B i
g gs
ij ijYukawa e i j d d i j d
ij iju 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
.1
2] .ij i j u dV cH hM V H
Q , , , L , ,U V
U D E VD E
The MSSM is obtained by defining chiral superfields
Grand Unification & Charge Quantization
u u
Q Qu uu u
d de edddd
q u du
u d
l
uu
uu
d d d
e
d
e
d
3 312EM L RQ B L T T
SU(4) SU(2) (2)C L RSU
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 L RQ q l Q q l SU
uq l
d e
Quarks & leptons fit into two irreducible reps.
Pati-Salam - lepton # = 4th color
t bQ H Q
Yukawa coupling unification
Title of talk SU(5) 12
spinor repsn.of SO( 10 )
tensor product of 5 spin ½ w/even no. + signs
GeorgiFritszch & Minkowski
10
5
1
Georgi & Glashow
Grand Unification - SO( 10 ) GUT
Title of talk 13
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 g
g g
at MGUT
Title of talk 14
Gauge coupling unification
Dimopoulos, Raby & WilczekPRD24, 1681 (1981)
LEP data !!
Amaldi, de Boer & Furstenau,PLB260, 447 (1991)
Title of talk 15
3
Title of talk 16
This assumes degenerate squarks and sleptons and degenerate gauginos at GUT scale.
If, for example, then can even have .
3 2 1M M M
3 0
See Raby, Ratz, Schmidt-Hoberg arXiv:0911.4249 [hep-ph]
Title of talk 17
Proton decay - dim 6 operators
cad
cil
Title of talk 18
0p e
Title of talk 19
4
0 4 5
2 433
4
716
30
1 10( )
( )
0.012GeV10
3 10 GeV
p
p G
G p
X
Super Kamiokande bound
yrsBr p
Theory
MBr p e g m
Ms
e
yr
Title of talk 20
Proton decay - dim 4 operators
10 5 5 ' Q L " L LU D D D E
0 0 0or ( , )p e
P
Title of talk 21
2 matter parity excludes dim 4 operators
F -F, H H Z
22
32 2 262 2
'10 ' 10
1G
G
g mGeV
M TeVm
2 5
4
' pp
m
m
Title of talk 22
10 1010 5 Q QQ L U U D E
Proton decay - dim 5 operators
p K
Title of talk 23
2 21/2
2 216
( )16
( ) (LF)
t
effT
MLF
m
c cA p K
M
c ~ Yukawa couplingsminimize LFmaximize MT
eff
2
0 0 01,
0
Thus for obtain
GT Deff
G T G
effG T G
M XM M
M X XM M
X M M M
2
Eg. "Natural" splitti
10 45 10 (10 )
ng
45 G
D
with MX B L
T
W
Title of talk 24
Higgs GUT breaking3 3 3
Higgs3
3ln( )
5
effG T
G
M
M
ò ò ò
ò
Minimal SU5 : Proton decays toooo fast !!33
( )
34
2.3 10 (92 ) at 90%
~ (1/3 - 3) 10
p Kyrs ktyr CL
yrs Theory
Title of talk 25
Minimal SU5 excluded !
Caveats:1. Family structure is standard2. 3 < 0
Title of talk 26
“Minimal” SO(10) Model
16 16 145
10 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
Possible UV completion to strings !!
Effective higher dimension operators, Small rep’s + Many predictions !!
3 family SO10 SUSY Model
D3 x U(1) Family Symmetry Superpotential Yukawa couplings c2 analysis Charged fermion masses &
mixing Neutrino masses & mixing
Title of talk 28
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 M
1
2
2
0
45 GB L M
Familon VEVs
assumed
Title of talk 29
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 30
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
3 3a aS M S M 1616 v
Extend to neutrino sector
Assume 3 new real para’s
Title of talk 31
compared to SM - 27 parameters CMSSM - 32 parameters
24 parameters at GUT scale
Global 2 analysis
Title of talk 32
c2 analysis including B physics
Albrecht, Altmannshofer, Buras, Guadagnoli, & Straub JHEP 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 g & b s l+ l-
m16 ~ 10 TeV
Title of talk 33
SM SM7 t 7 7A tan sign 2C C C
g
b s
t
SMs 7 7favors C
BR(B
at
X
)
2
l l C
SM SM7 7 7 7C C C C
tA 0
What is the tension ?
Title of talk 34
7 7SMC C
Belle arXiv:0904.0770
However …
*B K l l
Title of talk 35
Albrecht et al. JHEP 0710:055 (2007)
7 7Required SMC C
Title of talk 36
MSO10SM & Large tan( ) 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 m+ m- ] Suppresses Br( B t n ) & DMBs
B Xs g , Xs l+ l- tension ??
LHCb
Title of talk 37
MSO10SM & Large tan( )
predicts light gluinos ~ 300 – 500 GeV predicts light charginos and neutralinos
LHC
MSO10SM : Beautiful symmetry Many experimental tests !!
Title of talk 38
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
2
1 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 39
Outline
4 dimensional SUSY GUTs 5 dimensional orbifold GUTs String orbifolds orbifold GUTs Conclusions
Title of talk 40
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-RussellH.D.Kim, Raby & Schradin JHEP 0505:036 (2005)
Title of talk 41
H H
H H
c
c
3 f
10 5
amilyrd
Brane states
Bulk states
1st & 2nd
familiesin bulk
Hall & Nomura SU(5) GUT on M x S1/(Z2 x Z’2)
R
b- Yukawaunification
Suppressproton decay
GUT symmetry breakingHiggs D-T splittingvia orbifold BCs
Title of talk 42
5D Orbifold GUT
G.C. Unif. & Proton decay > 4D
0 pR
Mc ~ 1/pR < MG < M*Dienes et al., Hall & Nomura,Kim & S.R., Feruglio et al.
KK modes
Title of talk 43
5D Orbifold GUT
G.C. Unif. & Proton decay > 4D
0 R
Mc ~ 1/R < MG < M*
u 0
u
de
P
0Proton
egg
Dim 6 amp. ~ 1 / MC2
MC
Enhanced !!u u
Brane
Title of talk 44
5D Orbifold GUT
G.C. Unif. & Proton decay > 4D
0 R
Mc ~ 1/R < MG < M*
0 u
d
P
u
0Proton
egg
Dim 6 amp. ~ 1 / MC2
MC
Suppressed !!
u
Bulk
U
E
Title of talk 45
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 46
Outline
4 dimensional SUSY GUTs 5 dimensional orbifold GUTs String orbifolds orbifold GUTs Conclusions
Title of talk 47
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 48
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 compactification of E(8)xE(8) heterotic string
Title of talk 49
Compactify E(8)xE(8) heterotic stringon (T2)3/(Z3) + A3 only ( R5 >> ls ) SU(6) orbifold GUT
After Z2
SU(5) brane Z’2 = Z2 + A2
SU(4)xSU(2) brane
BULK
Title of talk 50
35 24 5 5 1 H Hu d
t20 20 10 10 Q = t
b
2 6 6 L = b
c
c
20 35 20 Q H tcu
Tree level coupling
Bulk states SU 6 SU 5
Gauge – Higgs unification !
3rd family
Title of talk 51
“Benchmark” model 1 - Spectrum
S
Title of talk 52
Yukawa couplings
Effective higher dimension operators !!
Neutrino masses via See-Saw !!
Title of talk 53
3 24R symmetry LR S V
4 1 1 1 1 1 1 0 0u d
R
Q U D L E V H H
Superpotential W has charge 2
Title of talk 54
Conclusions
Evolution of SUSY GUT Model Building
Bottom up 4D SUSY GUT + family symmetry test predictions via global 2 analysis Lift to 5D ( or 6D ) orbifold GUT Top down Derive from heterotic string, M or F theory includes Gravity !!