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 !!