Problems with the MSSM : mu & proton decay Stuart Raby KMI Nagoya University October 24, 2011.

Problems with the MSSM : mu & proton decay

Stuart Raby

KMINagoya University

October 24, 2011

Outline

Review the problems & proposed solutions in the literature

Discrete non-R symmetries & m Discrete R symmetries Unique Singlet extensions of the MSSM Conclusions

RMZ

4RZ

Outline

Review the problems & proposed solutions in the literature

Discrete non-R symmetries & m Discrete R symmetries Unique Singlet extensions of the MSSM Conclusions

RMZ

4RZ

Title of talk 4

(0)

(0) (1) (2)

(1) (2) (3)

(4) (5)

ij ij ije i j d i j u i j

ij i

d d u

u u j

i i i j i j i jijk k ijk k ijk k

i j i j i jijk k ijk k ijk k

u

i j iijk k

d

u

d

d

H H H

H H

Y L E Y Q D Y QU

L LH H

L L L E LQ D U D D

Q Q Q L U U D E Q Q Q

QU E L

H

H

H

W

i u u dH H H

General SU(3)C x SU(2)L x U(1)Y invariantsuperpotential up to operators of Dimension 5

Title of talk 5

(0)

    ij ij ije i j i j u i jd

ij i j

ud d

u u ud

Y L E Y Q D Y QU

L L

H H H

H H H H

W

MSSM

term: Need GM

0ij term: Weinberg operator for

neutrino mass

Title of talk 6

(0) (1) (2)i i i j i j i jijk k ijk k ijk kuL L L E LQ D U DH D

R parity violating operators

1 2 27 10

But

10 5 5 L L E L Q D U D D

0 3410 yearsp e

Title of talk 7

(1) (2) (3)

(4) (5)

i j i j i jijk k ijk k d

u ud d

ijk k

i j i iijk k

Q Q Q L U U D E Q Q Q

QU E L

H

H H H H

Dim 5 B & L violating operators

1,2 27 1 1

10 GeV

33 > 2.3 10 yearsp K

Outline

Review the problems & proposed solutions in the literature

Discrete non-R symmetries Discrete R symmetries Unique Singlet extensions of the MSSM Conclusions

RMZ

4RZ

R/Matter parity - Fayet & Farrar, Weinberg / Dimopoulos & Georgi Dimopoulos, Raby & Wilczek

Baryon triality - Ibanez & Ross

Proton hexality - Dreiner, Luhn & Thormeier

Title of talk 10

2

3

6

1 1 1 1 1 0 0

0 2 1 2 2 1 2

0 1 5 4 1 5 1

u d

M

B

P

Q U D L E H H

Matter parity - Baryon triality – Proton hexality -

3

2

6

M

B

P

Baryon triality & Proton hexalityNot consistent with Grand Unification !!

Anomaly free

Title of talk 11

2

2 3 6

0 0 0

0 0 0

0 0 0

1 1 5

1 0 3

1 0 3

1 0 3

0 2 4

mod( )

,

0 1 2

u

u

u

M

d

u

M

Q U H

H H

LH

U DD

Q LD

LLE

H L

QQQ L

UU D

M B

E

P

Z

Summary

What would we like to do ?

• Forbid the m term perturbatively

• Forbid dimension 3, 4 & 5 baryon and lepton

number violating operators

• And do this with a discrete symmetry

which is consistent with GUTs !

3

31

3

21

3

11

1(3· )

2

1 1(3· )

2 2

1 3 13· · ·

2 5 2

u d

u d

g g

g

g g

g

g g

g

H H

H H

A q q

A q q q q

qA qq q

10 5

10 5

10 5

1 3 0

for M odd1( mod )    ( mod )    ,    

/ 2 for M even24i

MA A

M

Anomaly free 0

0 Green-Schwarz cancellation

Anomaly coefficients

Title of talk 14

2 3    0 mod

1   0 mod

2 u dH H

A

q

A

q

Discre

Forbid

te R s

te

y ry

rm

mmet

Consider Non – R symmetry

0 mod u dH Hq q M

Anomaly cancellation :

m term allowed :

Summary

• M2 : eliminates Dim 3 & 4, B & L violating operators; LSP stable

• B3 : eliminates Dim. 4, B and Dim. 5, B & L violating operators; LSP unstable• P6 : eliminates Dim. 3, 4 & 5, B & L violating operators; LSP stable• MSSM consistent with GUTs BUT B3 & P6 are NOT !• m term allowed by ALL

Outline

Review the problems & proposed solutions in the literature

Discrete non-R symmetries Discrete R symmetries Unique Singlet extensions of the MSSM Conclusions

RMZ

4RZ

Lee, Raby, Ratz, Ross, Schieren,Schmidt-Hoberg & Vaudrevange Phys. Lett. B694, 491 (2011) Nucl. Phys. B850, 1 (2011)Kappl, Peterson, Raby, Ratz, Schieren & Vaudrevange Nucl. Phys. B847, 325 (2011)

Babu, Gogoladze & Wang Nucl. Phys. B660, 322 (2003)

Title of talk 18

2exp

superfield charg ,

1

+1

2

e

fermion charge

gaugino charg

Cons

e

ider

, ,u d

q

H H

M

q q q

i

M

chi q

q

ral

chiral

Superpotentia

Discrete R symmetry

q

l

q

10 5

Title of talk

3

31

3

21

3

11

13 3

2

1 13 5

2 2

1 3 13 11

2 5 2

u d

u d

R g g

g

R g g

g

R g g

g

H H

H H

A q q

A q q q q

q qA qq

10 5

10 5

10 5

2 3

1 3

0 mod    4 mod 2

3 10 mod 6    0 mod

5 2

u d

u d

R R

R

H H

HR

H

q q

q

A A

A A q

Ð

Ð

with = 3, 4, 6, 8, 12 or 24RM MZ

m term forbidden !

Title of talk 20

3    4 mod

Yukawa couplings

u dH Hq q q Mq 10 5

3    0 mod

BUT

q q M 10 5

Dimension 5 operators also forbidden !

Title of talk 21

0. m term is forbidden

Search for Discrete R symmetry, such that

Outline

Review the problems & proposed solutions in the literature

Discrete non-R symmetries Discrete R symmetries Unique Singlet extensions of the MSSM Conclusions

RMZ

4RZ

Title of talk 23

Unique discrete R symmetry consistentwith SO(10)

4RZ

1 1 0

SU( )

0

5

u dH Hq q q q10 5

16 10 15

10

= =

SO(10

0

= 1

)

u dH H

q q q q

q q q

Title of talk 24

2

2

0

2

3

3

3

1

0

2

,

0

u

u

u

u

d

Q U H

H H

LH

U DD

Q LD

LLE

H L

QQQ L

UU DE

W

4RZ

Title of talk 25

(0)

   p

p non perturbative

ij ij ije i j i j u i jd

ij i j

ud d

u u

Y L E Y Q D Y Q

L

H

H

UH H

H L

W

W W W

Title of talk 26

Non-perturbative effects

02 GS np

iS S W W

Title of talk 27

32

3 32 2

32

02

20

2

Pl

np Pl u d

Pl

Wm

M

W B m M m H H

mQQQ L UU DE

M

32

32 33 1

2 10 G V e

1

Pl

m

m

M

String Theory - fluctuating strings in 10 space-time dimensions E(8)xE(8) heterotic string compactified

on (T2)3 /(Z2 x Z2 ) orbifold w/

Kappl, Peterson, Raby, Ratz, Schieren & Vaudrevange

NPB 847, 325 (2011)

4RZ

String Theory - fluctuating strings in 10 space-time dimensions

• E(8)xE(8) heterotic string compactified on (T2)3 /(Z2 x Z2 ) orbifold • exact MSSM spectrum• F = D = 0 verified / stabilizes almost all moduli• symmetry eliminates dangerous baryon and lepton number violating operators• m = 0 perturbatively / m ~ m3/2 non-pert.

4RZ

4Discrete R symmetry defines MSSMRZ

String Theory - fluctuating strings in 10 space-time dimensions

• comes partially from the Lorentz symmetry of the internal dimensions• local SO(10) gauge symmetry• D(4) family symmetry / family hierarchy Ko, Kobayashi, Park & Raby, PRD 76, 035005 (2007)

• gauge – top Yukawa unification• non-trivial Yukawa matrices

4RZ

String Theory - fluctuating strings in 10 space-time dimensions• Higgs comes from chiral adjoint of

effective 6D SU(6) orbifold GUT

0

2

log ( )( ) ( )( )d uu d

Pl

K T T Z Z H H H H

WM

Brummer, Kappl, Ratz & Schmidt-Hoberg arXiv:1003.0084

Outline Review the problems & proposed

solutions in the literature Discrete non-R symmetries Discrete R symmetries Unique Singlet extensions of the MSSM Conclusions

RMZ

4RZ

Eg. 1 : GNMSSMRMZ

Additional MSSM singlet

0 3MSSM     u dN H H N W W

4 1 1 0 0 2

8 1 5 0 4 6

u dH H NM q q q q q10 5

4

2 2 23/2 P 3/2 3/2 3/2 ~ R u dm M m N m N m H H

W

Ross & Schmidt-Hoberg 1108.1284 [hep-ph]

Eg. 2 : allows axion solution to strong CP24

RZ2 3

P P

    u dN H H X NM M

W

5 9 16 12 1 5u dH H N Xq q q q q q

10 5

Second term generates 10 11~ 10 GeVN

Outline Review the problems & proposed

solutions in the literature Discrete non-R symmetries Discrete R symmetries Unique Singlet extensions Conclusions

RMZ

4RZ

Found unique symmetry forbids Dim 3, 4 & 5 ops. to all orders in perturbation theory m term generated non-

perturbatively Found heterotic orbifold

realization ! consistent with SU(5) : GNMSSM : allows axion solution to strong CP problem

4RZ

4,6,8,12,24RZ

8RZ

24RZ