Extra dimensioni e la fisica elettrodebole

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Extra dimensioni e la fisica elettrodebole
G.F. Giudice
Napoli, 9-10 maggio 2007
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SPACE DIMENSIONS AND UNIFICATION
Minkowski recognized special relativistic
invariance of Maxwells eqs ? connection between
unification of forces and number of dimensions
Electric magnetic forces unified in 4D space
time
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UNIFICATION OF EM GRAVITY
Next step
? 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 1919 mathematician Theodor Kaluza
writes a 5-dim 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 In the 80s the theory, known
as Kaluza-Klein becomes popular with supergravity
and strings
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GRAVITY
In General Relativity, metric (4X4
symmetric tensor) dynamical variable describing
space geometry (graviton)
Dynamics described by Einstein action

• GN Newtons constant
• R curvature (function of the metric)

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Consider GR in 5-dim
Choose
Dynamical fields
Assume space is M4?S1

• First considered as a mathematical trick
• It may have physical meaning

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All fields can be expanded in Fourier modes
From KK mass spectrum we can measure the geometry
of extra dimensions
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Suppose typical energy ltlt 1/R ? only zero-modes
can be excited
Expand SG keeping only zero-modes and setting ?1
To obtain correct normalization
Gravity EM unified in higher-dim space
MIRACLE?
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Gauge transformation has a geometrical meaning
Keep only zero-modes

• Gauge transformation is balanced by a shift in
  5th dimension
• EM Lagrangian uniquely determined by gauge
  invariance

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CHARGE QUANTIZATION
Matter EM couplings fixed by 5-dim GR Consider
scalar field ?
Expand in 4-D KK modes
Each KK mode n has mass n/R charge n?/R

• charge quantization
• determination of fine-structure constant
• new dynamics open up at Planckian distances

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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?

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Usual approach fundamental theory at MPl, while
?W is a derived quantity Alternative ?W is
fundamental scale, while MPl is a derived effect
We are confined in a 4-dim world, which is
embedded in a higher-dim space where gravity can
propagate
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COMPUTE NEWTON CONSTANT
Einstein action in D dimensions
Assume space R4?SD-4 g?? doesnt depend on extra
coordinates
Effective action for g??
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Suppose fundamental mass scale MD TeV
very large if R is large (in units of MD-1)
Arkani-Hamed, Dimopoulos, Dvali
Radius of compactified space

• 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 RMDgtgt1

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Gravitational interactions modified at small
distances
At r lt R, space is (3?)-dimensional (?D-4)
?
From SN emission and neutron-star heating MDgt750
(35) TeV for ?2(3)
?
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Testing extra dimensions at high-energy colliders
Probability of producing a KK graviton
Number of KK modes with mass less than E (use
mn/R)
Inclusive cross section
It does not depend on VD (i.e. on the Planck
mass) Missing energy and jet with characteristic
spectrum
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Contact interactions from graviton exchange

• Sensitive to UV physics
• d-wave contribution to scattering processes
• predictions for related processes
• Limits from Bhabha/di-? at LEP and Drell-Yan/
  di-? at Tevatron ?T gt 1.2 - 1.4 TeV

• Loop effect, but dim-6 vs. dim-8
• ??only dim-6 generated by pure gravity
• ?? gt 15 - 17 TeV from LEP

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TRANSPLANCKIAN REGIME
G-emission is based on linearized gravity, valid
at s ltlt MD2
Planck length
quantum-gravity scale
classical gravity
Schwarzschild radius
same regime
The transplanckian regime is described by
classical physics (general relativity) ?
independent test, crucial to verify gravitational
nature of new physics
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Gravitational scattering
Non-perturbative, but calculable for bgtgtRS (weak
gravitational field)
D-dim gravitational potential
Quantum-mechanical scattering phase of wave with
angular momentum mvb
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Gravitational scattering in extra dimensions
two-jet signal at the LHC
Diffractive pattern characterized by
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At bltRS, 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 MBH6 TeV and MD1.5
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 MD1 TeV)
Characteristic events with large multiplicity
(ltNgt MBH / ltEgt (MBH / MD)(?2)/(?1)) and
typical energy ltEgt TH
Transplanckian condition MBH gtgt MD ?
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WARPED GRAVITY
A classical mechanism to make quanta softer
For time-indep. metrics with g0?0 ? E g001/2
conserved .
(proper time d?2 g00 dt2)
On non-trivial metrics, we see far-away objects
as red-shifted
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Consider observer emitter as 3-d spaces
(branes) embedded in non-trivial 5-D space-time
geometries
Randall Sundrum
5th dim S1 / Z2 identify y ? y2?R,
y ? -y
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GRAVITATIONAL RED-SHIFT
Masses on two branes related by
Same result can be obtained by integrating SE
over y
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PHYSICAL INTERPRETATION

• Gravitational field configuration is non-trivial
• Gravity concentrated at y0, 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
• KK gravitons have large mass gap and are
  strongly coupled
• Clean signal at the LHC from G ? ll-

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Spin 2
Spin 1
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A SURPRISING TWIST
AdS/CFT correspondence relates 5-d gravity with
negative cosmological constant to
strongly-coupled 4-d conformal field theory
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,
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What screens the Higgs mass?
Symmetry
Dynamical EW breaking
Delayed unitarity violat.
Fundamental scale at TeV
Dynamics

• Very fertile field of research
• Different proposals not mutually excluded

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It is a problem of naturalness, not of
consistency!
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HIGGS AS PSEUDOGOLDSTONE BOSON
Gauge, Yukawa and self-interaction are
non-derivative couplings _Violate global symmetry
and introduce quadratic divergences
If the scale of New Physics is so low, why do LEP
data work so well?
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A less ambitious programme solving the little
hierarchy
Bounds on ? TeV
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LITTLE HIGGS
Explain only little hierarchy At LSM new
physics cancels one-loop power divergences
Collective breaking many (approximate) global
symmetries preserve massless Goldstone boson
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• It can be achieved with gauge-group replication
• Goldstone bosons in
• gauged subgroups, each
  preserving a non-linear global symmetry
• which breaks all
  symmetries
• Field replication Ex. SU2 gauge with F1,2
  doublets such that V(F1F1,F2F2) and F1,2
  spontaneously break SU2
• Turning off gauge coupling to F1 _
• Local SU2(F2) global SU2(F1) both spont. broken

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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 ?)
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New states have naturally mass
New states cut-off quadratically divergent
contributions to mH
Ex. littlest Higgs model
analogous to effect of stop loops in supersymmetry
Log term
Severe bounds from LEP data
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TESTING LITTLE HIGGS AT THE LHC

• Discover new states (T, W, Z, )
• Verify cancellation of quadratic divergences

f from heavy gauge-boson masses mT from T
pair-production ?T we cannot measure TThh
vertex (only model-dependent tests possible)
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f and gH from DY of new gauge bosons

Production rate and BR into leptons in region
favoured by LEP (gHgtgtgW)
Can be seen up to ZH mass of 3 TeV
MT from T production can be measured up to 2.5 TeV
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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 lt 2.5 TeV and mZ lt 3 TeV
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HIGGS AS EXTRA-DIM COMPONENT OF GAUGE FIELD
NEW INGREDIENTS FROM EXTRA DIMENSIONS
AM (Am,A5), A5 g A5 ?5 L forbids
m2A52
Higgs/gauge unification as graviton/photon
unification in KK
Correct Higgs quantum numbers by projecting out
unwanted states with orbifold The difficulty is
to generate Yukawa and quartic couplings without
reintroducing quadratic divergences
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HIGGSLESS MODELS
Breakdown of unitarity
The gauge KK modes delay unitarity violation
New ways of breaking gauge symmetries
no zero modes in restricted extra-D spaces
(Scherk-Schwarz mechanism)
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Scherk-Schwarz breaking
A field under a 2?R translation has to remain the
same, unless there is a symmetry (the field has
to be equal up to a symmetry transformation)
No more zero-modes!
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At the LHC discover KK resonances of gauge bosons
and test sum rules on couplings and masses
required to improve unitarity
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DUALITY
SM in warped extra dims ? strongly-inting 4-d
theory KK excitations ? hadrons of new strong
force Technicolor strikes back?
5-D gravity 4-D gauge theory Motion
in 5th dim RG flow UV brane
Planck cutoff IR brane
breaking of conformal inv. Bulk local symmetries
global symmetries
AdS/CFT
? Composite Higgs
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Technicolor-like theories in new disguise Old
problems
The presence of a light Higgs helps

• Light Higgs screens IR contributions to S and T
• (f pseudo-Goldstone
  decay constant) Can be tuned small for strong
  dynamics 4?f at few TeV

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Structure of the theory
Communicate via gauge (ga) and (proto)-Yukawa
(?i)
m??????mass of resonances g??coupling of
resonances
Strong sector characterized by
Take ?I, ga ltlt g??lt 4?
In the limit ?I, ga 0, strong sector contains
Higgs as Goldstone bosons Ex. H
SU(3)/SU(2)?U(1) or H SO(5)/SO(4) ?-model with
f m???/ g??
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ga , ?i break global symmetry ? Higgs mass New
theory addresses hierarchy problem ? reduced
sensitivity of mH to short distances (below m?-1)

• Ex.
• Georgi-Kaplan g?4?, f v, no separation of
  scales
• Holographic Higgs g? gKK, m? mKK
• Little Higgs g?, m??couplings and masses of new
  t, W, Z

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Production of resonances at m? allows to test
models at the LHC Study of Higgs properties
allows a model independent test of the nature of
the EW breaking sector Is the Higgs
composite? Holographic Higgs Gauge-Higgs
unification Little Higgs
fundamental? SM (with mH lt 180 GeV) supersymmetry
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Construct the Lagrangian of the effective theory
below m?

• From the kinetic term, we obtain the definition
  of f m? / g?
• ?Each extra H insertion gives operators
  suppressed by 1 / f
• Each extra derivative
  1 / m?

f symmetry-breaking scale m? new-physics
mass threshold

• Operators that violate Goldstone symmetry are
  suppressed by corresponding (weak) coupling

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Operators testing the strong self coupling of the
Higgs (determined by the structure of the ? model)
? and yf are SM couplings ci model-dependent
coefficients
Form factors sensitive to the scale m?
Loop-suppressed strong dynamics
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Effects in Higgs production and decay
All Higgs couplings rescaled by
Modified Higgs couplings to matter
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Dührssen 2003
SLHC Report 2002
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LHC can measure cHv2/f2 and cyv2/f2 up to
20-40 SLHC can improve it to about 10 A
sizeable deviation from SM in the absence of new
light states would be indirect evidence for the
composite nature of the Higgs ILC can test v2/f2
up to the level
ILC can explore the Higgs compositeness scale 4?f
up to 30 TeV
ECFA/DESY LC Report 2001
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• Effective-theory approach is half-way between
  model-dependent and operator analyses
• Dominant effects come from strong self-Higgs
  interactions characterized by
• From operator analyses, Higgs processes
  loop-suppressed in SM are often considered most
  important for searches
• However, operators h??? and h?gg are suppressed
  1/(16?2m?2)
• Since h is charge and color neutral, gauging
  SU(3)c?U(1)Q does not break the generator under
  which h shifts (Covariant derivative acting on h
  does not contain ? or g)
• Not the case for h??Z (loop, but not
  1/g???suppressed)

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Higgs decay rates
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Genuine signal of Higgs compositeness at high
energies In spite of light Higgs, longitudinal
gauge-boson scattering amplitude violate
unitarity at high energies
LHC with 200 fb-1 sensitive up to cH? ?0.3
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Higgs is viewed as pseudoGoldstone boson its
properties are related to those of the exact
(eaten) Goldstones O(4) symmetry
Strong gauge-boson scattering ? strong Higgs
production
Can bbbb at high invariant mass be separated from
background? h ? WW ? leptons is more promising
Sum rule (with cuts ??????and sltM2)
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In many realizations, the top quark belongs to
the strongly-coupled sector
At leading order in 1/f2
Modified top-quark couplings to h and Z
At ILC ghtt up to 5 with ?s800 GeV and L1000
fb-1 From gZtt, ?cR 0.04 with ?s500 GeV and
L300 fb-1
FCNC effects