Diapositiva 1

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A new dark matter candidate in low
tension brane-worlds
J.A.R
Cembranos, A. Dobado and A.L. Maroto.
Departamento de Física Teórica
Universidad Complutense de Madrid
28040
Madrid, Spain
Vietnam 2004 5th Rencontres du VietNam Hanoi
August 5 to August 11, 2004

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Extra dimensions and Brane Worlds
The Dark Matter problem
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The main motivations for considering extra
dimensions have a
theoretical origin
In the last thirty years virtually any new
development in theoretical physics required
the introduction of
extra dimensions
Modern Kaluza-Klein theories Supersymmetry
and supergravity Superstrings M-theory
PS The only important exceptions are GUTs but
still the most intersting from the
phenomenological point of view are the SUSY ones,
ie. the ones producing gauge coupling unification
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The first attempts to extend general relativity
to include electromagnetism date back to Theodor
Kaluza (1914) and Oscar Klein (1926) and other
people.
11D SUGRA produced a revival of the KK ideas in
the early 80s
The first string revolution of the 80s traslated
the interest to 10D with 6D compactified spaces
(Calabi-Yau, orbifolds...)
The second string revolution of the 90s
introduced new ideas such as non-perturbative
strings, dualities, branes and string
theories unification, i.e. the so called M-theory
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The main phenomenological problem of the old
string theories is that they could not be tested
since stringy effects were expected to appear at
the Planck scale
Mp 10 000 000 000 000 000 000 GeV
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However the new ideas coming from M-theory have
inspired new scenarios that could be testable.
These scenarios were developed to address the
hierarchy problem.
The first one was proposed by Arkani-Hamed,
Dimopoulos and Dvali (ADD)
The main idea is that our universe is 3-brane
living in a higher D4d dimensional space (the
bulk space) being the extra dimensions
compactified to some small volume (Brane World).
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In this picture the Standard model particles are
confined to the 3-brane but gravitons can
propagate along the whole bulk space.
graviton
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Now the fundamental scale of gravity is not the
Planck scale any more but another scale MD which
is supposed to be of the order of the electroweak
scale in order to solve the hierarchy problem
Then the following relation is found
The hierarchy between the Planck and the
electroweak scale is generated by the large
volume of the extra dimensions.
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The size R of the extra dimensions ranges from a
fraction of mm for d2 to about 10 Fermi for d6
There are also scenarios where the scale of the
extra dimensions is of the order of (1 TeV) -1.
Then all or some of the SM particles can
propagate along the bulk. This set up is quite
appropriate for model building and to deal with
gauge coupling unification, SUSY breaking,
neutrino spectrum, fermion masses and many other
things. (Antoniadis, Quirós...)
PS There are also scenarios where the hierarchy
is generated by the curvature of the extra
dimension. For example the Randall-Sumdrum (RS)
model where the geometry of the space-time is
AdS(5) and thus cannot be factorized
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The most interesting property of the ADD scenario
is that it is compatible with the present
experimental data but it gives rise to many new
phenomena that could be tested in the near future
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Is our universe a 3-brane?
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First we have the Newtons Law modified at short
distances
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From the point of view of particle physics the
main new effects in the ADD scenario are related
to the KK mode expansion of the bulk gravitons
31 dimensional coordinates
extra dimensions coordinates
M(n) n /R
KK tower of gravitons
D M 1 /R
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We expect two kind of effects from this KK tower
of massive gravitons
Graviton production
Virtual effects
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The rates for the different processes can be
computed by linearizing the bulk gravitational
field
Gravitons couple to the energy-momentum tensor of
the SM
Expanding the gravitational field in terms of the
KK modes one finds the Feynman rules
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To compute the total cross-section we sum
(integrate) over all the KK gravitons
( Mirabelli, Perelstein and Peskin)
The total cross-section is suppressed by powers
of MD which is supposed to be of the order of 1
TeV
The signature of these events is missing energy
with continuous spectrum
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Virtual effects can be taken into account by
considering the KK tower propagator
However there are divergences for more than one
extra dimension, even at the tree level, that
require regularization
This fact has given rise to the development of
the so called deconstructing or aliphatic idea
where the extra dimensions are latticed
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Nevertheless there is a more physical way to deal
with this problem. So far we have assumed that
the world-brane is completely rigid, i.e. it has
infinite tension.
However rigid objects does not exist in
relativistic theories.
When brane oscillations are taken into account
two new effects appear. First of all we have to
introduce new fields which represent the
position of the brane in the bulk space.
These fields are the Goldstone bosons
corresponding to the spontaneous symmetry
breaking of the translation invariance produced
by the presence of the brane (branons).
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In general the recoil of the brane produces an
effective coupling of the SM fields on the brane
with the bulk fields given by
(Bando, Kubo, Noguchi and Yoshioka)
Integrating out the GB fields
Therefore for small brane tension f ltlt MD the
KK modes decouple from the SM particles on the
brane
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Then for gravitons or any other bulk field
coupled to fermions on the brane we have
where
and is the brane tension. This solves
the divergence problem
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The conclusion is that for flexible branes ( f
ltlt MD) the only relevant degrees of freedom at
low energies in the ADD scenario are the SM
particles and the branons
SM particles
branons
As GB branons are expected to be nearly massless
and weakly interacting at low energies (compared
with f), and their interac tions can be described
by an effective lagrangian
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Lower dimensional example
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Induced metric on the brane
Bulk metric
Branon fields
Killing vectors corresponding to translations on
B
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Thus the induced metric is

branon fields
Where the coset metric is
and
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At low energies the dominant term in the brane
action is the Nambu-Goto term
So that we get
This is a NLSM defined on the coset K or
equivalently on the compact space B
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Higher derivative corrections can be obtained in
a systematic way by expanding the induced metric
Thus we obtain a sort of chiral lagrangian with
well defined chiral parameters (A.L. Maroto, J.A.
Cembranos and A.D.)
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In addition, for non factorizable spaces, which
are the generic ones, we can generate branon
masses
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The interaction of the branons with the SM
particles is given by
As in the case of the gravitons the branons
couple to the SM energy momentum tensor (Sumdrum,
Creminelli and Strumia)
Branons are massive, stable, weakly interacting
and are produced by pairs.
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From the corresponding Feynman rules it is
possible to compute any cross section for branon
production in terms of 3 parameters
N number of branons M branon mass f brane
tension scale
For example LC
The experimental signature would be one single
photon (or Z) and missing energy and momentum
since branons will not be detected
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For hadron colliders
Photon and Z production
Quark production
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Gluon production
The experimental signature would be one single
photon (or Z) or one monojet plus missing energy
and momentum
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PRESENT COLLIDER CONSTRAINTS
TEVATRON I
LEP II (L3)
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EXPECTED ACCESIBLE REGIONS IN FUTURE HADRON
COLLIDERS
TEVATRON II
LHC
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Branons are stable, weakly interacting
and massive

Natural WIMP candidates
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COSMOLOGICAL STANDARD MODEL
Homogeneity and isotropy ds2 dt2 - a2(t)
dr2/(1-kr2) r2(d?2 sin2? d?2)
Einstein equations H2 (t) (a/a)2 (8pG/3)
r - k / a2 k -1,0,1
W k - k /(a)2 W m rm / rc
W L L / rc rc 3H2(t) /
8pG
Wtot 1.020 .02 WL 0.730. 04
W DM 0.230. 04 W BaryonicMatter
0.044 0. 004
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ROTATION CURVES
Fritz Zwicky found a little deficit of the 98
in the mass by observing orbital speeds around
galaxies (1933)
Centripetal Gravitational acceleration
acceleration
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RELIC DENSITY
dni/dt -3Hni - lt sAv gt(ni)2- (nieq)2
Thermal equilibrium density nieq g/(2p)3 ?
f(p) d3p
When ?ltsAvgtni ltH , the DM is frozen out
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THE PARAMETER SPACE FOR COSMOLOGICAL BRANONS

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DIRECT DM SEARCHES
WIMPs scatter elastically with nuclei
nuclear recoil

• Detecting WIMPs by measuring the recoiling
  energy spectrum in the target

v/c ? 10-3
Direct interaction of the DM halo WIMPS with the
detector could make a nucleus recoil with
EK1-100 keV.
The rate of the WIMP interactions depends on the
local DM density and the relative WIMPs velocity .
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WIMP SEARCHES CONSTRAINTS ON BRANON PARAMETERS

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Conclusions
Brane-world scenarios are inspired on modern
string (M) theory and offer new insights on many
fundamental problems in particle physics.
If the fundamental gravitational scale MD is of
the order of 1 TeV gravitons can be produced in
future colliders as the LHC or LC.
In the limit MD gtgt f the only relevant modes
in the BW scenarios are the SM particles and the
branons. The branon production rates can be
determined in a model independent way in terms
of the brane tension.
Branons could be produced in colliders such as
the LHC and their properties studied in detail in
a future LC
Massive branons are natural candidates for dark
matter in ADD models. Present constraints are
consistent with this hypothesis and direct WIMP
search experiments will be able to test this
possibility in the near future.
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Thank you very much for your attention