Transcript Document 7183998

1
2
H
3
The SM and Beyond
The problems of the SM:
• Inconsistency at high energies due to Landau pole
• Large number of free parameters
• Formal unification of strong and electroweak interactions
• Still unclear mechanism of EW symmetry breaking
• CP-violation is not understood
• Flavour mixing and the number of generations is arbitrary
• The origin of the mass spectrum in unclear
The way beyond the SM:
• The SAME fields with NEW
interactions
• NEW fields with NEW
interactions
GUT, SUSY, String
Compositeness, Technicolour,
preons
4
Grand Unified Theories
GUT
1034 m
D=10
• 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
5
string paradigm seems to be possible
PART I : SUPERSYMMETRY
6
What is SUSY
• Supersymmetry is a boson-fermion symmetry
that is aimed to unify all forces in Nature including
gravity within a singe framework
Q | boson | fermion 
[b, b]  0, { f , f }  0 
Q | fermion | boson 
j
{Q , Q  }  2 ij (  ) P
i

• Modern views on supersymmetry in particle physics
are based on string paradigm, though low energy
manifestations of SUSY can be found (?) at modern
colliders and in non-accelerator experiments
7
Motivation of SUSY in Particle
Physics
Unification with Gravity
 Unification of gauge couplings
 Solution of the hierarchy problem
spin 2  spin 3/2  spin 1  spin 1/2  spin 0
 Dark matter in the Universe
 Superstrings
Unification of matter (fermions) with forces (bosons) naturally arises
from an attempt to unify gravity with the other interactions

j
{Qi , Q  }  2 ij (  ) P  {  ,   }  2(   ) P
   ( x) local coordinate transformation.
Local translation =
general relativity !
Supertranslation
x  x  i   i   ,
  ,
  
8
Motivation of SUSY in Particle
Physics

Unification of gauge couplings
SU c (3)
gluons
quarks
g3
Low Energy
SU L (2)
W,Z
leptons
g2
U Y (1)
photon
g1
i  i (  )  i (distance)





High Energy
GGUT (or G n + symm)
gauge bosons
fermions
g GUT
Q2
2
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Running of the strong coupling
Motivation of SUSY
RG Equations
d i
 bi i2 ,  i   i / 4  gi2 /16 2 , t=log(Q 2 /  2 )
dt
 b1   0 
 4 / 3
1/10 
  

 


SM : bi   b2    22 / 3   N Fam  4 / 3   N Higgs  1/ 6  MSSM : bi
 b   11 
 4 / 3
 0 
 3 

 


Input
 1 ( M Z )  128.978  0.027
 b1   0 
 2
 3/10 
   
 


  b2    6   N Fam  2   N Higgs  1/ 2 
 b   9 
 2
 0 
 3  
 


Unification of the Coupling Constants
in the SM and in the MSSM
sin 2  MS  0.23146  0.00017
 s ( M Z )  0.1184  0.0031
Output
M SUSY  103.4 0.9 0.4 GeV
M GUT  1015.80.30.1 GeV
-1
 GUT
 26.3  1.9  1.0
SUSY yields unification!
10
Motivation of SUSY
• Solution of the Hierarchy Problem
mH
v
102 GeV
m
V
1016 GeV
Destruction of the hierarchy by
radiative corrections
SUSY may also explain the origin
of the hierarchy due to radiative
mechanism
mH
m
10-14
1
Cancellation of quadratic terms

bosons
m2 

fermions
m2
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Motivation of SUSY
• Dark Matter in the Universe
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
SUSY provides a candidate for the
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Dark matter – a stable neutral particle
Cosmological Constraints
New precise cosmological data
h 2  1
  crit
vacuum  73%
 DarkMatter  23  4%
 Baryon  4%
Dark Matter in the Universe:
• Supernova Ia explosion
• CMBR thermal fluctuations
(news from WMAP )
Hot DM
(not favoured by
galaxy formation)
Cold DM
(rotation curves
of Galaxies)
SUSY
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Supersymmetry
( Super ) A lg ebra
[ P , P ]  0, [ P , M  ]  i( g  P  g  P ),
[ M  , M  ]  i ( g M   g M   g  M  g  M ),
[ Br , Bs ]  iCrst Bt , [ Br , P ]  [ Br , M  ]  0,
[Qi , P ]  [Qi , P ]  0,
Superspace
x  x , , 
 ,  1, 2
Grassmannian
2
2
parameters   0,    0
SUSY Generators

[Qi , M  ]  12 (  ) Qi , [Qi , M  ]   12 Qi (  ) ,
Q 
[Qi , Br ]  (br )ij Qj , [Qi , Br ]  Qj (br )ij ,

Q     i 

j
{{QQ, Q, Q
}  2} (2) P(,
i i j
 
ij

ij

) P
{Qi , Qj }  2 Z ij , Z ij  Z ij† , Zij  aijr br ,
{Qi , Qj }  2 Z ij , [ Z ij , anything ]  0,
 , ,  ,   1,2; i, j  1,2,..., N .


 i   


2
Q  0, Q  0
2
This is the only possible
graded Lie algebra
that mixes integer and
half-integer spins and
changes statistics
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Basics of SUSY
[Qi , P ]  [Qi , P ]  0
State
Energy helicity
Expression
# of states
vacuum
| E,  
1-particle
Qi | E,  | E,   1/ 2 
1
Qi Q j | E,  | E,   1 
2-particle
…
…
N-particle
Q1 Q2 ...QN | E,  | E,   N / 2 
 N
 
N
1
N
2
N ( N 1)
2
…
   2
N
Total # of states
Q | E ,   0
Vacuum = | E ,  
Quantum states:
k 0
N
k
N
  1
N
N
 2 N 1 bosons  2 N 1 fermions
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SUSY Multiplets
scalar spinor
Chiral multiplet N  1,  =0
helicity -1/2 0 1/2
# of states 1 2 1
Vector multiplet N  1,  =1/2
helicity -1 -1/2 1/2 1
# of states 1 1 1 1
( , )
( , A )
spinor vector
Members of a supermultiplet are called superpartners
Extended SUSY multiplets
N=4
SUSY YM
λ = -1
N=8
N  4S
helicity
# of states
-1 –1/2
1
0 1/2 1
4 6 4 1
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
spin
N 4
N 8
For renormalizable theories (YM)
For (super)gravity
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Matter Superfields
F ( x,  ,  )
- general superfield –reducible representation
 ( y, )  A( y )  2 ( y )   F ( y )
chiral superfield: D  0
( y  x  i )
 A( x)  i     A( x)  14  A( x)

spin=0  2 ( x )  i / 2  ( x)    F ( x)
spin=1/2
auxiliary
SUSY transformation
  A  2 ,

   i 2    A  2 F ,
  F  i 2    
component fields
Superpotential
W ()  W ( A  2   F )
W
 W ( A) 
A
F-component is a total derivative
W
1  2W
2   (
F
 )
2
A
2 A
 | is SUSY invariant
17
Gauge superfields
V V
real superfield
V ( x, , )  C ( x)  i ( x)  i  ( x)  i M ( x)  i M  ( x)

  v ( x)  i [ ( x)  i    ( x)]  i [ ( x)  i     ( x)]

 12  [ D( x)  12 C ( x)]
Gauge transformation
Covariant derivatives
C  C  A  A*
Wess-Zumino gauge
    i 2
C  M 0
M  M  2iF
v  v  i  ( A  A* )



D     i  

Field strength tensor
physical fields
2 V
W   D e D e V
1
4
 
DD

D    i   
V V    



W  i   D  (   ) F   2 18
D 
i
2

Superfields
SUSY Lagrangians
L  i | [(i i  12 mij i  j  13 yijk i  j k ) | h.c.]
Components

L  i  i   i  Ai* Ai  Fi * Fi
no derivatives
 [i Fi  mij ( Ai Fj  12  i j )  yijk ( Ai Aj Fk  i j Ak )  h.c.]
Constraint
L
 Fk*  k  mik Ai  yijk Ai Aj  0
 Fk
Fk

L  i   i   i  Ai* Ai  12 mij i j  12 mij* i j
*
 yijk i j Ak  yijk
 i j Ak*  V ( Ai , Aj )
V  Fk* Fk
19
Superfield Lagrangians
d
Action   d x L
4
4
xd L
4
 d  0,    d  
Grassmannian integration in superspace
Matter fields
L   d 2 d 2  i  i   d 2 (i  i  12 mij  i  j  13 yijk  i  j  k )  h.c.]
Gauge fields
L
1
4
Superpotential

2


1
1
d

W
W

d

W
W

D

F
F

i

D 


2
4 


2

Gauge transformation
2
 e
Gauge invariant interaction
ig 

 ig 
,    e

, V  V  i (    )
 gV
  e 
20
Gauge Invariant SUSY Lagrangian
LSUSY YM 
1
4
  d 2 d 2
ia
LSUSY YM   F F
1
4

 d  Tr(W W )   d  Tr(W W  )
 (e )    d  W (  )   d  W (  )

2
a
a
gV a
b
1
4
b
i
2
2
2
i
i
a

 i  D   12 D a D a
a

(  Ai  igvT Ai ) (  Ai  igvT Ai )  i i  (  i  igvaT a i )
a
†
a
a
a
a
 D gA T Ai  i 2 gA T   i  i 2 g i T  Ai  Fi † Fi
a
†
i
†
i
a
a
a
a
2
W
W † 1  2W

W
1

Fi  † Fi  2
 i j  2 † †  i j
Ai
Ai
Ai Aj
Ai Aj
W
D   gA T Ai , Fi  
Ai
a
†
i
a
 V= 12 D a D a  Fi † Fi
21
Spontaneous Breaking of SUSY
E  0 | H | 0 
Energy
E
1
4


1,2
j
 0 |{Q , Q }| 0 
i
E  0 | H | 0  0
j
{Q , Q  }  2 ij (  ) P
i

1
4
2
|
Q
|
0

|
0
 

if and only if
Q | 0  0
22
Mechanism of SUSY Breaking
Fayet-Iliopoulos (D-term) mechanism
(in Abelian theory)
O’Raifertaigh (F-term) mechanism
L  V |      d 4 V   D  0
W ()   3  m1 2  g  312
F1*  mA2  2 gA1 A2
F2*  mA1
F3*    gA12
 Fi  0
m
2
i
bosons
D-term
F-term


fermions
23
mi2
Minimal Supersymmetric
Standard Model (MSSM)
SUSY: # of fermions = # of bosons
N=1 SUSY:
( , ) ( , A )
SM: 28 bosonic d.o.f. & 90 (96) fermionic d.o.f.
There are no particles in the SM that can be superpartners
SUSY associates known bosons with new fermions
and known fermions with new bosons
Even number of the Higgs doublets – min = 2
Cancellation of axial anomalies (in each generation)
64
Tr Y 3  3( 271  271  27
 278 )  1  1  8  0
   
   
colour u L d L u R d R  L eL eR
Higgsinos
-1+1=0
24
Particle Content of the MSSM
Superfield
Gauge
a
G
Vk
V
Bosons
Fermions
a
gluino
g
gluon g
gluino g a
  , z)
zinowwk (kw( w
Weak W k (W  , Z ) wino
wino,,zino
, z)
b ( )b ( )
Hypercharge B( ) binobino
a
SU c (3) SU L (2) U Y (1)
8
1
0
1
3
0
1
1
0
1
2
1
1
1
2
3
2
1/ 3
3*
1
4 / 3
3*
1
2/3
1
1
2
2
1
1
25
Matter
LLi  ((,,ee))L
Li
Li  ( , e) L
i
L
sleptons
leptons
E
Ei
Eii  eRR
Ei  eR
Qii  ((uu,,dd))LL
Qi
Q
Qi  (u, d ) L
quarks U i  uRc
U i squarks UUi i uuRR
Di
D
Di  d Rc
Di i ddRR
Higgs
H1
H2
Higgses
{H
H1
2
higgsinos
H1 1
H
{ HH
22
SUSY Shadow World
One half is observed!
One half is NOT observed!
26
The MSSM Lagrangian
L  Lgauge  LYukawa  LSoftBreaking
The Yukawa Superpotential
superfields
WR  yU QL H 2U R  yDQL H1DR  yL LL H1ER   H1H 2
Yukawa couplings
Higgs mixing term
WNR  L LL LL ER  L' LLQL DR   ' LL H 2  BU R DR DR
R-parity
R  ()
3( B  L )  2 S
The Usual Particle : R = + 1
SUSY Particle :
R= -1
B - Baryon Number
L - Lepton Number
S - Spin
These terms are
forbidden in
the SM
27
R-parity Conservation
The consequences:
e

p
p
e
• The superpartners are created in pairs
• The lightest superparticle is stable
p
p
Physical output:
• The lightest superparticle (LSP)
should be neutral - the best candidate
is neutralino (photino or higgsino)
0
• It can survive from the Big Bang
and form the Dark matter in the Universe

0
0
28
Interactions in the MSSM
29
Creation of Superpartners
 
at e e colliders
max
sparticle
m
s

2
LEP II
Experimental signature:
missing energy and transverse momentum
30
SUSY Production at Hadron
Colliders
Annihilation channel
Gluon fusion, qq scattering
and qg scattering channels
No new data so far due to
insufficient luminosity
at the Tevatron
31
Decay of Superpartners
squarks
0
q L,R  q   i

q L  q '  i
q L,R  q  g
sleptons
0
l  l  i

l L l   i
chargino  i  e   e   i0

0
 i  q  q '  i
gluino
g  q  q 
g  g 
neutralino
Final sates
0
0
0
0
2 jets  ET
0

  ET
0
0
ET
 i  1  l   l 
 i  1  q  q '
 i   1  l   l
 i   1  l  l
l  l   ET
32
Soft SUSY Breaking
Hidden sector scenario:
four scenarios:
1. Gravity mediation
2. Gauge mediation
3. Anomaly mediation
4. Gaugino mediation
SUGRA
M SUSY
S-dilaton, T-moduli
 FT   FS 

M PL
M PL
m3/ 2
 FT  0,  FS  0
gravitino mass
1 TeV
Lsoft   mi2 | Ai |2  M i (i i   i  i )  BW (2) ( A)  AW (3) ( A)
i
i
mi2
B
m3/2 2 , M i
A
m3/ 2
33
Soft SUSY Breaking Cont’d
Gauge mediation
Messenger Φ
 FS  M
M PL M PL
mG
Scalar singlet S
W
S
1014
M
[GeV ]
gaugino
gravitino mass
LSP=gravitino
Anomaly mediation
Mi
Mi
bi2 i2 m3/2 2
 i  FS 
ci N
4 M
squark
2
mi2
  FS     i 

 N

 M PL   4 
Results from conformal anomaly = β function
i ()  FT ,S 
bi
bii m3/ 2
4
M PL
mi2
 S  M  FS  0
M1 : M 2 : M 3  b1 : b2 : b3
LSP=slepton
34
2
Soft SUSY Breaking Cont’d
Gaugino mediation
All scenarios produce
soft SUSY breaking terms
Soft = operators of dimension  4
Net result of SUSY breaking
 LSoft 
2
2
m
|
A
|
 0i i  M i i i

i
  A ijk Ai Aj Ak   Bij Ai A j
ijk
ij
scalar fileds
gauginos
SUSY spectra for various mediation mechanisms
35
We like elegant solutions
36
Parameter Space of the MSSM
i , i=1,2,3
• Three gauge coupligs
• Three (four) Yukawa matrices
• The Higgs mixing parameter
• Soft SUSY breaking terms
k
yab
, k  U , D, L, ( E )

SUGRA Universality hypothesis: soft terms are universal
and repeat the Yukawa potential
 LSoft  A{ yt QL H 2U R  ybQL H1DR  yL LL H1ER }  B  H1H 2
 m02  |  i |2  12 M 1/ 2   

i
Five universal
soft parameters:
versus
A, m0 , M1/ 2 , B  tan
m
and

in the SM
and

37
Mass Spectrum
LgauginoHiggsino   M 3aa   M   ( M   h.c.)
1
2
W  
  
H 
M (c)
1
2

M2

 2M cos 
W

(0)
2M W sin  




(c)
 1 
 
 2 
10 ,  20 ,  30 ,  40
M1
0
M Z cos  sin W M Z sin  sin W 
 B0 

 3


0
M
M
cos

cos
W

M
sin

cos
W
W
2
Z
Z

   0  M (0)  
 H1 
 M Z cos  sin W M Z cos  cosW

0

 0 



0 38 
 M Z sin  sin W M Z sin  cos W
 H2 
Mass Spectrum

m
m 
 mt ( At   cot  )
mt ( At   cot  ) 

2
mtR

2

mbL
m 
 mb ( Ab   tan  )
mb ( Ab   tan  ) 

2
mbR

2
tL
2
t
2
b
 t1 
 
t2 
 b1 
 
 b2 
mtL2  mQ2  mt2  16 (4M W2  M Z2 ) cos 2  ,
mtR2  mU2  mt2  23 ( M W2  M Z2 ) cos 2  ,
mbL2  mQ2  mb2  16 (2M W2  M Z2 ) cos 2  ,
2
mbR
 mD2  mb2  13 ( M W2  M Z2 ) cos 2  ,
m2L  mL2  m2  12 (2MW2  M Z2 )cos 2 ,
m2R  mE2  m2  (MW2  M Z2 )cos 2  .

m
m ( A   tan  ) 
m  

2
m R
 m ( A   tan  )

2
2
L
1 
 
 2 
39
SUSY Higgs Bosons
S  iP 

H0  v


H  

exp(
i
2 

2
H



 
H


4=2+2=3+1
S

v

)
2


0






S

v

(  )
H  H   exp(i
) H 
H  
2

2

0






S1  iP1 

H 2


 H   v1 
 , H   H2   
H1  

2
S2  iP2
 
 0 
2

v

H
H

2




 2 
H1
2




,




0
1

1
v12 +v 22 =v 2 , v 2 /v1  tan
8=4+4=3+5
mA2  mZ2
tan 2  tan 2  2 2
mA  mZ
G 0   cos  P1  sin  P2
A  sin  P1  cos  P2
Goldstone boson  Z 0
Neutral CP  1 Higgs
G    cos  ( H1 )*  sin  H 2
Goldstone boson  W 
H   sin  ( H1 )*  cos  H 2
Charged Higgs
h   sin  S1  cos  S 2
SM Higgs boson CP  1
H  cos  S1  sin  S 2
40
Extra heavy Higgs boson
The Higgs Potential
Vtree ( H1 , H 2 )  m12 | H1 |2  m22 | H 2 |2 m32 ( H1 H 2  h.c.)
g 2  g 2
g2
2
2 2

(| H1 |  | H 2 | ) 
| H1 H 2 |2
8
2
At the GUT scale: m12  m22  02  m02 , m32   B  0
Minimization
2
2


V
g

g
2
2
2
2
1

m
v

m
v

(
v

v
1 1
3 2
1
2 )v1  0,
2
 H1
4
V
g 2  g 2 2 2
2
2
 m2 v2  m3 v1 
(v1  v2 )v2  0.
 H2
4
 H1  v1  v cos  ,  H 2  v2  v sin  ,
1
2
Solution
4(m12  m22 tan 2  )
v  2
,
2
2
( g  g  )(tan   1)
2
2m32
sin 2   2
m1  m22
At the GUT scale
No SSB in SUSY theory !
4
2
v  2
m
0
'2
41
g g
2
Renormalization Group Eqns
gi2
i
i 

,
2
16
4
i  1, 2, 3
yk2
2
2
Yk 
,
t

log(
M
/
Q
)
GUT
2
16
k  U , D, L
 i  bi i2 ,
biMSSM  ( 335 ,1, 3)
13
YU  YU ( 163  3  3 2  15
1  6YU  YD ),
YD  YD ( 163  3  3 2  157 1  YU  6YD  YL ),
YL  YL (3 2  95 1  3YD  4YL ),
M i  bi i M i ,
13
AU  ( 163  3 M 3  3 2 M 2  15
1M 1 )  6YU AU  YD AD ,
AD  ( 163  3 M 3  3 2 M 2  157 1M 1 )  YU AU  6YD AD  YL AL ,
AL  (3 2 M 2  95 1M 1 )  3YD AD  4YL AL ,
B  3( 2 M 2  15 1M 1 )  3YU AU  3YD AD  YL AL ,
    2 (3 2  53 1  3YU  3YD  YL )
42
RG Eqns for the Soft Masses
mQ2  [ 163  3 M 32  3 2 M 22  151 1M 12  Yt ( t  At2 )  Yb ( b  Ab2 )]
2
2
mU2  [ 163  3 M 32  16

M

2
Y
(


A
1
t
t
t )]
15 1
mD2  [ 163  3 M 32  154 1M 12  2Yb (b  Ab2 )]
mL2  [3 2 M 22  53 1M 12  Y (  A2 )]
mE2  [ 125 1M 12  2Y (  A2 )]
mH2 1  [3 2 M 22  53 1M 12  3Yb ( b  Ab2 )  Y (  A2 )]
mH2 2  [3 2 M 22  53 1M 12  3Yt ( t  At2 )]
t  mQ2  mU2  mH2 2 , b  mQ2  mD2  mH2 1 ,   mL2  mE2  mH2 1
43
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
44
The Higgs Bosons Masses
CP-odd neutral Higgs A
CP-even charged Higgses H 
m m m
M 
g2
2
mH2   mA2  M W2
M 
g2  g'2
2
2
A
2
1
2
W
2
2
2
Z
v2
v2
CP-even neutral Higgses h,H
2
h, H
m
1 2
2
2
2 2
2
2
2
 [mA  M Z  (mA  M Z )  4mA M Z cos 2  ]
2
mh  M Z | cos 2 |  M Z !
2
4
t
Radiative corrections
2
t1
2
t2
3g m
m m
m  M cos 2  
log
 2 loops
2
2
4
16 M W
mt
2
h
2
Z
2
45
Constrained MSSM
Requirements:
• 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
Parameter space:
Allowed region
in the parameter
space of the MSSM
A0 , m0 , M1/ 2 ,  , tan 
100 Gev  m0 , M1/ 2 ,   2 Tev
3m0  A0  3m0 , 1  tan   70
46
SUSY Fits

2

3

1
( i1 ( M Z )   MSSMi
( M Z )) 2

i 1


( M Z  91.18) 2

2
Z
( M b  4.94) 2

2
b

2
i

Minimize
( M t  174) 2
 t2
( M   1.7771) 2
 2
(Br(b  s )-3.14 10-4 ) 2

 2 (b  s )



(h 2  1) 2

2

(M-M exp )

(m LSP -m  ) 2

2
LSP
(for h  1)
2
2
2
M
2
(for M<M exp )
(for m LSP charged)
Exp.input
data
1 ,  2 ,  3
mt
mb
m
MZ
b  s
 Universe
Fit
low tan
Parameters
high tan
M GUT , GUT
M GUT , GUT
Yt 0 , Yb0  Y0
Yt 0  Yb0  Y0
m0 , m1/ 2
m0 , m1/ 2
tan 
tan 

( A0 )

A0
47
Low and High tanβ Solutions
Requirements:
• EWSB
• bτ unification
Low tanβ
solution
High tanβ
solution
•bτ unification is the
consequence of GUT
• Non working for the
light generations
48
Allowed Regions in Parameter
Space
All the requirements
are fulfilled
simultaneously !
• μ is defined
from the EWSB
• A0  0
 - is the best
fit value
49
Masses of Superpartners
50
Allowed regions of parameter space
 tan   4
From the Higgs searches
 >0
From
a
measurement
Fit to all constraints
In allowed region one
fulfills all the constraints
simultaneously and has
the suitable amount of
the dark matter
tan   35
Fit to Dark Matter constraint
tan  51 50
Mass Spectrum in CMSSM
SUSY Masses in GeV
Fitted SUSY Parameters
Symbol
Low tan  High tan 
tan 
1.71
35.0
m0
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
Symbol
Low tan 
High tan 
10 ( B),  20 (W 3 )
214, 413
170, 322
 30 ( H1 ),  40 ( H 2 ) 1028, 1016
1 (W  ),  2 ( H  ) 413, 1026
481, 498
322, 499
g
1155
950
eL , eR
L
303, 270
663, 621
290
658
qL , qR
1028, 936
1040, 1010
1 , 2
279, 403
537, 634
b1 , b2
953, 1010
835, 915
t1 , t2
727, 1017
735, 906
h, H
95, 1344
119, 565
A, H

1340, 1344 565, 571
52
The Lightest Superparticle
property
0
LSP   1
stable
• Gauge mediation LSP  G
stable
• Gravity mediation
signature
jets/leptons  E T
ET
  0
photons/jets  E T



G
,
hG
,
ZG
1
NLSP   1
lepton  E T
 l R
l R  G
  0
stable
1
• Anomaly mediation LSP  
lepton  E T
stable
 L
0
• R-parity violation
• Modern limit
LSP is unstable  SM particles
M LSP  40 GeV
Rare decays
Neutrinoless double  decay
53
The Higgs Mass Limit

Indirect limit from
radiative corrections
 Direct limit from Higgs
non-observation
at LEP II (CERN)
113 <
m
H
< 200 GeV
At 95 % C.L.
54
Higgs Searches
mH  113.4 GeV at
95 % C.L.
114 -115 GeV
Event
55
The Higgs Mass Limit
(Theory)

The SM Higgs
mH  134 GeV
 SUSY Higgs
mH  130 GeV
56
SUSY Searches at LEP
neutralinos
~
m0  40 GeV
charginos
~ +  100 GeV
m
squarks
sleptons
~
ml
 100 GeV
57
SUSY Searches at Tevatron
The reach of Tevatron in m0 / m1/ 2 plane
Exclusion:
World’s Best Limits
mq~  300 GeV
~  195 GeV
mg
Dilepton
Channel
3 jet channel
58
Tevatron Discovery Reach
59
SUSY Searches at LHC
5 σ reach in jets  E T channel
Reach limits for various channels
-1
at 100 fb
60
Superparticles
Discovery of
the new world
of SUSY
Back to 60’s
New
discoveries
every year
61
PART II: EXTRA DIMENSIONS
62
Why don’t we see extra dimensions
63
Kaluza-Klein Approach
Pseudo-Euclidean space
E4d  M 4  Kd
compact space
Minkowski space
Metrics
ds 2  GMN ( X )dX M dX N  g ( x)dx  dx   mn ( x, y)dy mdy n
( x, y)    ( n ) ( x)Yn ( y)
Fields
n 0
Masses
n12  n22  ...  nd2
m m 
R2
2
n
Couplings
g (4) 
K-K modes
2
g (4 d )
V( d )
Eigenfunctions of Laplace
operator on internal space K d
Radius of the compact space
V( d )
Rd
64
Multidimensional Gravity
Action
SE   d
4 d
X Gˆ
1
R (4 d ) [Gˆ MN ]
16 GN (4 d )
K-K Expansion


1


(4)
(0)
SE   d x  g 
R [ g  ]  non  zero KK modes 


16 GN (4)

4
Newton constant
GN (4)
1
 GN (4 d )
Vd
V  Rd
Plank Mass
M Pl  (GN (4) )
Reduction formula
M  (GN (4 d ) )
( 1/ 2)
M
2
Pl
 Vd M
(  d 12 )
d 2
65
Low Scale Gravity
M
M
2
Pl
R M
d
2 d
R
1 TeV  R 1030 / d 17 cm
d 2 R
0.1 mm
d  3 R 10
7
R
cm R
-1
-1
10
3
1  M Pl 


M M 
2/ d
10
eV
100 eV
d  6 R 1012 cm R -1 10 MeV
10
10
Modified Newton potential
1
1 |n|r / R 
V (r )  GN (4) m1m2  e
 GN (4) m1m2  r   r e

n
n0


m1m2
V (r )  GN (4)
,
r R
r
d+1
m1m2
d ( 2 )
V (r )  GN (4 d ) d 1 (2 )
, r R
1
r
( 2 )

1  mn r
r
66
Brane World
Compact Dimensions
Non-compact dimensions
Kink
soliton
R
Energy
density
brane
Localization on the brane
D4-brane
(Potential well)
D4-brane
Bulk
Space-time of Type I superstring
67
The ADD Model
graviton
GMN  MN 
SM
2
M
1 d / 2
hˆMN ( x, y )
1 -i n m y m / R
(n)
hˆMN ( x, y )   hMN
( x)
e
Vd
n
metric
K-K gravitons
Interactions with the fields on the brane
1  ( n )
MN
4
ˆ
ˆ
ˆ
Sint   d xˆ GTMN h ( x, y )    d x
T h ( x)
M Pl
n
The # of KK gravitons with masses mn  E  M
ER
d /2
ER
2

 ( E )  Sd 1  n d 1  Sd 1  n d 1dn 
Rd E d
(d  1)
n 0
0
4 d
Emission rate
1
( E )
2
M Pl
Ed
M d 2
68
Particle content of ADD model
(4+d)-dimensional picture:
• (4+d)-dimensional massless graviton + matter
4-dimensional picture
• 1 massless graviton G (0) (spin 2) + matter
• KK tower of massive gravitons G ( n ) (spin 2)
• (d-1) KK spin 1 decoupling fields
2
(
d
 d  2) / 2 KK tower of real scalar decoupling fields (d  2)
•
• KK tower of scalar fields (zero mode – radion)
The SM fields are localized on the brane,
while gravitons propagate in the bulk
The “gravitational” coupling is
1/ M
1 d / 2
69
HEP Phenomenology
New phenomena: graviton emission & virtual graviton exchange
• KK states production
d 2
dtdm
e e G
 
(n)
(e e   )
M Pl2
d 1 d m
Sd 1 d  2 m
M
dt
1
M d 2
bg
LHC
M  5 TeV
70
HEP Phenomenology II
• Virtual graviton exchange
1
A 2
M Pl
e e G
(n)
 f f ( HH , gg )
 

P  P 
3(d  1) T T 
n T s  m2 T  d  2 s  m2 

n
n 

s 0.5 TeV
G (n)
q
-q
S
 
M 1.5 TeV
Spin=2
1
2
M Pl
Sd 1

2M 4
1
n s  m2 
n

1
2
M Pl
M Pl2 m d 1dm
Sd 1 d  2 
2
M
s

m
0

s d / 21 [( d 1) / 2]
s k 1  d 2 k 
  ck ( 2 ) ( )
i ( 2 )

M
M
M
k 1


SM
Angular distribution
71
Randall-Sandrum Models
E5  M 4  S / Z 2
1
S   d 4x
R

D4-brane
dy Gˆ {2M 3 R (5) [Gˆ MN ]  }
Bulk
 R
  d 4 x  g (1) ( L1  1 )   d 4 x  g (2) ( L2   2 )
B1
B2
Metric
 ( y)  k | y |
ds 2  e2 ( y ) dx  dx  dy 2
y0
Positive
tension
y
y 
Negative
tension
Matter
warp factor
1   2  24M 3k ,   24M 3k 2
D4-brane
graviton
radion
Perturbed Metric ds 2  e2 ( y ) (  h ( x, y))dx  dx  (1   ( x))dy 2
72
Randall-Sandrum Model cont’d
Brane 2
Wrap factor
Brane 1
• Massless graviton
• massive K-K gravitons
mn   n ke  kR
Hierarchy
Problem !
• massless radion
Seff
e
2 ( R )
3
M
M Pl2 
(e2 k R  1)
k
 1 (0) 

 n ( n ) 
1
1
4

  d z
h T  
h T 
T 
B
2 2
 3 
n 1 
 M Pl
  M Pl e  k R
• Massless graviton
• massive K-K gravitons
• massless radion
mn   n k
1 TeV
M Pl

73
HEP Phenomenology
The first KK graviton mode M ~ 1 TeV
qq  G (1)  l l  , gg  G (1)  l l 
• Drell-Yan process
• Excess in dijet process
qq , gg  G (1)  qq , gg
  (k / M Pl )ek R
Exclusion plots for resonance production
Excluded
Excluded
10 fb 1
Run I
Dj
D-Y
Run II
Tevatron
100 fb 1
D-Y
LHC
74
HEP Phenomenology II
  (k / M Pl )ek R
The x-section of D-Y production
First KK mode
0.1    1
Tevatron (M ~ 700 GeV)
First and subsequent KK modes
0.1    1
LHC (M ~ 1500 GeV)
75
HEP Phenomenology III
pp  G (1)  e e
Angular dependence
spin 0  f    1, spin 1  f    1  cos 2 
qq  G (1)  l  l  , f    1  cos 4 
gg  G (1)  l  l  , f    1  3cos 2   4 cos 4 
LHC
LHC
76
ED Conclusion
ADD Model
2/ d
1
 M 
R
• The MEW/MPL hierarchy is replaced by
1030 / d


M  M Pl 
• 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
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)
77
What comes beyond
the Standard Model ?
78