EXTRA DIMENSIONS

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EXTRA DIMENSIONS IN PARTICLE
PHYSICS
Ferruccio Feruglio
EPS conference Aachen, July 2003
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SET-UP
brane
in the 1st part of this talk
bulk
length
length
volume
only gravity is admitted to the bulk (few
exceptions)
KK modes graviton momentum along ED is
quantized in units of 1/R. To the 4D observer,
gravitons come in infinite copies with 4D masses
n/R (a tower)
warped geometry branes can carry some energy
density and, by the laws of GR, they may warp
the space-time geometry.
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particles
full space-time metric in D 4?
contains
KK modes
4D graviton
and its
radion
one combination of specifies the
volume of the extra space e.g. ? 1
much as
other particles, specifying the shape of the ES
or the fluctuations of the brane, can be present
(not covered by this review)
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General motivation
unification of gravity with other fundamental
interactions Kaluza-Klein (1919-1926), still
valid today. String theories, candidates for a
unified description of all interactions, are
formulated in D 10 (or D 11)
specific motivations
1. Hierarchy problem
2. little hierarchy problem
3. flavour problem
4. problems of conventional GUTs
5. cosmological constant
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HIERARCHY PROBLEM
(L0 here)
there is only one fundamental scale in D4?
dimensions
all KK gravitons contribute
Arkani-Hamed, Dimopoulos, Dvali Antoniadis
only the 4D graviton zero mode contributes
4D gravity is weak because the graviton wave
functions is diluted in a big volume.
.
Now we should explain why
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excluded R Sun-Earth distance
of special interest sizeable deviations from
Newton law
clearly allowed
KK graviton states can be produced - at
colliders - in processes of astrophysical and/or
cosmological relevance
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Sub-mm tests of gravity
we expect
degeneracy of the 1st KK level
wavelength of the 1st KK mode
EOT-WASH ex/0202008
Further improvements are an experimental
challenge!
important deviations in this range are expected
also in other scenarios (more on this later on)
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FLAVOUR I ? and LED

• LED provide a nice argument for the smallness of
  ? masses
• standard Yukawa couplings to a singlet fermion
  who lives in the bulk

originates from
Dienes, Dudas, Gherghetta, Arkani-Hamed,Dimopoulos
, Dvali, March-Russell, Barbieri, Creminelli,
Strumia
can we test this idea?
if some states are sufficiently light
(not unconceivable R 0.02 mm)
then, few might take part in ??
oscillations
but
large mixing angles between and
are excluded (SN1987A)
oscillations into disfavoured by both
atmospheric and solar ? data
effects subdominant, if present
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reviews Cheung Hewett, Spiropulu
Sanders this conf.
Collider bounds on LED
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KK graviton production in association with a ?
or a jet
rescued by the very large phase space
single KK production
combined 95 CL limits on from LEP
and Tevatron
Giudice, Strumia
2
virtual graviton exchange
sensitive to UV physics divergent amplitudes
already at the tree-level for parametrized in
terms of effective operators (or computed in
string theory)
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energy-momentum tensor
d8 (tree-level)
d6 (one-loop)
Y is C-even and singlet under all gauge and
global symmetries (flavour universal)
Chang, Lebedev, Loinaz, Takeuchi
No more d?8 operators from fermion-gauge boson
sectors alone
Giudice, Strumia
present 95 CL limits
dilepton (LEP) diphoton (Tevatron)
(Hera)
cut-off scale
contact interaction (LEP) dijet, Drell-Yan
(Tevatron)
(Hera)
If, naively, then Y gives the
strongest bound on
remember GIM where
otherwise
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Limits on from astrophysics (in
TeV)
Hannestad, Raffelt
they are the strongest limits on fundamental
scale
bounds rapidly soften for higher ??
They rely on the (essentially) gapless spectrum
of KK gravitons
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cosmology reminder
The universe has a standard evolution up to
temperatures of order
above the cooling proceeds mainly by
bulk graviton production (instead of standard
adiabatic expansion) ?2 barely consistent with
BBN
such a low makes inflation and
baryogenesis problematic

both astrophysical and cosmological problems are
eliminated if the spectrum of KK gravitons has a
sufficient gap
for instance
evades all the astrophysical bounds
of present hottest
astrophysical object
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How can we make ?
1. KK spectrum also depends on the shape of ES,
not just from R
Dienes
2. New relation between and
due to warped geometry
in RS set-up the branes carry some energy
density and this warps the surrounding ST
in a loose sense, since V cannot be precisely
defined
Randall, Sundrum
if a large
can be obtained with a natural
KK modes are now at and
astrophysical and cosmological bounds do not apply
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collider phenomenology
radion
KK gravitons
(unevenly spaced)
large anomalous coupling to gluons. At hadron
colliders - production mainly through gluon
fusion - decay into dijet or into ZZ if kin.
allowed (similar to Higgs. Indeed radion-Higgs
mixing possible) no significant bound
from present data
resonance enhancements at hadron colliders in
Drell-Yan processes a portion of the parameter
space already probed by Tevatron
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Up to now
SM fields confined on a brane having vanishing
width
strong and e.w. interactions successfully tested
only up to
a part of (or allUED) the SM fields might live
in a sized ED
motivations for
early SUSY breaking via compactification
Antoniadis
more recently solutions to the little
hierarchy problem
indirect evidence for a gap between the Higgs
mass and the EW symmetry breaking scale
EW precision tests ? search for
new physics
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LITTLE HIERARCHY PROBLEM
from the solution to the big hierarchy
problem finite corrections controlled by the
mass of some new particle
from EWPT
or even
lighter expected (think, for instance to the
chargino in constraint MSSM)
new light weakly interacting particles not seen
in either direct searches or in EWPT
modest gap (factor 10) can be filled
1. by a moderate fine-tuning of the parameters in
the underlying theory
2. by looking to specific theories where this gap
is natural
in ED with

• can be protected by either
• SUSY or
• - gauge symmetry

new states are expected at the TeV scale
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Pomarol, Quiros Barbieri, Hall, Nomura
Ghilencea, Groot Nibbelink, Nilles Scrucca,
Serone, Silvestrini, Zwirner,
1. SUSY
broken by boundary conditions on an interval of
size L
EWSB triggered by the top Yukawa couplings
is finite and calculable in terms of 2
parameters (L,M)
including two-loop
corrections
Barbieri, Marandella, Papucci
characteristic spectrum
mild experimental bounds momentum conservation
along ED preserved by gauge interactions as in UED
Appelquist, Cheng, Dobrescu
- no single KK mode production - no 4f operators
from tree-level KK exchange
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2. gauge symmetry Higgs-gauge unification
Manton 1979
Yang-Mills theory in Dgt4 gauge group G
4D vector bosons
4D scalars
D gauge vector bosons
Example G SU(3)
(8 independent generators)
unseen
unseen
we can eliminate the unseen by compactification
on an orbifold
all fields required to have a well-defined
parity
the unseen states have no zero modes because
they are odd
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4D viewpoint SU(2)xU(1) gauge symmetry 1 Higgs
doublet
Csaki, Grojean, Murayama Burdman, Nomura
general problems
solutions

• - large corrections from branes
• at y0,L
• choose the right group
• e.g.

Higgs embedding Y(H)1/2 usually leads to wrong
D5 from D-terms if SUSY D?6
includes Higgs self-interactions
Higgs self-coupling for EWSB
key feature residual gauge symmetry
absence of quadratic divergences from gauge
sector (crucial)
D5 forbidden D6 absent in specific models
Von Gersdorff, Irges, Quiros
realistic Yukawa couplings interactions of H are
universal if minimally coupled
Wilson lines
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and here
we put fermions here
Csaki, Grojean, Murayama Scrucca, Serone,
Silvestrini
invariant under both local
and residual gauge transformations
however may reintroduce quadratic
divergences for at 1 or 2 loops
features

• naturally light Higgs boson
• KK gauge vector bosons of an extended group G
• not necessarily KK replica for fermions

remarkable progress towards a realistic model in
the last year!
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FLAVOUR II
In ED we have a new tool to understand fermion
mass hierarchy geometry
examples
D.B. Kaplan, Arkani-Hamed, Schmaltz, Mirabelli
generations are copies in ED. FS broken by a
non-trivial Higgs VEV
Dvali, Shifman
several generations may arise as independent zero
modes of a single higher-dimensional fermion.
Troitsky, Libanov, Nougaev, Frere Biggio,
Feruglio, Masina, Perez-Victoria
related to the properties of
compactification mechanism unexplained
in D4!
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can we test these ideas?
most stringent bounds from FCNC
Del Aguila, Santiago Delgado, Pomarol, Quiros
Lillie, Hewett,
KK modes of gauge bosons have non-constant
wave functions
after rotation from flavour basis to mass
eigenstate basis
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Sub-mm gravity (again)
all previous statements assume that some dynamics
stabilizes the radion at the right scale
in explicit models of weak scale
compactification (not a theorem)
Chacko, Perazzi
radion coupling to matter m gravity-like
observable deviations from Newtons law at 100
?m even for
Kolb, Servant, Tait
radion becomes cosmologically active if
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generic problems of ED models with cut-off scale
potentially large corrections to EW observables,
conflict with EWPT
how can we understand approximate B and L
conservation?
B L violating operators dgt4 are
allowed by known low-energy symmetries
suggest
gauge coupling unification
SUSY 1-loop LO

• the running is log
• high sensitive to light particle content
• unification conditions
  at

2-loop, thresholds
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approximate B L conservation gauge coupling
unification
natural within UV desert
possible, but not a generic feature of IR desert
problematic if
especially if complemented by a Grand Unified
picture where
- particle classification clarified
- unification condition automatic
at
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GRAND UNIFICATION AND ED
Urgent problems of conventional 4D GUTs
The Problem DT splitting

• - fine-tuned in minimal models
• baroque Higgs structure in non-minimal ones
• usually spoiled by radiative corrections after
  SUSY breaking
• or by non-renormalizable operators

Altarelli, Feruglio, Masina
p-decay
Hisano, Murayama, Yanagida Goto, Nihei
minimal SUSY SU(5) predictions
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both solved if GSU(5) is broken by
compactification
in SUSY version additional states and one more
parity
the zero modes of can be removed by
appropriate parity assignment
if then, for a 4D observer
SU(5) does not exist in 4D!
and parities fixed from
gauge sector
AUTOMATIC DT SPLITTING
Kawamura
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p-decay
Altarelli, Feruglio Hebecker, March-Russel
d5 operators arise from a mass
term
such a term is forbidden by a U(1) symmetry
characteristic of the bulk action and
extendible to the whole theory
no d5 (and d4) p-decay
Hall, Nomura
gauge coupling unification preserved
Hall, Nomura Contino, Pilo, Rattazzi, Trincherini
testp-decay dominated by d6 operators
Hebecker, March-Russel Hall, Nomura
uncertainties mixing angles and c no
uncertainties from SUSY breaking
brane coupling
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cosmological constant ? and ED
Two problems
1. why ? is nearly zero?
2. cosmic coincidence why
now?
(nothing to say about this here)
massless graviton universally coupled to all
sources
1.
4D general covariace
then vacuum energy curves our space-time
this is what we measure
in Dgt4 this is not necessarily true ? can curve
the ED space leaving our space flat
this might occur if depends on the
wavelength of the source
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wavelength ?
coupling
standard cosmology
vacuum energy is the source with the largest
wavelength a large ?? does not curve our 4D space
time
Dvali, Gabadadze, Porrati Dvali, Gabadadze,
Shifman
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here ED are infinite ,
otherwise a massless 4D graviton exists
one testable prediction
gravity modified below departure from Newton
potential at the sub- mm scale expected
above gravity
becomes strong and should be soften e.g. by
string theory (production of Regge states)
The fine-tuning is not eliminated
but the hierarchy becomes stable
- effective field theory necessitates careful
treatment
Rubakov, Luty, Porrati, Rattazzi
- closely related picture derivable from string
theory
Antoniadis, Minasian, Vanhove
Sundrum Arkani-Hamed, Dimopoulos, Dvali, Gabadadze
- related approaches
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Laurels beckoned us, so we started out With
Nightingale towards a mountain height. While I
grappled with the sheer cliffs below, She seized
her prize in easy, graceful flight.
What I may perhaps never ever
reach, Took but a brief
moment for the bird O
Heaven don't be so unjust, I plead,
Grant me wings too. Let my prayer be
heard.


Roland von Eotvos