Minimal Supersymmetric 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 = 2Cancellation of axial anomalies (in each generation)

3 64 81 127 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

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

The MSSM Lagrangian

The 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 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 couplings Higgs 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

' '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

These terms are forbidden in

the SM

Superfields

Violate: Lepton number Baryon number

' 6 9, 10 , 10L L B

R-parity

pThe consequences:

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

e

e

p

p

• 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

3( ) 2( ) B L SR 3( ) 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

p

Interactions in the MSSM

Creation of Superpartners at colliders

Annihilation channel

Gluon fusion, ee, qq scatteringand qg scattering channels

Decay of Superpartners

0

,

,

'

iL R

iL

L R

q q

q q

q q g

0

i

L il

l l

l

g q q

g g

0 0

1

0 0

1

0

1

0 0

1

'

i

i

i l

li l

l l

q q

l

squarks

sleptons

chargino neutralino

gluino

0

0'

i ie

i i

e

q q

Final sates

2 jets T

T

T

T

l l E

E

E

E

Spontaneous 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

Soft SUSY Breaking

Hidden sectorMSSM

SUSY Messengers

Gravitons, gauge, gauginos, etc

2 20 ij | | A BSoft i i i i i ijk i j k i j

i ijk ij

L M m A A A A A A

scalar fieldsgauginos

Over 100 of free parameters !

Breaking via F and D terms in a hidden sector

Soft SUSY Breaking

0SF

4i S

i i

FM c N

M

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 23/ 2 3/ 2B , A i im m M m

1 TeV

Gauge mediation Scalar singlet S

Messenger Φ W S

1410

[ ]S

GPL PL

F M Mm

M M GeV

gravitino mass

gaugino squark

2 22

4S i

iPL

Fm N

M

MSSM Parameter Space

Five universal soft parameters: 0 1/ 2 2 1, , , tan / and A m M B v v 0 1/ 2 2 1, , , tan / and A m M B v v

versus m and in the SM

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

mSUGRA Universality hypothesis (gravity is colour and flavour blind):Soft parameters are equal at Planck (GUT) scale

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

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

Mass 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

3

0102

B

W

H

H

W

H

1

2

0 0 0 01 2 3 4( , , , )

Mass 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

SUSY Higgs Bosons

0 v vexp( )2 2

20

S iP SH

H iH

H

( ) vexp( ) 2

20

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

4=2+2=3+1

8=4+4=3+5

The 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

( , ) | | | | ( . .)

(| | | | ) | |8 2

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

g g gH H H H

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

2 2 22 2 2 2

1 2 1 2

( , ) | | | | ( . .)

(| | | | ) | |8 2

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

g g gH H H H

2 22 2 2 211 1 3 2 1 2 12

1

2 22 2 2 212 2 3 1 1 2 22

2

( ) 0,4

( ) 0.4

V g gm v m v v v v

H

V g gm v m v v v v

H

2 22 2 2 211 1 3 2 1 2 12

1

2 22 2 2 212 2 3 1 1 2 22

2

( ) 0,4

( ) 0.4

V g gm v m v v v v

H

V g gm v m v v v v

H

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 !

2 2 2 2 21 2 0 0 3 0At the GUT scale: , m m m m B

1 1 2 2cos , sin ,H v v H v v

Higgs Boson’s Masses2

23

22 23

22 23

tan 1

1 cot

tan 1 cot 1cos sin

1 cot 1 tan

tan 1( cos sin )

1 cot

i i

i i

i i

odd

i j H v

evenZ

i j H v

chW

i j H v

VM m

P P

VM m M

S S

VM m M

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

The 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

Renormalization 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

RG 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

Radiative EW Symmetry Breaking

Due 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