Transcript CERNFermiSchool

BEYOND THE
STANDARD MODEL
G.F. Giudice
Quic kTime™ and a
TIFF (Unc ompres sed) dec ompres sor
are needed to see this pic ture.
CERN-Fermilab HCP Summer School
CERN June 8-17, 2009
(I)
Supersymmetry (general structure)
(II)
Supersymmetry (phenomenology)
(III) Extra Dimensions
(IV) Strong dynamics, Little Higgs & more
1
Supersymmetry
• Evades Coleman-Mandula (Poincaré  internal group is the largest
symmetry of the S-matrix)
• Relates particles with different spin  involves space-time transformations
Quantum dimensions
z
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
x
(not described by ordinary
numbers)
y
3-d space
4-d space-time
superspace
translations/rotations
Poincaré
supersymmetry
• Special ultraviolet finiteness properties
New concept of space
Just a mathematical curiosity?
Local susy contains gravity
Too beautiful to be ignored by nature?
2
A solution in search of a problem
In quantum theory, the
vacuum is a busy place
Particle-antiparticle pairs can
be produced out of nothing,
borrowing an energy E for a
time t E t ≤ h
Virtual particles are like
ordinary particles, but have
unusual mass-energy relations
The Higgs field propagating in vacuum “feel” them with
strength E   mH ≈ Emax (maximum energy of virtual particles)
temperature
T
If interacts with ,
after a while, we expect
E ≈T
3
 mH ≈ Emax
What is the maximum energy?
MGUT = 1016 GeV? MPl = 1019 GeV?
Having MW << MPl requires tuning up to 34th digit !
temperature
T
E = 10-17 T
The “stability” of the hierarchy MW / MPl requires an explanation
Higgs mass is “screened” at energies above mH 
new forces and new particles within LHC energy range
What is the new phenomenon?
4
A problem relevant for low-energy supersymmetry:
hierarchy/naturalness
3GF
2
2
2
2
2
2
m 
2mW  mZ  m H  4mt    0.2 
2 
4 2
2
H
  < TeV
 mH 182 GeV (95% CL limit on SM Higgs)

If susy is effective at the Fermi scale:
Higgs
top
chiral symmetry
supersymmetry
+
stop
=0
˜ H  0 
 m
 m H  0
˜ H  m H 
 m
The Fermi scale (mH) is induced only by susy breaking

5
Dynamical supersymmetry breaking
• If susy unbroken at tree-level, it remains unbroken to all
orders in perturbation theory
• Non-perturbative effects can break susy with mS ~ e-1/ MP
• stable against quantum corrections
(because of symmetry)
Weak scale
• naturally much smaller than MP
(because of dynamics)
Supersymmetric SM with mS < TeV solves
the Higgs naturalness problem
Can we construct a realistic theory?
6
Supersymmetry transformation corresponds to group element
ixP Q Q 
G x,,  e

Translation
Susy

susy
4-d space

Ga,0,0 : x,, x  a,,
G0, ,: x,, x  i i,   ,  
superspace
In superspace differential operators
represent action of generators
P   i 
translation

Q    i ÝÝ 



  Ý
Ý
Q 
 i  Ý Ý 
Ý
7
Superfields


Function of superspace  x,,
Power series in 
x,, A(x)   (x)   (x)  B(x)  C(x)
  V  (x)  (x)   (x)  D(x)

• finite number of component fields
• contains fields with different spin
• compact description of susy multiplets
• easy to write susy Lagrangians
8
General  is reducible. Additional constraints:



A(x)

2

(x)

i

  A(x) 
CHIRAL SUPERFIELD
DÝ  0
F(x) 
i
1
  (x)      A(x)
4
2
components:
A(x) complex scalar field, (x) Weyl spinor, F(x) auxiliary field
SUSY ACTION FOR A CHIRAL SUPERFIELD
4
4  
Kinetic term for A and 
d
x
d
 

F*F eliminated via e.o.m.
4
2
Superpotential: holomorphic
d
x
d
 W 

function that defines interactions
E.g.: 2
m
W  m   L        m 2 A  A
=h2 required for
2
cancellation of 2
W 
3
 L  A  h.c.   A A
2

2
In general: no quadratic divergences in susy theory
9
VECTOR SUPERFIELD
Global symmetry of superpotential
can be made local ( chiral)
  e i 
  e i 
if we introduce a vector superfield V=V+ such that

 i( )
  e
L  eV 

is made invariant

V V  i   
When expanded in components, V contains
(x) Weyl spinor, V (x) vector field, D(x) auxiliary field

+ gauge degrees of freedom
10
superparticle
Q
superspace

Chiral multiplet:
A
boson
(integer spin)
fermion
(half-integer spin)

Vector multiplet:

V
Gravity
multiplet:
G
g
11
Supersymmetric Standard
Model
particles
Sparticle
s
quark
s
lepton
s
Higgs
doublet
s
squark
s
slepton
s
Higgsino
s
winos
bino
gluino
s
12
New particles, new interactions, but no new free parameters
Ex: SU(3) color
interactions
all vertices controlled by the SU(3) coupling
there is a quartic scalar
vertex
sparticles enter interactions in pairs:
sparticle parity = (-1)
(number of
sparticles)
13
is conserved

1st problem: indirect new-physics effects
Any FT can be viewed as an effective theory below a UV cutoff
d4
Leff  L
g gauge
 Yukawa
1 d5 1 d6
g,   L  2 L  ...


 has physical meaning: maximum energy at which the
theory is valid. Beyond , new degrees of freedom

Higgs naturalness gives an upper bound on . However,
1
15
qqql
p
decay



10
GeV
2

1
L number  l lHH  mass    1013 GeV

1
individual L  2 e   HF   e    108 GeV

1
quark flavour  2 s   d s   d mK    106 GeV

2
1 
1 
4
LEP1,2  2 H D H ,
e

e
l

l



10
GeV 14

2


B number 
New theories at TeV are highly constrained
A first problem:
f  QL DRc H1  QLU Rc H 2  LL E R H1 
U Rc DRc DRc  QL DRc LL  LL LL E Rc  H 2 LL
4


1 mS
-10
 p  4 
 10 sec
 TeV 
Violate B or L

Usually one invokes R-parity (it could follow from gauge
symmetry of underlying theory)
R-parity = + for 
SM particles, R-parity =  for susy particles
• no tree-level virtual effects from susy
Important for
phenomenology
• susy particles only pair produced
• LSP stable (missing energy + dark matter)
Flavor gives powerful constraints on the theory
15
2nd problem: supersymmetry breaking
Break susy, but keep UV behavior  soft breaking
16
mS
mS 
gaugino mass
mS2  
scalar mass
mS  3
A - term
• Soft susy breaking introduces a dimensionful parameter mS

• Susy particles get masses of order mS
• Susy mass terms are gauge invariant
• Treat soft terms as independent; later derive them from theory
• Different schemes make predictions for patterns of soft terms
17
Two robust features of low-energy susy:
EW breaking & gauge coupling unification
ELECTROWEAK SYMMETRY BREAKING
Higgs potential
0 2
1
V m H
2
1
m H
2
2
0 2
2

g 2  g2
0 2
0 2
 m H H  h.c.
H1  H 2
8
2
3
0
1
0
2

• m1,2,32 = O(mS2) determined by soft terms
• quartic fixed by supersymmetry
• Stability along H1 = H2  m12 + m22 > 2 |m32|
• EW breaking, origin unstable  m12 m22 < m34
18
2
EW breaking induced by quantum corrections
RG running:
gauge effects
Yukawa effects
• If t large enough  SU(2)U(1) spontaneously broken
• If s large enough  SU(3) unbroken
19
• Mass spectrum separation m22 < weak susy < strong susy
HIGGS SECTOR
8 degrees of freedom  3 Goldstones = 5 degrees of freedom
2 scalars (h0,H0), 1CP-odd scalar (A0), 1 charged (H)
3 parameters (m1,2,32 )  MZ = 2 free param. (often mA and tan)
mh  mZ cos2 , mh  mA  m H , m 2H   mA2  mW2
m
2
h, H
1  2
 mA  mZ2
2 
m
2
A
m

2 2
Z

 4 sin 2 m m 

2
2
A
2
Z
m
Large tanmh
mH
mH

mH±
MZ
decoupling
region
mh
MZ
mA
20
mS IS THE SEED OF EW BREAKING
EW breaking is related to susy breaking, mS  mZ
stop
top
32t
m   2
8
2
2

2
k 2 dk 2
32t
 2
2
2
k  mt 8

2
k 2 dk 2
32t 2 
  2 mS ln
2
2
2
k  mt  mS
4
mS
• mS plays the role of 2 cutoff
• The quantum correction is negative and drives EW breaking
2
2
2
2
m

m
tan


1
2
2
2
m


2m
Minimum of the potential
Z
2
2
tan  1
1/ 2
2


mZ
10%
2
˜
2  m2 
 mt  300 GeV 

Tension
  

with data
˜t
3 4 2 m
2
2
˜ t 1 TeV
mh  mZ  2 t v ln 114 GeV  m
21
2
mt
“Natural” supersymmetry has already been ruled out
22
Connection susy breaking  EW breaking
at the basis of low-energy supersymmetry
• Susy particle content dynamically determines EW
breaking pattern
• Higgs interpreted as fundamental state, like Q and L
• Higgs mass determined by susy properties and
spectrum
After LEP, “natural” susy is ruled out
• Source of “mild” tuning (is it observable at LHC?)
• Missing principle?
23
GRAND UNIFICATION
• Fundamental symmetry principle to embed all gauge
forces in a simple group
• Partial unification of matter and understanding of
hypercharge quantization and anomaly cancellation
To allow for unification, we need to unify g,g’,gS from
effects of low-energy degrees of freedom (depends on
the GUT structure only through threshold corrections)
SM
susy
mZmS
dg2
bi
i

d ln Q 4 
GUT ?
MGUT
SM
susy
b3=7, b2=19/6, b1=41/6
b3=3,
b2=1,
b1=11
24
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
25
3 equations, 2 unknowns
(GUT, MGUT): predict S
in terms of  and sin2W
sexp =0.11760.0020
• success of susy
• does not strongly
depend on details of soft
terms
• remarkable that MGUT is
predicted below MP and
above p-decay limit
26
THEORY OF SOFT TERMS
• Explain origin of supersymmetry breaking
• Compute soft terms
Similar to EW breaking problem
• Origin of EW breaking 
V H   m H   H
2
H
2
4
 
L

D
H
D H  H
• Compute EW breaking effects 


Gauge boson
mass

gauge
W,Z
Yukawa
q,l
Fermion
mass
EW
27

Invent a new sector which breaks supersymmetry
Couple the breaking sector to the SM superfields
But
STr M   1
2J
2
2J  1M J2  0
J
at tree level, with
canonical kinetic terms
sparticle < particle
SUSY
???
Squarks, sleptons,
gauginos, higgsinos
What force mediates susy-breaking effects?
28
GRAVITY AS MEDIATOR
Gravity couples to all forms of energy
Assume no force stronger than gravity couples the two sectors
Susy breaking in hidden sector
mS = FX / MP
mS = TeV  FX1/2 = 1011 GeV
ATTRACTIVE SCENARIO
• Gravity a feature of local supersymmetry
• Gravity plays a role in EW physics
• No need to introduce ad hoc interactions
BUT
• Lack of predictivity (102 parameters)
• Flavour problem
For simplicity, most analyses take universal m, M and A
29
Searching for supersymmetry at the LHC
• At a hadron collider, the total energy of the parton
system is not known
• The initial momentum of the parton system in the
transverse direction is zero
ET is a characteristic signal of supersymmetry
Background:
•  (mostly produced by W/Z or heavy quarks)
• incomplete solid angle coverage
• finite energy resolution of the detectors
• mismeasurement of jet energies
30
Colored particles have large cross sections at the LHC
 TeV g˜   pb
If MC tools for SM background
are fully validated, If detector
response is properly

understood, then TeV susy
particles can be discovered
with low integrated luminosity
Already with 10 fb-1,
parameter space is
explored up to 1-2 TeV in
gluino and squark masses
However, determining parameters
and masses is a much more
complicated issue 31
• Many new particles in final
states
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
• Kinematics of the event
cannot be fully
reconstructed: unknown CM
frame and pairs of particles
carrying missing energy
Precise determination of masses and couplings is essential
• Confirm supersymmetric relations
• Understand pattern of supersymmetry breaking
• Identify “unification” relations
• Determine the DM mass
• Reconstruct relic abundance
32
Susy mass (differences) from edges in invariant mass
distributions
Consider the decay chain
˜ 20
q˜  q 
max m 2 

˜ 20  
˜ 10

 
through Z 0 or ˜ exchange
 is obtained for ˜ and 
maxm 
 m  m
 
0
1
 

˜2
 
 at rest in ˜ ref frame
0
2

˜1
Consider two-body decay
˜ 20
q˜  q 
˜ 20  ˜ 



max m 2 
 


˜ 10

 is obtained for
 max m 
 
 m

˜2

and

˜ 20 ref frame
back to back in 
 m 2  m 2 

˜1
˜


1
1


2
 m 2 
 m˜ 

˜ 2 

Repeating this technique along complicated
chains and combining different channels, one
can solve for (most) masses
33
This technique doesn’t exploit the kinematic constraints on ET
pp  g˜ g˜
 qq˜
 qqqq10 10
 q10
New techniques to derive all masses from kinematic distributions
Example:
W “transverse mass” from Wl
mT2  m2  m2  2ET ET  pT  pT  mW2
mW obtained from end-point of mT
The end-point of the “gluino stranverse mass” has a kink

structure when
plotted as a function of the test LSP mass
The location of the kink corresponds to the physical mg and
m ISR, finite resolution, background and finite width can smear end-points
34
ET may not be the discovery signature
(even in gravity mediation)
If the gravitino is the LSP:
~
~
Long-lived charged particle at the LHC (G)
Distinctive ToF and
energy loss signatures
“Stoppers” in ATLAS/CMS caverns:
• Measure position and time of stopped ~time and energy of 
 Reconstruct susy scale and gravitational coupling
35
GAUGE MEDIATION
Soft terms are generated by quantum effects at
a scale M << MP
mZ
M
F MP
• If M << F, Yukawa is the only effective source of flavour
breaking (MFV); flavour physics is decoupled (unlike sugra
or technicolour)
• Soft terms are computable and theory is highly predictive
• Free from unknowns related to quantum gravity
36
BUILDING BLOCKS OF GAUGE MEDIATION
SUSY
Messengers
SUSY SM
gauge loop
SUSY SM: observable sector with SM supermultiplets
SUSY: “hidden” sector with <X> = M + 2 F
Messengers: gauge charged, heavy (real rep), preserve
gauge unification (complete GUT multiplet)
Ex.:
2
2
   5  5 of SU(5) with f  X, V  M 2     F  h.c.


Parameters: M, F, N (twice Dynkin index; N=1 for 5+5)
37
Gaugino mass at one loop, scalar masses at two loops:
g 2 (Q) F
M g˜ Q 
N
2
16
M
g2 F
mS 
16 2 M
g4
2
F
˜ Q2 (M)  2c
m
N 2
2 2
16  M

F/M ~ 10-100 TeV, but M arbitrary
To dominate gravity and have no flavour problem
2
F
g
F
 102
MP
16 2 M
From stability:

M  1015 GeV
F  M  M 10 100 TeV
MGUT

From
perturbativity up to the GUT scale: N  150 /ln
M

38
• Theory is very predictive
• Gaugino masses are
“GUT-related”, although
they are not extrapolated
to MGUT
• Gaugino/scalar mass
scales like N1/2
• Large squark/slepton
mass ratio and small A do
not help with tuning
39
Higgs mass is the
strongest constraint: stop
masses at several TeV
40
Crucial difference between gauge and gravity mediation
F
m3 / 2 
 in gravity m3 / 2  mS , in gauge m3 / 2
3M P
2


F
 
 2 eV
100 TeV 
In gauge mediation, the gravitino is always the LSP
q
M g˜ a  a ˜
1  ˜
1  2
˜ L 
~
m
  F G  h.c.
G L   F JQ G   F 
4 2


~
q
m˜ 2
on mass shell
F
Goldberger-Treimanino
relation


NLSP decays travelling an average distance
4

100 GeV 5 
F
E2
 
1 0.1 mm

 
2
 mNLSP  100 TeV  mNLSP
From microscopic to astronomical distances
41
0 or ~
R are the NLSP (NLSP can be charged)
In gravity-mediation, “missing energy” is the signature
Susy
particles
NLSP
~
R
0
F 106 GeV
E
F 106 GeV
E


F 106 GeV
E

F 106 GeV
Stable
charged
particle
Intermediate region very interesting
(vertex displacement; direct measurement of F)
42
DARK MATTER
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Indirect evidence for DM is solid
• rotational curves of galaxies
• weak gravitational lensing of distant galaxies
• velocity dispersion of galaxy satellites
• structure formation in N-body simulations
• Opportunity for particle physics
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• Intriguing connection weak-scale
physics  dark matter
43
T >> M
T≈M
T << M
44
Relic abundance
 
mn
c
4 


k
If  =
128 m 2
2
3
3
x
g

T
 f S 

45 g1/* 2 H 02 M P3
0.22  m 
  


k TeV 
2
Weak-scale particle candidate for DM

No parametric connection to the weak scale
Observation provides a link MDM  <H>
Many BSM theories have a DM candidate
Susy has one of the most appealing
45
Supersymmetric Dark Matter
R-parity  LSP stable
RG effects  colour and electric neutral massive particle is LSP
Heavy isotopes exclude gluino, direct searches exclude sneutrino
Neutralino or gravitino are the best candidates
NEUTRALINO
Because of strong exp limits on supersymmetry,
current eigenstates are nearly mass eigenstates:
Bino, Wino, Higgsino
46
BINO
~
B
~
B
~
f
f
f
HIGGSINO
~
H
~
H
W,Z
W,Z
WINO
~
W
~
W
W,Z
W,Z
47
Wino
Bino
1.1 
m˜ e R
M1
1.5 
3


DM h  0.105  0.008
2
m˜

L
M2
Higgsino
1.5 
m˜ t



Neutralino: natural DM candidate for light supersymmetry
Quantitative difference after LEP & WMAP
Both MZ and DM can be reproduced by low-energy
supersymmetry, but at the price of some tuning.
Unlucky circumstances or wrong track?
48
TO OBTAIN CORRECT RELIC ABUNDANCE
• Heavy susy spectrum: Higgsino (1 TeV) or Wino (2.5 TeV)
• Coannihilation Bino-stau (or light stop?)
• Nearly degenerate Bino-Higgsino or Bino-Wino
• S-channel resonance (heavy Higgs with mass 2m)
• TRH close to Tf
All these possibilities have a very critical behavior
with underlying parameters
• Decay into a lighter particle (e.g. gravitino)
49
How can we identify DM at the LHC?
Establishing the DM nature of new LHC discoveries
will not be easy. We can rely on various hints
• If excess of missing energy is found, DM is the prime
suspect
• Reconstructing the relic abundance (possible only for
thermal relics and requires high precision; LHC + ILC?)
• Identify model-dependent features (heavy neutralinos,
degenerate stau-neutralino, mixed states, mA = 2 m)
• Compare with underground DM searches
50
SPACE DIMENSIONS AND UNIFICATION
Minkowski recognized special

B
relativistic invariance of

E



E



t
Maxwell’s eqs  connection 

E
between unification of forces 

B

0

B

J


t
and number of dimensions
Electric & magnetic forces unified in 4D space time
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t, x  x   (t, x )
space - time

EM potentials E   
A
, B   A  A   (, A)
t
EM fields E ,B  F
 0

Ex

  A   A 
E y

E z
current
E x
0
Bz
By
E y
Bz
0
Bx
E z 

By 
Bx 

0 
, J  J   ( , J)
Maxwell' s eqs
   F   J 
51
Next step:
UNIFICATION OF EM & GRAVITY
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 New dimensions?
1912: Gunnar Nordström proposes gravity
theory with scalar field coupled to T
1914: he introduces a 5-dim A to describe both
EM & gravity
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1919: mathematician Theodor Kaluza writes a 5dim theory for EM & gravity. Sends it to Einstein
who suggests publication 2 years later
1926: Oskar Klein rediscovers the theory, gives
a geometrical interpretation and finds charge
quantization
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In the ‘80s the theory, known as Kaluza-Klein
52
becomes popular with supergravity and strings
GRAVITY
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In General Relativity, metric g (4X4 symmetric tensor)
dynamical variable describing space geometry (graviton)
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

ds  g dx dx
2

Dynamics described by Einstein action
1
SG 
16 GN
4
d
 x g R(g)
• GN Newton’s constant
•R
curvature (function of the metric)
53
SˆG 
Consider GR in 5-dim
Choose

Dynamical fields

1
16 Gˆ N
5
d
 x gˆ R(gˆ)
g   2 A A
gˆ MN ( xˆ )  
  A

gˆ MN
Assume space is M4S1

  A 
( xˆ )
 
 g , A , 
x5
R
(t,x)
• First considered as a mathematical trick
• It may have physical meaning
54
Extra dim is periodic or “compactified”
x5  2  R  x5
All fields can be expanded in Fourier modes
 n x 5 
 (n ) (x)
 ( xˆ )  
expi

 R 
n 2 R


(n )

(x) Kaluza-Klein modes
5-dim field  set of 4-dim fields:
(n )

Each  has a fixed momentum p5=n/R along 5th dim

extra
dimensions
D-dim
particle


E2 = p 2 + p2extra + m2
4-d space
KK mass
mass
From KK mass spectrum we can measure
the geometry of extra dimensions
55
Suppose typical energy << 1/R 
only zero-modes can be excited
R
r << R
2-d plane
r >> R
Expand SG keeping only
zero-modes and setting =1
1-d line

1
S
(g)

 G
16 GN
ˆS (gˆ )  S (g(0) )  S (A(0) ) 
G
MN
G
EM
 S (A)   1
 EM
4
SG
To obtain correct normalization:

d
4
x g R(g)
4

d
x
F
F


dx 5 2 R

1



ˆ
GN
GN
Gˆ N
SEM    16 GN
Gravity & EM unified in higher-dim space: MIRACLE?

56
Gauge transformation has a geometrical meaning
g   2 A A
gˆ MN ( xˆ )  
  A

dsˆ 2  gˆ MN ( xˆ ) dxˆ M dxˆ N
  A 
( xˆ )
 
Keep only zero-modes:
d
sˆ  g
2
Invariant under local

(0)



dx dx  
x5
A(0)
(0)
dx
5
 A
(0)

dx

 2
 x5  
(where g and 
 A(0)    do not transform)
• Gauge transformation is balanced by a shift in 5th dimension
uniquely determined by gauge invariance
• EM Lagrangian
57
CHARGE QUANTIZATION
Matter EM couplings fixed by 5-dim GR
S
Consider scalar field 
 d xˆ
5
2


n

n 2  (n )2 
4
(0)

(0)
(n )

S   dx 5   d x g   i
A 
 2

R
R  

n


2
R
Expand in 4-D
KK modes:
Each KK mode n has: mass n/R

gˆ gˆ MNM  N
n/R
charge

• charge quantization
• determination of fine-structure constant
2
4GN


4 R 2
R2
 R
4GN

31
 4 10
m  5 10 GeV 
17
1
• new dynamics open up at Planckian distances
58

Not a theory of the real world
=1 not consistent ( dynamical field leads to
inconsistencies: e.g. F(0)F(0)=0 from eqs of motion)
• Charged states have masses of order MPl
• Gauge group must be non-abelian (more dimensions?)
Nevertheless
• Interesting attempt to unify gravity and gauge interactions
• Geometrical meaning of gauge interactions
• Useful in the context of modern superstring theory
• Relevant for the hierarchy problem?
59
60
Usual approach: fundamental theory at MPl, while W is
a derived quantity
Alternative: W is fundamental scale, while MPl is a
derived effect
New approach requires
• extra spatial dimensions
• confinement of matter on subspaces
Natural setting in string theory  Localization of gauge theories
on defects (D-branes: end points
of open strings)
We are confined in a 4-dim world,
which is embedded in a higher-dim
space where gravity can propagate
61
COMPUTE NEWTON CONSTANT
Einstein action in D dimensions
1
S 
16 Gˆ N
D
E
D
d
 x gˆ R(gˆ)
Assume space R4SD-4: g doesn’t depend on extra coordinates

Effective
action for g
SE 

Gˆ N 
1
M DD2
VD4  R D4
VD4
16 Gˆ N
d
4
x g R(g)
1 VD4

GN
Gˆ N
D4
2

MPl  MD RM D 
62
Suppose fundamental mass scale
D4
2
MPl  MD RM D 
MD ~ TeV
very large if R is large (in units of MD-1)
Arkani-Hamed, Dimopoulos, Dvali
5 104 eV  0.4 mm
D 4  2
20 keV  105  m
1
7
MeV

  30 fm
D 4  4
1
Radius of
compactified space
R
1
D 4  6
• Smallness of GN/GF related to largeness of RMD

• Gravity is weak because it is diluted in a large space
(small overlap with branes)
• Need dynamical explanation for RMD>>1
63
Gravitational interactions modified at small distances
m1m2
FN (r)  GN 2
at r  R
r
At r < R, space is (3+)-dimensional
(=D-4)
(4  ) m1m 2
ˆ
FN (r) GN

2
r
mm
 GN R 12 2
r
V (r)  GN

m1m2
1  exp r 

r
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From SN emission and
neutron-star heating:
MD>750 (35) TeV for =2(3)

64
Probing gravity at the LHC?
graviton
gluon
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Gravitational wave
jet + ET
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Gravitational deflection
dijet
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Black hole
multiparticle event
Gravitational phenomena into collider arena
65
graviton
Probability of producing
a KK graviton
gluon
 pp  G
E2
 2
M Pl
s
jet  GN 1028 fb

1 event  run LHC for 1016 tU

Number of KK modes with mass less than E (use m=n/R)
(n )
n
D4
 ER
Inclusive cross section
D4
E D4 M Pl2

M DD2
D4

E
 pp  G(n ) jet    sM D2
D
n

It does not depend on VD (i.e. on the Planck mass)
Missing energy
and jet with characteristic spectrum
66
67
Contact interactions from graviton exchange
• Sensitive to UV physics
• d-wave contribution to scattering processes
4
• predictions for related processes
T
4T
• Limits from Bhabha/di- at LEP and Drell
1 
1
T  T T  
T T Yan/ di- at Tevatron: T > 1.2 - 1.4 TeV

2 
D2
L
• Loop effect, but dim-6 vs. dim-8
4
L 2 

2


1
  
f   5 f 



2 f  q,l

• only dim-6 generated by pure gravity
•  > 15 - 17 TeV from LEP
68
G-emission is based on linearized gravity, valid at s << MD2
TRANSPLANCKIAN REGIME
 GD  
3 
c


P  
Planck length
Schwarzschild
radius
RS 
classical limit
transplanckian limit
1
 2
1  8
   3 

   2  2 
 



quantum-gravity scale
1
 1
 GD s 


 c3 


1
 1
 0 :
RS  P
D
RS  P
 s  M  :
classical
gravity
same
regime
The transplanckian regime is described by classical physics
(general relativity)  independent test, crucial to verify
gravitational nature of new physics
69
Gravitational scattering
Non-perturbative, but calculable for b>>RS
(weak gravitational field)
b > RS
GD mM
D-dim gravitational potential: V (r)   1
r
D 4 
Quantum-mechanical scattering phase
of wave with angular momentum mvb
 1
m v

bc 
GD mM 
b    bc  
b

 b 
 v

b
bc
GD s





L mvb 1 rel.
b 1
E 

4GD s
b
70
Gravitational scattering in extra dimensions:
two-jet signal at the LHC
Diffractive pattern
characterized by
1
GD s 
bc  




71
b < RS
At b<RS, no longer calculable
Strong indications for black-hole formation
BH with angular momentum, gauge quantum numbers, hairs
(multiple moments of the asymmetric distribution of gauge charges and energy-momentum)
Gravitational and gauge radiation during collapse
 spinning Kerr BH
~ RS2
10 pb (for MBH=6 TeV and MD=1.5 TeV)
Hawking radiation until Planck phase is reached
TH ~ RS-1 ~ MD (MD / MBH)1/1)
Evaporation with  ~ MBH(+3)/(+1) / MD2(+2)/(+1)
(10-26 s for MD=1 TeV)
Characteristic events with large multiplicity (<N> ~ MBH / <E>
~ (MBH / MD2)/(+1)) and typical energy <E> ~ TH
Transplanckian condition MBH >> MD ?
72
WARPED GRAVITY
A classical mechanism to make quanta softer
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For time-indep. metrics with g0=0  E |g00|1/2 conserved
.
(proper time d2 = g00 dt2)
Schwarzschild metric
g00 1
2GN M
r

E obs  E em

E em
g00 1  
GN M
rem
On non-trivial metrics, we see far-away objects as red-shifted
73
GRAVITATIONAL RED-SHIFT
ds2  e2K|y| dx  dx   dy 2
Masses on two branes related by

mR
 e RK
m0
Same result can be obtained
by integrating SE over y
y=0
y=R
g00=1 g00=e-2RK

R  10 K
1

mR
MZ

m0
MGUT
74
PHYSICAL INTERPRETATION
• Gravitational field configuration is non-trivial
• Gravity concentrated at y=0, while our world confined at y=R
• Small overlap  weakness of gravity
WARPED GRAVITY AT COLLIDERS
• KK masses mn = Kxne-RK [xn roots of J1(x)] not equally spaced
• Characteristic mass Ke-RK ~ TeV
• KK couplings
(0)
(n ) 

G
G
L  T  
   
M Pl n1   
   e RK M Pl  TeV
• KK gravitons have large mass gap and are “strongly” coupled
• Clean signal
at the LHC from G  l+l
75
Spin 2
Spin 1
76
A SURPRISING TWIST
AdS/CFT correspondence relates 5-d gravity with
negative cosmological constant to strongly-coupled 4-d
conformal field theory
Warped gravity with
SM fermions and
gauge bosons in bulk
and Higgs on brane
Technicolor-like theory
with slowly-running
couplings in 4 dim
Theoretical developments in extra dimensions have
much contributed to model building of 4-dim theories
of electroweak breaking: susy anomaly mediation,
susy gaugino mediation, Little Higgs, Higgs-gauge
unification, composite Higgs, Higgsless, …
77
DUALITY
SM in warped extra dims  strongly-int’ing 4-d theory
KK excitations  “hadrons” of new strong force
Technicolor strikes back?
TeV brane
Planck brane
5-D gravity
5th dim
4-D gauge theory
Motion in 5th dim
UV brane
IR brane
RG flow
IR
AdS/CFT
RG flow
Planck cutoff
breaking of conformal inv.
Bulk local symmetries global symmetries
UV
5-D warped
gravity

large-N
technicolor
 Composite Higgs
78
What screens the Higgs mass?
boson
fermion
vector
 a
  e ia 
no m 
A  A   a
Spont. broken global
symm.
Chiral
symmetry
Gauge
symmetry
LITTLE HIGGS

SUPERSYMMETRY

no
m 2 2
5
no
m 2 A A 
Symmetry
HIGGS-GAUGE UNIF.
mH
TECHNICOLOR
HIGGSLESS
EXTRA DIMENSIONS
Dynamical EW
breaking
Delayed
unitarity violat.
Fundamental
scale at TeV
• Very fertile field of research
• Different proposals not mutually excluded
Dynamics
79

QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
M Z2
Necessary tuning
2
M Z2
28

10
2
M GUT
n
Cancellation of
Existence of
electron self-energy
+-0 mass difference
KL-KS mass difference
gauge anomaly
positron

charm
top
cosmological constant
CAVEAT
EMPTOR
a dna ™em i Tkciu Q
rosserpmoced )desserpmocnU ( F FI T
.e rutc ip s iht ees o t dedeen era
It is a problem of naturalness, not of consistency!
10-3 eV??
80
HIGGS AS PSEUDOGOLDSTONE BOSON

 f
2
e
i / f
  f
e :
ia
Non - linearly realized symmetry
  

    a
h  h  a forbids m 2 h 2
Gauge, Yukawa and self-interaction are non-derivative couplings
Violate global symmetry and introduce quadratic divergences

➤
Top sector
●
●
➤
No fine-tuning
If the scale of New Physics is so low,
why do LEP data work so well?
81
--
H  a H W a B
LEP1
H  D H
2
iH  D H L   L
LEP2
MFV

e  e 

e    5eb    5b
+
10 9.7
9.2 7.3
1
L 2O

6.1 4.5
4.3 3.2
2
1

q



q
6.4 5.0

L u u  
2
H  dR d u u  qL F  9.3 12.4
new
physics
Bounds on  [TeV]
5.6 4.6

Little Higgs
strong
Composite Higgs
dynamics
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decompressor
are needed to see this picture.
energy
1 TeV
10 TeV
A less ambitious programme: solving the little hierarchy
82
LITTLE HIGGS
Explain only little hierarchy
One loop m 
2
H
GF

2
m 
2
SM
2
SM
  SM 

GF
 TeV
At SM new physics cancels one-loop power divergences
Two loops mH2 
GF2

4
4
mSM
2   
2
GF mSM
 10 TeV   LH
“Collective breaking”: many (approximate) global symmetries
preserve massless Goldstone boson
ℒ1
ℒ2
H
ℒ1 ℒ2 2
m  2

2
4 4
2
H
83
Realistic models are rather elaborate
Effectively, new particles at the scale f cancel
(same-spin) SM one-loop divergences with
couplings related by symmetry
Typical spectrum:
Vectorlike charge 2/3 quark
Gauge bosons EW
triplet + singlet
Scalars (triplets ?)
84
New states have naturally mass
New states cut-off quadratically divergent contributions to mH
Ex.: littlest Higgs model
Log term:
analogous to effect of stop
loops in supersymmetry
Severe bounds from LEP data
85
TESTING LITTLE HIGGS AT THE LHC
• Discover new states (T, W’, Z’, …)
• Verify cancellation of quadratic divergences
f from heavy gauge-boson masses
mT 2t  2T

f
2 T
mT from T pair-production
T : we cannot measure TThh vertex
(only model-dependent tests possible)
86
f and gH
from DY of
new gauge
bosons
Production rate and BR
into leptons in region
favoured by LEP (gH>>gW)
Can be seen up to ZH mass of 3 TeV
MT from T production can be
measured up to 2.5 TeV
87
T  bW   2T  tZ  2T  th  2T
Measure T width?
Cleanest peak from
In order to precisely extract T from measured cross
section, we must control b-quark partonic density
Possible to test cancellation with 10% accuracy
for mT < 2.5 TeV and mZ < 3 TeV
88
Concept of symmetry central in modern physics
invariance of physics laws under
transformation of dynamical variables
Now fundamental and familiar concept, but hard
to accept in the beginning
Ex.: Earth’s motion does not affect c
Lorentz tried to derive it from EM
dynamics determine symmetries
Einstein postulates c is constant (invariance
under velocity changes of observer) symmetries determine dynamics
QuickTime™ and a
TIFF (Uncomp resse d) de com press or
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Einstein simply postulates what
we have deduced, with some
difficulty and not always
satisfactorily, from the
fundamental equations of the
electromagnetic field
89
General relativity deeply rooted in symmetry
SM: great success of symmetry principle
Impose SU(3)SU(2)U(1)  determine particle
dynamics of strong, weak and EM forces
Will symmetries completely determine the
properties of the “final theory”?
Or new principles are needed to go beyond
our present understanding?
90
Complexity
life  biochemistry  atomic physics  SM  “final theory”
Microscopic probes
Breaking of naturalness would require new principles
• the “final theory” is a complex phenomenon
with IR/UV interplay
• some of the particle-physics parameters are
“environmental”
91
A different point of view
Vacuum structure of string
theory
~ 10500 vacua
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(N d.o.f in M config. make MN)
Expansion faster than
bubble propagation
Big bang  universe expanding
like an inflating balloon
Unfolding picture of a fractal
universe  multiverse
92
Not a unique “final” theory with
parameters = O(1)  allowed by symmetry
but a statistical distribution
In which vacuum do we live?

Determined by
“environmental selection”
• Large and positive  blows structures apart
• Large and negative  crunches the Universe too soon
Weinberg
Is the weak scale determined by “selection”?
Are fermion masses determined by “selection”?
Will these ideas impact our approach to the final theory?
The LHC will address this question!
SPLIT SUPERSYMMETRY abandons the
hierarchy problem, but uses unification & DM
93
CONCLUSIONS
LHC will soon begin operation:
Unveiling the mechanism of EW breaking
Higgs?
Unconventional Higgs?
Alternative dynamics?
If Higgs is found,
New physics at EW scale curing the UV
sensitivity? (many theoretical options,
none of which is free from tuning)
New principle in particle physics?
94