hanoi, vietnam 2004antonio dobado1 a new dark matter candidate in low tension brane-worlds j.a.r...

Hanoi, VietNam 2004Hanoi, VietNam 2004 Antonio DobadoAntonio Dobado 11

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 20045th Rencontres du VietNam

Hanoi August 5 to August 11, 2004


Extra dimensions and Brane Worlds

The Dark Matter problem


The main motivations for considering extra dimensions have a theoretical origin

* Modern Kaluza-Klein theories* Supersymmetry and supergravity* Superstrings* M-theory

PS: The only important exceptions are GUT’s but still the most intersting from the phenomenological point of view are the SUSY ones, ie. the ones producing gauge coupling unification

In the last thirty years virtually any new development in theoretical physics required the introduction of extra dimensions


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 80’s

The first string revolution of the 80’s traslated the interest to 10D with 6D compactified spaces (Calabi-Yau, orbifolds...)

The second string revolution of the 90’s introduced new ideas such asnon-perturbative strings, dualities, branes and string theoriesunification, i.e. the so called M-theory


The main phenomenological problem of the old string theoriesis 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


However the new ideas coming from M-theory have inspirednew scenarios that could be testable.

These scenarios were developed to address the hierarchyproblem.

The first one was proposed by Arkani-Hamed, Dimopoulos andDvali (ADD)

The main idea is that our universe is 3-brane living in a higherD=4+ dimensional space (the bulk space) being the extradimensions compactified to some small volume (Brane World).


In this picture the Standard model particles are confined to the3-brane but gravitons can propagate along the whole bulk space.

graviton


Now the fundamental scale of gravity is not the Planck scaleany more but another scale MD which is supposed to be of theorder of the electroweak scale in order to solve the hierarchyproblem

Then the following relation is found

The hierarchy between the Planck and the electroweak scale isgenerated by the large volume of the extra dimensions.


The size R of the extra dimensions ranges from a fraction of mm for =2 to about 10 Fermi for =6

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 thecurvature of the extra dimension. For example the Randall-Sumdrum (RS) model where the geometry of the space-time is AdS(5) and thuscannot be factorized


The most interesting property of the ADD scenario is that it is compatible with the present experimental data but it gives riseto many new phenomena that could be tested in the near future


Is our universe a 3-brane? Is our universe a 3-brane?


First we have the Newton’s Law modified at short distances


From the point of view of particle physics the main neweffects in the ADD scenario are related to the KK modeexpansion of the bulk gravitons

3+1 dimensional coordinates

extra dimensions coordinates

M(n)= n /RKK tower of gravitons

M= 1 /R


We expect two kind of effects from this KK tower of massivegravitons

Graviton production Virtual effects


The rates for the different processes can be computed bylinearizing 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


To compute the total cross-section we sum (integrate) over allthe KK gravitons

The total cross-section is suppressed by powers of MD which issupposed to be of the order of 1 TeV

The signature of these events is missing energy with continuousspectrum

( Mirabelli, Perelstein and Peskin)


Virtual effects can be taken into account by considering theKK 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 calleddeconstructing or aliphatic idea where the extra dimensionsare latticed


Nevertheless there is a more physical way to deal with thisproblem. So far we have assumed that the world-brane iscompletely 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 effectsappear. 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 invarianceproduced by the presence of the brane (branons).


In general the recoil of the brane produces an effective couplingof 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 << MD the KK modes decouple from the SM particles on the brane


Then for gravitons or any other bulk field coupled to fermionson the brane we have

where

and is the brane tension. This solves the divergence problem


SM particles branons

The conclusion is that for flexible branes ( f << MD) the onlyrelevant degrees of freedom at low energies in the ADD scenarioare the SM particles and the branons

As GB branons are expected to be nearly massless and weaklyinteracting at low energies (compared with f), and their interactions can be described by an effective lagrangian


Lower dimensional example


Branon fields

Killing vectors corresponding to translations on B

Induced metric on the brane

Bulk metric


Thus the induced metric is

Where the coset metric is

branon fields

and


At low energies the dominant term in the brane action is theNambu-Goto term

So that we get

This is a NLSM defined on the coset K or equivalently onthe compact space B


Higher derivative corrections can be obtained in a systematicway by expanding the induced metric

Thus we obtain a sort of chiral lagrangian with well definedchiral parameters (A.L. Maroto, J.A. Cembranos and A.D.)


In addition, for non factorizable spaces, which are the generic ones, we can generate branon masses


The interaction of the branons with the SM particles is given by

As in the case of the gravitons the branons couple to the SMenergy momentum tensor (Sumdrum, Creminelli and Strumia)

Branons are massive, stable, weakly interacting and are produced by pairs.


From the corresponding Feynman rules it is possible to compute any cross section forbranon production in terms of 3 parametersFor example: LC N: number of branons

M: branon massf: brane tension scale

The experimental signature would be one single photon (or Z) and missing energy and momentum since branons will not be detected


For hadron colliders:

Photon and Z production Quark production


The experimental signature would be one single photon (or Z) or one monojet plus missing energy and momentum

Gluon production


PRESENT COLLIDER CONSTRAINTSPRESENT COLLIDER CONSTRAINTS

LEP II (L3)

TEVATRON I


TEVATRON II

EXPECTED ACCESIBLE REGIONS IN FUTURE HADRON COLLIDERSEXPECTED ACCESIBLE REGIONS IN FUTURE HADRON COLLIDERS

LHC


Branons are stable, weakly interacting and massive

Branons are stable, weakly interacting and massive

Natural WIMP candidatesNatural WIMP candidates


COSMOLOGICAL STANDARD MODEL

Homogeneity and isotropy: ds2 = dt2 - a2(t) [dr2/(1-kr2) + r2(d2 + sin2 d2)]

Einstein equations:

H2 (t) =(a’/a)2 = (8G/3) k / a2 k = -1,0,+1

k

= - k /(a’)2

m =

m / c

= / c

c = 3H2(t) / 8G

0.73±0.

04

0.0003

<0.0147

Non Baryonic

<0.23 ± 0.04

Spatial curvature:

k=0.02 ± 0.02

H0.039

S0.005

tot

= 1.02±0 .02

0.73±0. 04

DM = 0.23±0. 04

BaryonicMatter

0.044 ±0. 004


Solar System

ROTATION CURVES

Fritz Zwicky found a “little” deficit of the 98% in the mass by observingorbital speeds around galaxies (1933)

Centripetal Gravitational

acceleration acceleration


DARK HALO


RELIC DENSITY

Thermal equilibrium density:

nieq =g/(2)3 f(p) d3p

When =<Av>ni <H ,

the DM is frozen out

dni/dt = -3Hni - < Av >[(ni)2- (nieq)2]

WIMPs are produced when T>> mi; annihilation/pair

creation maintain thermal equilibrium

When interaction rates are high enough, the density drops as

exp(- mi/T) and as T drops below mi: annihilation continues and production becomes suppressed

freeze out

Cold DM relic density:i h2 mi Avi

TFO~mi / 20


THE PARAMETER SPACE FOR COSMOLOGICAL BRANONSTHE PARAMETER SPACE FOR COSMOLOGICAL BRANONS


DIRECT DM SEARCHES

WIMPs scatter elastically with nuclei

nuclear recoil

v/c 10-3

Direct interaction of the DM halo WIMPS

with the detector could make a nucleus recoil with EK~1-100 keV.

The rate of the WIMP interactions depends on the local DM density and the relative WIMPs velocity .

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


WIMP SEARCHES CONSTRAINTS ON BRANON PARAMETERSWIMP SEARCHES CONSTRAINTS ON BRANON PARAMETERS


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 beproduced in future colliders as the LHC or LC.

In the limit MD >> 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.

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.

Branons could be produced in colliders such as the LHC and their properties studied in detail in a future LC

hanoi, vietnam 2004antonio dobado1 a new dark matter candidate in low tension brane-worlds j.a.r...

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