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