title of talk1 unification & b-l in string theory stuart raby b-l workshop, lbl september 21,...
TRANSCRIPT
Title of talk 1
Unification & B-L in String Theory
Stuart Raby
B-L Workshop, LBL September 21, 2007
Phenomenology
charge quantization gauge coupling unification Yukawa unification neutrino masses
Title of talk 3
uu u u
e
u uQ
ddQ
d dd ed
q u du
u d
l
uu d
ee
udd
u
dd
3
2EM LYQ T
Pati-Salam SU(4)CxSU(2)LxSU(2)R
3 3 = 2EM L RQ T T B L
(5) (1)
(10)
(4) (
2) 2
( )
C L R
SU U
SO
SU SU SU
31 510 5 1
16
Q + Q
Title of talk 5
spinor repsn.of SO( 10 )
Charge quantization
Title of talk 6
Phenomenology
charge quantization gauge coupling unification Yukawa unification neutrino masses
Title of talk 7
Gauge coupling unification
163 10 GeVGM
Title of talk 8
Phenomenology
charge quantization gauge coupling unification Yukawa unification neutrino masses
Title of talk 9
Phenomenology
charge quantization gauge coupling unification Yukawa unification neutrino masses
Title of talk 10
Phenomenology
charge quantization gauge coupling unification Yukawa unification neutrino masses
SO(10) SUSY GUT w/ L.E. SUSY
MSee-Saw ~ (.01 -.1) MG
Title of talk 11
4 D GUT problems
GUT symmetry breaking
Higgs doublet – triplet splitting
Solution ?
Orbifold GUTs
Title of talk 12
M4 x S1/(Z2xZ2’)
P P’
P & P’ parity affect boundary conditionsat fixed points
Orbifold SUSY GUTs in 5 or 6DP & P’ boundary conditions can
break N=2 N=1 SUSY give chiral gauge theory gauge symmetry breaking Higgs doublet-triplet splitting
All this first observed in heterotic string in 10D
Title of talk 14
Outline
Orbifold GUTs / String Orbifolds Kobayashi, SR, Zhang hep-ph/0403065 , hep-ph/0409098 Mini-Landscape : search for MSSM LNR3VW hep-th/0611095, hep-th/0611203 Road to the MSSM w/ R-parity LNR3VW 0708.2691 [hep-th]
Title of talk 15
E8 x E8 heterotic string
Constructing MSSM / Caveats
SUSY solution at MS
100’s moduli ( geometric & more )
moduli stabilization & SUSY breaking ?? save for later
gauge & Yukawa couplings fcns. of moduli tune to desired values
Title of talk 16
E8 x E8 heterotic string in 10DCompactify 6D on
(T2)3
Then mod by Z6-II = (Z3 x Z2) and Add Wilson lines
Z6 embedded in E8 x E8 gauge latticeas shift V6 : consistent with mod. inv. !
Title of talk 17
First consider (T2)3/Z3 + W3 [Wilson line in SU3 torus]
Massless modesFrom Untwisted sector + (G2 , SU3) twisted sector
E6 GUT in 5 or 6D
Title of talk 18
E6 Orbifold GUT on M4 x S1/(Z2xZ2’)
Title of talk 19
Then add Z2 orbifold + W2 [Wilson Line] [in long direction]
E6 SO(10) SU(4)xSU(2)LxSU(2)R
F3 = (4,2,1), F3c = (4c,1,2) , H = (1,2,2)
P P’ ( V2 ) ( V2+ W2 )
Title of talk 20
T1 twisted sector
2 Light fam’s
Vector-like exotics
Local GUT SO(10)
Title of talk 21
E6 Orbifold GUT on M4 x S1/(Z2xZ2’)
Vector-like Exotics
Title of talk 22
Advantage of Orbifold & Local GUTs
1. Local SO(10) GUT with 16s at fixed points guarantees charge quantization
2. Orbifold GUT with SU(5) or larger
in bulk allows for gauge coupling unification at string scale
Title of talk 23
Mini-Landscape searchhep-th/0611095
Lebedev, Nilles, SR, Ramos-Sanchez,
Ratz, Vaudrevange & Wingerter
Title of talk 24
Buchmuller, Hamaguchi, Lebedev & Ratz Z6-II orbifold
hep-ph/0511035, hep-ph/0512326
Looked for and found SM gauge group in 4D with 3 families and vector-like
exotics
Search for MSSM Spectra in heterotic orbifolds
Title of talk 25
Mini-Landscape search Z6-II orbifold1. V6 breaks to SO(10) [or E(6)]
2. 2 families [ 16 [or 27] ] in T1 twisted sect. 3. Generate 2 Wilson lines W3 , W2 4. Identify ‘inequivalent’ models5. Select models with6. Select models with 3 net (3,2)7. Select models with non-anom.8. Select models with 3 SM families + Higgses + vector-like exotics
(5) (10)SMG SU SO
1( ) (5)U Y SU
Title of talk 26
Mini-Landscape search LNRRRVW
Title of talk 27
Mini-Landscape search LNRRRVW
93 MSSM-like models orprobability ~ 1/300
“Fertile patch” in heterotic landscape !!
Title of talk 28
Road to the MSSM w/ R-parityLNRRRVW 0708.2691 [hep-th]
1. Check R parity 2. Check for D = 0 directions 3. Check all exotics get large mass4. Check light Higgs 5. Check charged fermion masses 6. Check neutrino masses 7. Check dimension 5 B & L
violating ops.
Title of talk 29
R parity
i B LR e
2Z Forbid Dim 2 & 3 operators
Family Reflection symmetry or Matter parity
3
23f
- 2 /B L S f S f
Title of talk 30
Generalized matter parity Z2
2 2
& = 2 / 2 2 / 2 1
nS n f
f f
Ζ
Z Z
0, 2, 2/3, 2/5, 4/5, 2/7, 4/7, ....f
Identify “suitable” B-L standard for SM particles vector-like on exotics maximal no. SM singlets w/
Allow right-handed neutrino masses
Title of talk 31
Results
Title of talk 32
Consider one “Benchmark” Model
G = SU(3)xSU(2)x [SU(4)xSU(2)’]xU(1)9
1. Spectrum2. term3. Yukawa couplings4. Neutrino masses5. Dim. 5 ops.
Title of talk 33
Orbifold GUT - SU(6) Local GUT - SO(10) x SO(4)
166
3 31 1 1 1 1 1 13 2 2 2 2 2 2 2 23
V 2 3 3 0 0 0 0 0
W
Title of talk 34
Spectrum
S
Title of talk 35
term
1 1nS ~ MZ
Yukawa couplings
Not realistic - YET
Title of talk 36
Neutrino masses via See-Saw
YES !!
Dimension 5 operators –
suppressed ~
BUT generated again when integrating out states - problem ??
6S
Title of talk 37
Proton decay
IF families at local GUT fixed points Dimension 6 ops. fixed by 1/ MC
2
Expect MC < MG
Dimension 5 ops. unsuppressed - Unless find symmetry
R-parity forbids Dimension 3 & 4 B & L violation
p
Title of talk 38
Conclusions
We find MSSM in “fertile patch” of E(8)xE(8) heterotic string
Important to test string theory
SUSY breaking and lifting flat directions ??
Almost realistic “Benchmark” models !!! w/ Caveat
MSSM Orbifold & Local GUT