problems with the mssm : mu & proton decay stuart raby kmi nagoya university october 24, 2011
TRANSCRIPT
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