BEYOND THE STANDARD MODEL
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H
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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
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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
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PART I : SUPERSYMMETRYPART I : SUPERSYMMETRY
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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
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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 !
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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
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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
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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
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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
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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
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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
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Basics of SUSYBasics of SUSYQuantum states: | ,E Vacuum = | , 0Q E
Energy helicity
State Expression # of states
vacuum 1
1-particle
2-particle
… … …
N-particle
| ,E
| , | , 1/ 2iQ E E
| , | , 1i jQ Q E E
1 2... | , | , / 2NQ Q Q E E N
1N N
( 1)2 2
N NN
1NN
Total # of states 1 1
0
2 2 2N
N N N Nk
k
bosons fermions
[ , ] [ , ] 0i iQ P Q P
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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
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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|
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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
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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
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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
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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
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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
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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
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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
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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
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SUSY Shadow WorldSUSY Shadow World
One half is observed! One half is observed! One half is NOT observed! One half is NOT observed!
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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
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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
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Interactions in the MSSMInteractions in the MSSM
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Creation of Superpartners Creation of Superpartners at collidersat colliderse e
maxsparticle 2
sm
Experimental signature: missing energy and transverse momentum
LEP II
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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
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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
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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
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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
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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
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36
We like elegant solutionsWe like elegant solutions
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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
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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, , ,
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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
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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
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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 !
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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
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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
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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
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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
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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
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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
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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
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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 !
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50
Masses of SuperpartnersMasses of Superpartners
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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
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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
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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
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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.
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Higgs SearchesHiggs Searches
114 -115 GeVEvent
mH 113.4 GeV at 95 % C.L.
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The Higgs Mass LimitThe Higgs Mass Limit (Theory)
The SM Higgs
mH 134 GeV
SUSY HiggsmH 130 GeV
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SUSY Searches at LEPSUSY Searches at LEP
~
~
~
charginos
neutralinos
m+ 100 GeV
m0 40 GeV
ml 100 GeV
sleptons
squarks
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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
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Tevatron Discovery ReachTevatron Discovery Reach
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SUSY Searches at LHCSUSY Searches at LHC
5 σ reach in jets E T channel Reach limits for various channels at 100 fb
-1
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SSuperparticlesuperparticles
Discovery of the new world
of SUSY
Back to 60’s
New discoveries every year
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PART II: EXTRA DIMENSIONSPART II: EXTRA DIMENSIONS
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63
Why don’t we see extra dimensionsWhy don’t we see extra dimensions
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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)
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What comes beyond What comes beyond the Standard Model ?the Standard Model ?