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
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
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