Unification Hints

(3) (2) (1)SU SU U

The Standard Model: Partial Unification

Matter Sector “chiral”

L

u

d

L

u

d

L

u

d

RuRu

Ru

(3)SU

Family Symmetry?

(2)SU

Neutral

Up

Down

(2)SU

Family Symmetry?

e

Le

ReL

RL

R

L

c

s

L

c

s

L

c

s

L

t

b

L

t

b

L

t

b

RdRd

Rd Rc

RcRc Rs

RsRs

RtRt

Rt Rb

Rb

Rb

Ru cLu

Standard Model parameters

1 2 3, ,g g g 1

2

tan W

g

g

, , , ,i i iZ H u d lM M m m m

1 2 3, , , 5(1 ) CKM

d

W u c t U s

b

Cabibbo, Kobayashi, Maskawa

QCD

} (3)SU

} (2)SU

???ee

?3 0e

Q Q 5 :L

Grand Unification (5) (3) (2) (1)SU SU SU U

-ucuc u duc u d

u dec

} (3)SU

} (2)SU?3 0

eQ Q

dc

dc

dcee

5 :L

10 :L

1/ 3cdQ

Grand Unification (5) (3) (2) (1)SU SU SU U (10)SO

(10(16 ) 1) ) (5 ( )L LL L , ,

ce L e R

LH states SU(2) doublets

{

-ucuc u duc u d

u dec

} (3)SU

} (2)SU

dc

dc

dcee

5 :L

10 :L

Grand Unification (5) (3) (2) (1)SU SU SU U (10)SO

(10(16 ) 1) ) (5 ( )L LL L

-tctc t btc t b

t bc

bc

bc

bc

-ucuc u ducu d

u dec

-ucuc u ducu d

u dec

dc

dc

dc

ee

-cccc c sccc s

c sc

sc

sc

sc

Generations (?)

-ucuc u duc u d

u dec

dc

dc

dcee

5 :L

10 :L

Grand Unification (5) (3) (2) (1)SU SU SU U

} : New lepto-quark gauge interactionsX

XM

} u

u

dc

e+X

4XM 32 1610 yrs, 10XM GeV

0p e

Neutrino Mass

<H> <H>

L L

R

22

R

L

R

qH mm

m m

Grand Unification

R Xm M

+5

-ucuc u duc u d

u dec

} (3)SU

} (2)SU

dc

dc

dcee

5 :L

10 :L

Gauge Couplings (5) (3) (2) (1)SU SU SU U

5 3 2 1g g g g

1 2 3 5( ) ( ) ( )X X XM M Mg g g g

XM

2 2

1 1ln

( ) ( )X

ii Z i X Z

Mb

g M g M M

q

q

g

g

g

g+

P

r eci

sio

n M

easu

rem

ets

30

60

50

40

20

10

0

Log 10 [Energy Scale (GeV)]3 5 7 9 11 13 15 17

1-1

2-1

3-1

Either: No Grand Unificationor: more particles...

Either: No Grand Unificationor: more particles...

Sup

ersy

mm

etry

thre

shol

d

Log 10 [Energy Scale (GeV)]3 5 7 9 11 13 15 17

1-1

2-1

3-1

TeV scale supersymmetry

2sin 0.2337 0.0015W . 0.2312 0.0002c f Expt

String theory

World sheet

( , )X

1( , )

4 'FreeS d d h h X X

}

String tension

Elementary particles string excitations

Open Closed

String Structure : 1st string revolution

Ghost free condition :

D=10 Fermionic (+SUSY)E8

SO(32)

Type I

Type IIA

Type IIB

String excitations :2

'string

Jm C

J

m2Compactification

D=10 D=4 +(D=6)compactified – radius R

Kaluza Klein & winding modes '

n Rm p

R

Gauge structure : restricted by anomaly cancellation Green Schwarz

8 8 8 6†. . ( 10) ( 4) ( 1 )e g E E D E E D N SUSY

6 (10), (5) (3) (2) (1)E SO SU SU SU U +chiral structure for q, l ; multiplet structure determined by topologyof manifold : Calabi Yau - 3 generation examples known

Supersymmetry

(c.f. D=26 Bosonic)†

String Structure : 2nd string revolution

E8

SO(32)

Type I

Type IIA

Type IIB

D=11 supergravity

M

String dualities

'. .e g R

R

Kaluza Klein winding modes'

n Rm p

R

n p

D-branes

Submanifold on which open strings start or end

String phenomenology

Can obtain gauge and multiplet st

ru

cture + underlying

e.g. het

GUT stru

erotic st

ctu

re

ring

Wilson line breaking at the compactification scale can elegantly

solve the doublet triplet splitting pro

blem

u d (3) (2) (1) + 3(10+5 1) + H + H (MSSM) SU SU U

Many other possibilities - not necessarily with GUT structure -

possibly with a low scale of unificati

on

How can we distinguish them?

Sup

ersy

mm

etry

thre

shol

d

Log 10 [Energy Scale (GeV)]3 5 7 9 11 13 15 17

1-1

2-1

3-1

TeV scale supersymmetry

2sin 0.2337 0.0015W . 0.2312 0.0002c f Expt

I

GGR, D.Ghilencea

SUSY gauge coupling unification

2sin 0.2334 0.0025 0.25( 0.119)W s 0.2311 0.0007 ( )Expt

2sin 0.2311 0.0007W

20.134 0.01 4(sin 0.2334)s W 0.119 0.01 ( )Expt

I

Unification Hints

× 3,2,1

E10-60

TeV MPla

nck

Gravitationalcoupling

1/r2+n

1/rp Gauge coupling

?

Unification at a TeV?

Warped Unification

2 2 2 , 0kyds e dx dx dy y R

RS1

( ) RH PlanckM R e M TeV Brane

All scales up to Planck scale present - logarithmic running of gauge couplings!

Randall, SchwarzSundrum, Delgardo,...

Choi, Kim, Kim

×

D=5

1ga

2 aM R 1

8 2 a O 1

8 2,

a ba lnM /k ba

lnkR ba ln1/MKKR ba lnMKK/

I

2sin 0.2334 0.0025 0.25( 0.119)W s 0.2311 0.0007 ( )Expt

2sin 0.2312 0.0007W

20.134 0.01 4(sin 0.2334)s W 0.119 0.01 ( )Expt

16(3.5 2).10UM GeV

Updated fit :

E10-60

MP

3,2,1

GN(Q) Q2

Unification with gravity?

SUSY coupling unification

10 24 3

4( ...)

' 'HSeff i

iL d x ge R Trk

F

2' 1/ only scalestringM 110

}

4d xV

}

4 310 10

'' ',

64 16 4String

N String NG GV V

2 2

1ln

( )string

i ii Z s

i

tring Z

Mb

g M g

k

M

17. 3.6 10string string PlanckM g M GeV

Gauge unification - Heterotic String

....close...but not close enough!

16. . (3.5 2).10Uc f M GeV

1 2

2

14

itorui s

d db Z

1 2 1 2

221 1 2 2 2 1 1 2

2 2

2 ( )torusn m Z

Z exp i m n m n exp TUn Tn Um mTU

1 2 ,T R R 1 2U R R

String Threshold Effects (WCHS) 6 ,T G 6 2 4T T T

N=2

2 1{ 0 1 2 1}

KK modesWinding modes

4

2 22 41

3 3ln 4 ( )

4 2i

i s s

ib i M R M Re

12 2

1( ) 1 ,iT ikT

kT e e

2 ( ),T iR U i

Dixon,Kaplunovsky,Louis

2 large i R R

Threshold sensitivity

1/ cx RM

1cRM

2cRM

To preserve insensitivity to heavy thresholds (no power law sensitivity) need 2cRM

...but still have to bring into agreement with experiment?UM

Ghilencea,GGR

Weakly coupled heterotic strings with Wilson line breaking

1I Iym

ii dyA T

iW e I rank G i

/M M D

Discrete group D G

( ) ( )x dx Physical states :

2 2 2 3 3 2 /( ), , i NND Diagonal a a a a a D Z a e e.g.

(5) (3) (2) (1) ( are singlets - X,Y bosons massive)aSU SU SU U A D

2

2 2

111

" " ( 3, complete reps)D D DD DD D

R R R R R N q l

111

(Higgs split reps - doublet triplet splitting)DDD

R R

/( )diagonalM D D

( ) ( )iW x dx

, (5

2)

2log( ) log( )( ) (

l ()

4 4og )

X Y SUi im m m

(3) (2) 1)) ((5S SUU SU U

2 2 22

1( ) ( )nM n

R 1n

0n

.

.

.

Reduction in X,Y boson contribution -equivalent to reduction in unification scale.

,X Y

3,2,1 }

(14)

3,2,1

22

5241 12 2 2 2 2 2

sinsin (5 )(3 2 1)2( ) log ln 2 ln

2 3 4 4jX Y i ji i

i GUTHiggs jX s s

bb bQQ

M M R M R

1 log2 2

i iGUT

X

b bQ

M

N=3, n=1 N=7, n=1 N=7, n=2 N=7, n=3

3.64 (4.12) 3.68 (4.43) 3.71 (3.78)) 4.81 (6.75)

-0.25 (-0.27) -0.25 (-0.28) -0.25 (-0.25) -0.30 (-0.36)

2.81 (3.10) 2.84 (3.29) 2.86 (2.90) 3.50 (4.61)

0.49 (0.54) 0.50 (0.57) 0.50 (0.51) 0.60 (0.73)

Quantitative effect of Wilson lines :

2sM R

No Higgs KK modes

Higgs KK modes

2D 1D or 2D (matter KK modes degenerate)GGR

0X

X

MM

13

0X

X

MM

3

1 2 2 0

-13 . . 1.04 expc f t

nD Z

0

. . =10 expX

X

MMc f t

String profile from gauge unification

Bring into agreement with experimentXM prediction

Preserve accuracy of prediction (insensitivity to

unknown thresholds)

s Improve prediction

20.122 0.01 4(sin 0.2334)s W . . 0.119 0.003(?)c f

11 66 . . (2.5 2).10 7 10s c f eM GeV G V

2, larges sM R M

WCHS + Wilson line ( 2, N=7) sM R

WCHS + Wilson line ( 2, N=7) sM R

†† 15U 11 s(c.f SCHS ... can fit M with R 10 but unchanged)GeV