beyond the standard model

4

The SM and BeyondThe SM and Beyond

• Inconsistency at high energies due to Landau poleInconsistency at high energies due to Landau pole• Large number of free parametersLarge number of free parameters• Formal unification of strong and electroweak interactionsFormal unification of strong and electroweak interactions• Still unclear mechanism of EW symmetry breakingStill unclear mechanism of EW symmetry breaking• CP-violation is not understoodCP-violation is not understood• Flavour mixing and the number of generations is arbitraryFlavour mixing and the number of generations is arbitrary• The origin of the mass spectrum in unclearThe origin of the mass spectrum in unclear

The problems of the SM:The problems of the SM:

The way beyond the SM:The way beyond the SM:

• The SAME fields with NEW The SAME fields with NEW interactions interactions

GUT, SUSY, StringGUT, SUSY, String

• NEW fields with NEW NEW fields with NEW interactionsinteractions

Compositeness, Technicolour,Compositeness, Technicolour, preonspreons

5

Grand Unified TheoriesGrand Unified Theories

• Unification of strong, weak and electromagnetic interactions within Grand Unified Theories is the new step in unification of all forces of Nature• Creation of a unified theory of everything based on string paradigm seems to be possible

3410 m

D=10

GUT

6

PART I : SUPERSYMMETRYPART I : SUPERSYMMETRY

7

What is SUSYWhat is SUSY

• Supersymmetry is a boson-fermion symmetrythat is aimed to unify all forces in Nature including gravity within a singe framework

• Modern views on supersymmetry in particle physicsare based on string paradigm, though low energymanifestations of SUSY can be found (?) at moderncolliders and in non-accelerator experiments

| | | |Q boson fermion Q fermion boson

[ , ] 0, { , } 0 b b f f { , } 2 ( )ji ijQ Q P

8

Motivation of SUSY in Particle Motivation of SUSY in Particle PhysicsPhysics

Unification with Gravity

2 3/2 1 1/2 0spin spin spin spin spin 2 3/2 1 1/2 0spin spin spin spin spin

Unification of matter (fermions) with forces (bosons) naturally arisesfrom an attempt to unify gravity with the other interactions

{ , } 2 ( ) { , } 2( )

( ) local coordinate transformation.

ji ijQ Q P P

x

{ , } 2 ( ) { , } 2( )

( ) local coordinate transformation.

ji ijQ Q P P

x

Unification with Gravity Unification of gauge couplings Solution of the hierarchy problem Dark matter in the Universe Superstrings

,

,

Supertranslation

x x i i

,

,

Supertranslation

x x i i

Local translation = general relativity !

9

Motivation of SUSY in Particle Motivation of SUSY in Particle PhysicsPhysics

Unification of gauge couplings

c L Y

3 2 1

SU (3) SU (2) U (1) (or + symm)

,

nGUT

GUT

Low Energy High Energy

G G

gluons W Z photon gauge bosons

quarks leptons fermions

g g g g

c L Y

3 2 1

SU (3) SU (2) U (1) (or + symm)

,

nGUT

GUT

Low Energy High Energy

G G

gluons W Z photon gauge bosons

quarks leptons fermions

g g g g

Running of the strong coupling

2

2( ) (distance)Qi i i

10

Motivation of SUSY Motivation of SUSY

1

2

( ) 128.978 0.027

sin 0.23146 0.00017

( ) 0.1184 0.0031

Z

MS

s Z

M

M

2 2 2 2 2, / 4 /16 , t=log(Q / )ii i i i i

db g

dt

1

2

3

0 4 / 3 1/10

: 22 / 3 4 / 3 1/ 6

11 4 / 3 0i Fam Higgs

b

SM b b N N

b

1

2

3

0 2 3/10

: 6 2 1/ 2

9 2 0i Fam Higgs

b

MSSM b b N N

b

RG EquationsRG Equations

InputInput

OutputOutput

3.4 0.9 0.4

15.8 0.3 0.1

-1GUT

10 GeV

10 GeV

26.3 1.9 1.0

SUSY

GUT

M

M

SUSY yields unification! SUSY yields unification!

Unification of the Coupling Constantsin the SM and in the MSSM

Unification of the Coupling Constantsin the SM and in the MSSM

11

Motivation of SUSYMotivation of SUSY• Solution of the Hierarchy ProblemSolution of the Hierarchy Problem

2

16

v 10 GeV

m V 10 GeV

Hm

-14 10 1Hm

m

Destruction of the hierarchy byDestruction of the hierarchy byradiative correctionsradiative corrections

Cancellation of quadratic termsCancellation of quadratic terms

2 2

bosons fermions

m m SUSY may also explain the originof the hierarchy due to radiativemechanism

SUSY may also explain the originof the hierarchy due to radiativemechanism

12

Motivation of SUSYMotivation of SUSY• Dark Matter in the UniverseDark Matter in the Universe

SUSY provides a candidate for the Dark matter – a stable neutral particle

The flat rotation curves of spiral

galaxies provide the most direct

evidence for the existence of large

amount of the dark matter.

Spiral galaxies consist of a central

bulge and a very thin disc, and

surrounded by an approximately

spherical halo of dark matter

13

Cosmological ConstraintsCosmological ConstraintsNew precise cosmological data

2 1

73%

23 4%

4%

vacuum

DarkMatter

Baryon

h

crit • Supernova Ia explosion• CMBR thermal fluctuations

(news from WMAP )

Dark Matter in the Universe:

Hot DM(not favoured by galaxy formation)

Cold DM(rotation curvesof Galaxies)

SUSYSUSY

14

SupersymmetrySupersymmetry

12

( ) lg

[ , ] 0, [ , ] ( ),

[ , ] ( ),

[ , ] , [ , ] [ , ] 0,

[ , ] [ , ] 0,

[ , ] ( ) , [

tr s rs t r r

i i

i i

Super A ebra

P P P M i g P g P

M M i g M g M g M g M

B B iC B B P B M

Q P Q P

Q M Q Q

12

†

, ] ( ) ,

[ , ] ( ) , [ , ] ( ) ,

{ , } 2 ( ) ,

{ , } 2 , , ,

{ , } 2 , [ , ] 0,

, , , 1, 2; , 1, 2,..., .

i i

i i j i j ir r j r r j

ji ij

i j ij ij rij ij ij r

i j ijij

M Q

Q B b Q Q B Q b

Q Q P

Q Q Z Z Z Z a b

Q Q Z Z anything

i j N

12

( ) lg

[ , ] 0, [ , ] ( ),

[ , ] ( ),

[ , ] , [ , ] [ , ] 0,

[ , ] [ , ] 0,

[ , ] ( ) , [

tr s rs t r r

i i

i i

Super A ebra

P P P M i g P g P

M M i g M g M g M g M

B B iC B B P B M

Q P Q P

Q M Q Q

12

†

, ] ( ) ,

[ , ] ( ) , [ , ] ( ) ,

{ , } 2 ( ) ,

{ , } 2 , , ,

{ , } 2 , [ , ] 0,

, , , 1, 2; , 1, 2,..., .

i i

i i j i j ir r j r r j

ji ij

i j ij ij rij ij ij r

i j ijij

M Q

Q B b Q Q B Q b

Q Q P

Q Q Z Z Z Z a b

Q Q Z Z anything

i j N

, ,

Superspace

x x , ,

Superspace

x x

Grassmannian parameters

, 1, 2

Q i

Q i

22 0, 0 SUSY Generators

This is the only possiblegraded Lie algebrathat mixes integer andhalf-integer spins and changes statistics

22 0, 0Q Q { , } 2 ( )

ji ijQ Q P

16

SUSY MultipletsSUSY MultipletsChiral multiplet

Vector multiplet

1, =0N helicity

# of states

-1/2 0 1/2

1 2 1

1, =1/2N helicity

# of states-1 -1/2 1/2 1 1 1 1 1

( , )

( , )A

scalar spinor

spinor vector

Members of a supermultiplet are called superpartners

Extended SUSY multiplets

N=4 SUSY YM helicity -1 –1/2 0 1/2 1

λ = -1 # of states 1 4 6 4 1

N=8 SUGRA helicity -2 –3/2 –1 –1/2 0 1/2 1 3/2 2

λ = -2 # of states 1 8 28 56 70 56 28 8 1

4N S spin 4N 8N

For renormalizable theories (YM)

For (super)gravity

17

Matter SuperfieldsMatter Superfields( , , )F x

14

( , ) ( ) 2 ( ) ( )

( ) ( ) ( )

2 ( ) / 2 ( ) ( )

y A y y F y

A x i A x A x

x i x F x

- general superfield –reducible representation

chiral superfield:

( )y x i

component fieldsspin=0

spin=1/2

auxiliary

SUSY transformation

2 ,

2 2 ,

2

A

i A F

F i

Superpotential

2

2

( ) ( 2 )

1( ) 2 ( )

2

W W A F

W W WW A F

A A A

F-component is a total derivative

0D

is SUSY invariant|

18

Gauge superfieldsGauge superfieldsV V real superfield

1 12 2

( , , ) ( ) ( ) ( ) ( ) ( )

( ) [ ( ) ( )] [ ( ) ( )]

[ ( ) ( )]

V x C x i x i x i M x i M x

v x i x i x i x i x

D x C x

Gauge transformation V V *

*

2

2

( )

C C A A

i

M M iF

v v i A A

D D

Wess-Zumino gauge

0C M

physical fields

Field strength tensor

214

V VW D e D e

22 ( )iW i D F D

D i

Covariant derivatives

D i

19

SUSY LagrangiansSUSY Lagrangians1 12 3| [( ) | . .]i i i ij i j ijk i j kL m y h c

Superfields

Components

* *

12 [ ( ) ( ) . .]

i i i i ii

i i ij i j i j ijk i j k i j k

L i A A F F

F m AF y A A F A h c

no derivatives

Constraint

* *1 12 2

* * ( , )

i i i ij i j iji i j

ijk i j k ijk k i ji j

L i A A m m

y A y A V A A

* 0k k ik i ijk i jk

LF m A y A A

F

*k kV F F

kF

20

Superfield LagrangiansSuperfield Lagrangians

2 2 2 1 12 3 ( ) . .]i i i i ij i j ijk i j kL d d d m y h c

Grassmannian integration in superspace 0, d d

Gauge fields

2 2 21 1 14 2 4 L d W W d W W D F F i D

Gauge transformation , , ( )ig ige e V V i

Gauge invariant interaction gVe

4 Action d x L 4 4 d x d L

Superpotential

Matter fields

21

2 21 1 4 4

2 2 2 2

Tr(W ) Tr(W )

( ) ( ) ( )

SUSY YM

gV a bia ib i i

L d W d W

d d e d d

W W

Gauge Invariant SUSY LagrangianGauge Invariant SUSY Lagrangian

1 1 4 2

†

† † †

2 2† 1 1

2 2† † †

( ) ( ) ( )

2 2

aa a a a aSUSY YM

a a a a a ai i i i i ii

aa a a a ai i i i i i ii

i i i j i ji i i j i j

L F F i D D D

A igv T A A igv T A i igv T

D gA T A i gA T i g T A F F

F FA A A A A A

W W W W

† †12, V=a a a a

i i i i ii

D gA T A F D D F FA

W

22

Spontaneous Breaking of SUSYSpontaneous Breaking of SUSY

0 | | 0E H { , } 2 ( )ji ijQ Q P

{ , } 2 ( )

ji ijQ Q P

21 14 4

1,2

0 |{ , } | 0 | | 0 | 0jiE Q Q Q

0 | | 0 0E H if and only if | 0 0Q

Energy

23

Mechanism of SUSY BreakingMechanism of SUSY BreakingFayet-Iliopoulos (D-term) mechanism 4| 0L V d V D

(in Abelian theory)

O’Raifertaigh (F-term) mechanism2

3 1 2 3 1( )W m g

*1 2 1 2

*2 1

* 23 1

2

F mA gA A

F mA

F gA

0iF

2 2i i

bosons fermions

m m

D-term F-term

24

Minimal Supersymmetric Minimal Supersymmetric Standard Model (MSSM)Standard Model (MSSM)

SM: 28 bosonic d.o.f. & 90 (96) fermionic d.o.f.

SUSY: # of fermions = # of bosons ( , ) ( , )AN=1 SUSY:

There are no particles in the SM that can be superpartners

Even number of the Higgs doublets – min = 2

Cancellation of axial anomalies (in each generation)3 64 81 1

27 27 27 27

L L R R L L R

3( ) 1 1 8 0

colour u d u d e e

Tr Y

Higgsinos

-1+1=0

SUSY associates known bosons with new fermions and known fermions with new bosons

25

Particle Content of the MSSMParticle Content of the MSSM

a a

k

(3) (2) (1)

g g 8 1 0

W ( , ) , ( , ) 1 3 0

g B( ) ( ) 1 1 0

( , ) ( , ) 1 2 1

c L Y

k

i L i L

a

k

i

Superfield Bosons Fermions SU SU U

Gauge

gluon gluino

Weak W Z wino zino w w z

Hyperchar e bino b

Matter

L e L e

G

V

V

LE

*

*

1 1

2 2

1

2

1 1 2

( , ) ( , ) 3 2 1/ 3

3 1 4 / 3

3 1 2 / 3

1 2 1

1 2 1

i R i R

i L i L

ci R i R

ci R i R

i

i

i

i

E e E e

Q u d Q u d

U u U u

D d D d

Higgs

H H

H H

QU

D

HH

a a

k

(3) (2) (1)

g g 8 1 0

W ( , ) , ( , ) 1 3 0

g B( ) ( ) 1 1 0

( , ) ( , ) 1 2 1

c L Y

k

i L i L

a

k

i

Superfield Bosons Fermions SU SU U

Gauge

gluon gluino

Weak W Z wino zino w w z

Hyperchar e bino b

Matter

L e L e

G

V

V

LE

*

*

1 1

2 2

1

2

1 1 2

( , ) ( , ) 3 2 1/ 3

3 1 4 / 3

3 1 2 / 3

1 2 1

1 2 1

i R i R

i L i L

ci R i R

ci R i R

i

i

i

i

E e E e

Q u d Q u d

U u U u

D d D d

Higgs

H H

H H

QU

D

HH

sleptons leptons

squarks quarks

Higgses { higgsinos {

a g

( , )

)

,

(

kw w z

gluino

wino zino

bino b

( , )

( , )

i L

i R

i L

i R

i R

L e

E e

Q u d

U u

D d

1

2

H

H

26

SUSY Shadow WorldSUSY Shadow World

One half is observed! One half is observed! One half is NOT observed! One half is NOT observed!

27

The MSSM LagrangianThe MSSM Lagrangian

The Yukawa SuperpotentialThe Yukawa Superpotential

2 1 1 1 2R U L R D L R L L RW y Q H U y Q H D y L H E H H

Yukawa couplingsYukawa couplings Higgs mixing termHiggs mixing term

gauge Yukawa SoftBreakingL L L L

' '2NR L L L R L L L R L B R R RW L L E L Q D L H U D D

R-parityR-parity3( ) 2( ) B L SR

B - Baryon NumberB - Baryon NumberL - Lepton NumberL - Lepton NumberS - SpinS - Spin

The Usual Particle : R = + 1The Usual Particle : R = + 1SUSY Particle : R = - 1SUSY Particle : R = - 1

superfields

These terms are forbidden in

the SM

28

R-parity ConservationR-parity Conservation

The consequences:

• The superpartners are created in pairs• The lightest superparticle is stable

e

e

p

p

p

p

Physical output: • The lightest superparticle (LSP) should be neutral - the best candidate is neutralino (photino or higgsino) • It can survive from the Big Bang and form the Dark matter in the Universe

0

0

0

29

Interactions in the MSSMInteractions in the MSSM

30

Creation of Superpartners Creation of Superpartners at collidersat colliderse e

maxsparticle 2

sm

Experimental signature: missing energy and transverse momentum

LEP II

31

SUSY Production at Hadron SUSY Production at Hadron CollidersColliders

Annihilation channel

Gluon fusion, qq scatteringand qg scattering channels

No new data so far due toinsufficient luminosity at the Tevatron

32

Decay of SuperpartnersDecay of Superpartners

0

,

,

'

L R i

L i

L R

q q

q q

q q g

0

i

L l i

l l

l

g q q

g g

0 0

1

0 0

1

0

1

0 0

1

'

i

i

li

lli

l l

q q

l

squarks

sleptons

chargino neutralino

gluino

0

0'

ei i

i i

e

q q

Final sates

2 jets T

T

T

T

l l E

E

E

E

33

Soft SUSY BreakingSoft SUSY BreakingHidden sector scenario:

four scenarios:1. Gravity mediation2. Gauge mediation3. Anomaly mediation4. Gaugino mediation

SUGRA 0, 0T SF F S-dilaton, T-moduli

3/ 2ST

SUSYPL PL

FFM m

M M

gravitino mass

2 2 (2) (3)| | ( ) B ( ) A ( )i isoft i i i i ii i

L m A M W A W A 2 2

3/ 2 3/ 2B , A i im m M m

1 TeV

34

Soft SUSY Breaking Soft SUSY Breaking Cont’dCont’d

Gauge mediation 0SF Scalar singlet S

Messenger Φ W S

1410

[ ]S

GPL PL

F M Mm

M M GeV

gravitino mass

Anomaly mediation

4i S

i i

FM c N

M

2 2

2

4S i

iPL

Fm N

M

,3/ 2

( )

4T Si

i i i iPL

FM b b m

M

2 2 2 23/ 2i i im b m

1 2 3 1 2 3: : : :M M M b b b

LSP=slepton

Results from conformal anomaly = β function

S M

gaugino squark

LSP=gravitino

35

Soft SUSY Breaking Soft SUSY Breaking Cont’dCont’d

Gaugino mediation

SUSY spectra for various mediation mechanisms

All scenarios produce soft SUSY breaking terms

Soft = operators of dimension 4

ijA Bijk i j k i jijk ij

A A A A A

2 20 | | i i i i i

i

m A M

SoftL

scalar fileds gauginos

Net result of SUSY breaking

36

We like elegant solutionsWe like elegant solutions

37

Parameter Space of the MSSMParameter Space of the MSSM

2 1 1 1 2{ }Soft t L R b L R L L RL A y Q H U y Q H D y L H E B H H 2 2 1

0 1/ 22| |ii

m M

Five universal soft parameters: 0 1/ 2, , , tanA m M B and

versus m and in the SM

SUGRA Universality hypothesis: soft terms are universal and repeat the Yukawa potential

• Three gauge coupligs• Three (four) Yukawa matrices• The Higgs mixing parameter • Soft SUSY breaking terms

• Three gauge coupligs• Three (four) Yukawa matrices• The Higgs mixing parameter • Soft SUSY breaking terms

, i=1,2,3i

, , , , ( )kaby k U D L E

38

Mass SpectrumMass Spectrum

1

2(0)

0 cos sin sin sin

0 cos cos sin cos

cos sin cos cos 0

sin sin sin cos 0

Z Z

Z Z

Z Z

Z Z

M M W M W

M M W M WM

M W M W

M W M W

1

2(0)

0 cos sin sin sin

0 cos cos sin cos

cos sin cos cos 0

sin sin sin cos 0

Z Z

Z Z

Z Z

Z Z

M M W M W

M M W M WM

M W M W

M W M W

2( ) 2 sin

2 cos

Wc

W

M MM

M

2( ) 2 sin

2 cos

Wc

W

M MM

M

(0) ( )1 1n 32 2 ( . .)c

gaugino Higgsi o a aL M M M h c (0) ( )1 1

n 32 2 ( . .)cgaugino Higgsi o a aL M M M h c

0

3

0102

B

W

H

H

W

H

1

2

0 0 0 01 2 3 4, , ,

39

Mass SpectrumMass Spectrum2

2

2

( cot )

( cot )tL t t

t

t t tR

m m Am

m A m

22

2

( tan )

( tan )bL b b

b

b b bR

m m Am

m A m

22

2

( tan )

( tan )L

R

m m Am

m A m

2 2 2 2 212

2 2 2 2 2

(2 )cos 2 ,

( ) cos 2 .

L L W Z

R E W Z

m m m M M

m m m M M

2 2 2 2 216

2 2 2 2 223

2 2 2 2 216

2 2 2 2 213

(4 )cos 2 ,

( ) cos 2 ,

(2 )cos 2 ,

( ) cos 2 ,

tL Q t W Z

tR U t W Z

bL Q b W Z

bR D b W Z

m m m M M

m m m M M

m m m M M

m m m M M

1

2

t

t

1

2

b

b

1

2

40

SUSY Higgs BosonsSUSY Higgs Bosons0 v v

exp( )2 22

0

S iP SH

H iH

H

( )v

exp( ) 22

0

S

H H i H H

1 10 211 2

1 2 0 2 221 2

1

2 2 21 2 2 1

v, ,2

v2

v +v =v , v /v tan

S iP HH H

H H S iPH H

H

01 2 0

1 2*

1 2*

1 2

1 2

1 2

cos sin

sin cos 1

cos ( ) sin

sin ( ) cos g

sin cos SM 1

cos sin

G P P Goldstone boson Z

A P P Neutral CP Higgs

G H H Goldstone boson W

H H H Char ed Higgs

h S S Higgs boson CP

H S S Extra h

eavy Higgs boson

2 2

2 2tan 2 tan 2 A Z

A Z

m m

m m

4=2+2=3+1

8=4+4=3+5

41

The Higgs PotentialThe Higgs Potential2 2 2 2 2

1 2 1 1 2 2 3 1 2

2 2 22 2 2 2

1 2 1 2

2 2 2 2 21 2 0 0 3 0

( , ) | | | | ( . .)

(| | | | ) | |8 2

At the GUT scale: ,

treeV H H m H m H m H H h c

g g gH H H H

m m m m B

2 2 2 2 21 2 1 1 2 2 3 1 2

2 2 22 2 2 2

1 2 1 2

2 2 2 2 21 2 0 0 3 0

( , ) | | | | ( . .)

(| | | | ) | |8 2

At the GUT scale: ,

treeV H H m H m H m H H h c

g g gH H H H

m m m m B

2 22 2 2 211 1 3 2 1 2 12

1

2 22 2 2 212 2 3 1 1 2 22

2

1 1 2 2

( ) 0,4

( ) 0.4

cos , sin ,

V g gm v m v v v v

H

V g gm v m v v v v

H

H v v H v v

2 22 2 2 211 1 3 2 1 2 12

1

2 22 2 2 212 2 3 1 1 2 22

2

1 1 2 2

( ) 0,4

( ) 0.4

cos , sin ,

V g gm v m v v v v

H

V g gm v m v v v v

H

H v v H v v

Minimization Solution

2 2 22 1 2

2 2 2

23

2 21 2

4( tan ),

( )(tan 1)

2sin 2

m mv

g g

m

m m

2 2 22 1 2

2 2 2

23

2 21 2

4( tan ),

( )(tan 1)

2sin 2

m mv

g g

m

m m

At the GUT scale

2 22 '2

40v m

g g

2 2

2 '2

40v m

g g

No SSB in SUSY theory !

42

Renormalization Group EqnsRenormalization Group Eqns

2

16 133 2 13 15

16 73 2 13 15

92 15

,

( 3 6 ),

( 3 6 ),

(3 3 4 ),

i i i

U U U D

D D U D L

L L D L

b

Y Y Y Y

Y Y Y Y Y

Y Y Y Y

2

16 133 2 13 15

16 73 2 13 15

92 15

,

( 3 6 ),

( 3 6 ),

(3 3 4 ),

i i i

U U U D

D D U D L

L L D L

b

Y Y Y Y

Y Y Y Y Y

Y Y Y Y

2 22 2

2 2, , log( / )

16 4 16 1, 2,3 , ,

i i ki k GUT

g yY t M Q

i k U D L

2 2

2 22 2

, , log( / )16 4 16

1, 2,3 , ,

i i ki k GUT

g yY t M Q

i k U D L

16 133 3 2 2 1 13 15

16 73 3 2 2 1 13 15

92 2 1 15

12 2 1 15

2 32 15

,

( 3 ) 6 ,

( 3 ) 6 ,

(3 ) 3 4 ,

3( ) 3 3 ,

(3 3 3

i i i i

U U U D D

D U U D D L L

L D D L L

U U D D L L

U

M b M

A M M M Y A Y A

A M M M Y A Y A Y A

A M M Y A Y A

B M M Y A Y A Y A

Y Y

)D LY

16 133 3 2 2 1 13 15

16 73 3 2 2 1 13 15

92 2 1 15

12 2 1 15

2 32 15

,

( 3 ) 6 ,

( 3 ) 6 ,

(3 ) 3 4 ,

3( ) 3 3 ,

(3 3 3

i i i i

U U U D D

D U U D D L L

L D D L L

U U D D L L

U

M b M

A M M M Y A Y A

A M M M Y A Y A Y A

A M M Y A Y A

B M M Y A Y A Y A

Y Y

)D LY

335( ,1, 3)MSSM

ib

43

RG Eqns for the Soft MassesRG Eqns for the Soft Masses

2 1 1

2 2 2 2 2 2 2 2 2, , t Q U H b Q D H L E Hm m m m m m m m m

44

Radiative EW Symmetry BreakingRadiative EW Symmetry BreakingDue to RG controlled running of the mass terms from the Higgs potential they may change sign and trigger the appearance of non-trivial minimum leading to spontaneous breaking of EW symmetry - this is called Radiative EWSB

45

The Higgs Bosons MassesThe Higgs Bosons MassesCP-odd neutral Higgs ACP-even charged Higgses H

CP-even neutral Higgses h,H

2 2 21 2

2 2 2

A

A WH

m m m

m m M

2 2 2 2 2 2 2 2 2,

1[ ( ) 4 cos 2 ]

2h H A Z A Z A Zm m M m M m M

Radiative corrections

2

2 ' 2

2 22

2 22

gW

g gZ

M v

M v

1 2

2 22 42 2 2

2 2 4

3cos 2 log 2

16t tt

h ZW t

g m m mm M loops

M m

1 2

2 22 42 2 2

2 2 4

3cos 2 log 2

16t tt

h ZW t

g m m mm M loops

M m

| cos 2 | !h Z Zm M M | cos 2 | !h Z Zm M M

46

Constrained MSSMConstrained MSSM

• Unification of the gauge couplings• Radiative EW Symmetry Breaking• Heavy quark and lepton masses• Rare decays (b -> sγ) • Anomalous magnetic moment of muon• LSP is neutral • Amount of the Dark Matter• Experimental limits from direct search

Requirements:

Allowed regionin the parameterspace of the MSSM

0 0 1/ 2, , , , tanA m M

Parameter space: 0 1/ 2100 , , 2 Gev m M Tev 0 0 03 3 , 1 tan 70m A m

47

SUSY FitsSUSY Fits1 1 23

21

22

2 2

2 2

2 2

-4 2

2

2 22

2

2exp

2M

( ( ) ( ))

( 174)( 91.18)

( 4.94) ( 1.7771)

(Br(b s )-3.14 10 )

(b s )

( 1) (for 1)

(M-M ) (

i Z MSSMi Z

i i

tZ

Z t

b

b

M M

MM

M M

hh

exp

2LSP

LSP2LSP

for M<M )

(m -m ) (for m charged)

1 2 3, ,

t

b

Z

Universe

m

m

m

M

b s

2

0 0 0

0 1/ 2

0

,

,

,

tan

( )

GUT GUT

t b

M

Y Y Y

m m

A

0 0 0

0 1/ 2

0

,

,

tan

GUT GUT

t b

M

Y Y Y

m m

A

Exp.input data

Fit

low tanParameters

high tan

Minimize

2

48

Low and High tanLow and High tanβ Solutionsβ SolutionsRequirements:• EWSB• bτ unification

Low tanβsolution

High tanβsolution

•bτ unification is the consequence of GUT• Non working for the light generations

49

Allowed Regions in Parameter Allowed Regions in Parameter SpaceSpace

• μ is defined from the EWSB• 0 0A

- is the best fit value

All the requirementsare fulfilled simultaneously !

50

Masses of SuperpartnersMasses of Superpartners

51

Allowed regions of parameter spaceAllowed regions of parameter space

tan 35 tan 50

Fit to all constraints

Fit to Dark Matter constraint

tan 4 From the Higgs searches

> 0a measurementFrom

In allowed region one fulfills all the constraints simultaneously and has the suitable amount of the dark matter

52

Mass Spectrum in CMSSMMass Spectrum in CMSSM

Symbol Low tan High tan

214, 413 170, 322

1028, 1016 481, 498

413, 1026 322, 499

1155 950

303, 270 663, 621

290 658

1028, 936 1040, 1010

279, 403 537, 634

953, 1010 835, 915

727, 1017 735, 906

h, H 95, 1344 119, 565

A, H 1340, 1344 565, 571

SUSY Masses in GeV

Fitted SUSY Parameters

Symbol Low tan High tan

tan 1.71 35.0

m 0 200 600

m 1/2 500 400

(0) 1084 -558

A(0) 0 0

1/ GUT 24.8 24.8

M GUT 16

1.6 •10 16

1.6 •10

0 03 1 4 2( ), ( )H H

0 0 31 2( ), ( )B W

1 2( ), ( )W H

g,L Re e

L,L Rq q

1 2,

1 2,b b

21,t t

53

The Lightest SuperparticleThe Lightest Superparticle

• Gravity mediation 0

1LSP stable

property signature

jets/leptons E T

• Gauge mediation LSP G stable E T

0

1NLSPRl

0

1 , ,G hG ZG photons/jets E T

Rl G lepton E T

• Anomaly mediation

0

1LSPL

stable

stablelepton E T

• R-parity violation LSP is unstable SM particles

Rare decaysNeutrinoless double decay• Modern limit 40 GeVLSPM

54

The Higgs Mass Limit

Indirect limit from radiative corrections

Direct limit from Higgs non-observation at LEP II (CERN)

113 < mH < 200 GeV

At 95 % C.L.

55

Higgs SearchesHiggs Searches

114 -115 GeVEvent

mH 113.4 GeV at 95 % C.L.

56

The Higgs Mass LimitThe Higgs Mass Limit (Theory)

The SM Higgs

mH 134 GeV

SUSY HiggsmH 130 GeV

57

SUSY Searches at LEPSUSY Searches at LEP

~

~

~

charginos

neutralinos

m+ 100 GeV

m0 40 GeV

ml 100 GeV

sleptons

squarks

58

SUSY Searches at TevatronSUSY Searches at Tevatron

mq 300 GeV

mg 195 GeV~

~

The reach of Tevatron in 0 1/ 2/m m plane

Exclusion:World’s Best Limits

Dilepton Channel

3 jet channel

59

Tevatron Discovery ReachTevatron Discovery Reach

60

SUSY Searches at LHCSUSY Searches at LHC

5 σ reach in jets E T channel Reach limits for various channels at 100 fb

-1

61

SSuperparticlesuperparticles

Discovery of the new world

of SUSY

Back to 60’s

New discoveries every year

62

PART II: EXTRA DIMENSIONSPART II: EXTRA DIMENSIONS

63

Why don’t we see extra dimensionsWhy don’t we see extra dimensions

64

Kaluza-Klein ApproachKaluza-Klein Approach

4 4d dE M K

2 ( ) ( ) ( , )M N m nMN mnds G X dX dX g x dx dx x y dy dy

( )

0

( , ) ( ) ( )nn

n

x y x Y y

Pseudo-Euclidean space

Minkowski space

compact space

Metrics

Fields

K-K modes

Eigenfunctions of Laplaceoperator on internal space Kd

2 2 22 2 1 2

2

... dn

n n nm m

R

Radius of the compact space

Masses

Couplings (4 )(4)

( )

d

d

gg

V

( )d

dV R

65

Multidimensional GravityMultidimensional Gravity

4 (4 )

(4 )

1ˆ ˆ[ ]16

d dE MN

N d

S d X G R GG

4 (4) (0)

(4)

1[ ] modes

16EN

S d x g R g non zero KKG

(4) (4 )

1N N d

d

G GV

( 1/ 2)(4)( )Pl NM G

12( )

(4 )( ) dN dM G

dV R

Action

K-K Expansion

Newton constant

Plank Mass

2 2dPl dM V M Reduction formula

66

Low Scale GravityLow Scale Gravity

1 2(4)( ) , r R N

mmV r G

r

d+1d1 2 2

(4 ) 1 12

( )( ) (2 ) , r R

(

)N d d

mmV r G

r

2/2 2 1

Rd

d d PlPl

MM R M

M M

30/ 171 TeV R 10 cmdM -1 3

7 -1

12 -1

2 0.1 R 10 e

3 10 c R 100 e

6 10 c R 10 Me

d R mm V

d R m V

d R m V

| | /1 1 1(4) 1 2 (4) 1 2

0

( ) nm r n r RN Nr r r

n n

V r G m m e G mm e

Modified Newton potential

10

10

10

67

Brane WorldBrane WorldCompact Dimensions Non-compact dimensions

Kink soliton

Energy density

brane

SMSM NewNew

D4-braneD4-brane

Bulk

Localization on the brane

R

(Potential well)

Space-time of Type I superstring

68

The ADD ModelThe ADD Model1 / 2

2 ˆ ( , ) MN MN MNdG h x y

M

( )4 4int

1ˆˆ ˆˆ ( , ) ( )nd MNMN

n Pl

S d x GT h x y d x T h xM

/ 21 1

1 10 0

2( )

( 1)

ER dERd d d d

d dn

E S n S n dn R Ed

SM

graviton

m-i n /( ) 1ˆ ( , ) ( ) e my Rn

MN MNn d

h x y h xV

metric

K-K gravitons

Interactions with the fields on the brane

The # of KK gravitons with masses nm E M

Emission rate 2 2

1( )

d

dPl

EE

M M

69

Particle content of ADD modelParticle content of ADD model

4-dimensional picture• 1 massless graviton (spin 2) + matter• KK tower of massive gravitons (spin 2)• (d-1) KK spin 1 decoupling fields• KK tower of real scalar decoupling fields• KK tower of scalar fields (zero mode – radion)

(0)G( )nG

2( 2) / 2d d ( 2)d

(4+d)-dimensional picture:• (4+d)-dimensional massless graviton + matter

The SM fields are localized on the brane, while gravitons propagate in the bulk

The “gravitational” coupling is 1 / 21/ dM

70

HEP PhenomenologyHEP PhenomenologyNew phenomena: graviton emission & virtual graviton exchange

• KK states production

221

1 2 2

1dPl md d d

M ddS m

dtdm M dt M

( )ne e G ( )e e

bg

LHC5 TeVM

71

HEP Phenomenology IIHEP Phenomenology II• Virtual graviton exchange

( ) ( , )ne e G f f HH gg

2 2 2

1 3( 1)

2nPl n n

T TP P dA T T

M s m d s m

( )nG

Spin=2

Angular distribution

SM

2 2

2 11 1

12 2 20

1Pl Pl

dPl

d dM Mn n

M m dmS S

s m M s m

[( 1) / 2]/ 2 1 1 21

4 2 21

( ) ( ) ( )2

dd k d kd

kk

S s si c

M M M M

q

q-1.5 TeVM 0.5 TeVs

72

Randall-Sandrum ModelsRandall-Sandrum Models

PlankPlankTeVTeV

D4-brane D4-brane

Bulk

15 4 2/E M S Z

0y y y

4 3 (5)ˆ ˆ{2 [ ] }R

MN

R

S d x dy G M R G

1 2

4 (1) 4 (2)1 1 2 2( ) ( )

B B

d x g L d x g L

Metric2 2 ( ) 2yds e dx dx dy

warp factor

Positive tension

Negative tension

Matter( ) | |y k y

3 3 21 2 24 , 24M k M k

Perturbed Metric 2 2 ( ) 2( ( , )) (1 ( ))yds e h x y dx dx x dy

graviton radion

73

Randall-Sandrum Model cont’dRandall-Sandrum Model cont’d

32 2( 1)k RPl

MM e

k

HierarchyProblem !

PlM

1 TeVk RPlM e

Brane 1

• Massless graviton• massive K-K gravitons

• massless radion

kRn nm ke

Brane 22 ( )Re Wrap factor

2

4 (0) ( )

1

1 1 1

2 3nn

eff BnPl

S d z h T h T TM

• Massless graviton• massive K-K gravitons• massless radion

n nm k

74

HEP PhenomenologyHEP PhenomenologyThe first KK graviton mode M ~ 1 TeV

• Drell-Yan process • Excess in dijet process

(1) (1)

(1)

, gg

,gg ,gg

qq G l l G l l

qq G qq

Tevatron LHC

Exclusion plots for resonance production

Excluded Excluded

D-Y

Dj

Run I

Run II D-Y

110 fb

1100 fb

( / ) k RPlk M e

75

HEP Phenomenology IIHEP Phenomenology IIThe x-section of D-Y production

Tevatron (M ~ 700 GeV) LHC (M ~ 1500 GeV)

First KK mode First and subsequent KK modes

( / ) k RPlk M e

0.1 1 0.1 1

76

HEP Phenomenology IIIHEP Phenomenology III(1)pp G e e

2

(1) 4

(1) 2 4

0 f 1, spin 1 f 1 cos

, f 1 cos

gg , f 1 3cos co

4 s

spin

qq G l l

G l l

LHC

Angular dependence

LHC

77

ED ConclusionED ConclusionADD Model• The MEW/MPL hierarchy is replaced by• The scheme is viable• For M small enough it can be checked at modern and future colliders• For d=2 cosmological bounds on M are high (> 100 TeV), but for d>2 are mild

2/130/10

d

d

Pl

R M

M M

RS Model• The MEW/MPL hierarchy is solved without new hierarchy• A large part of parameter space will be studied in future collider experiments• With the mechanism of radion stabilization the model is viable• Cosmological scenarios are consistent (except the cosmological constant problem)

78

What comes beyond What comes beyond the Standard Model ?the Standard Model ?

beyond the standard model

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