Hanoi, VietNam 2004Antonio Dobado1 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 Madrid, Spain Vietnam th Rencontres du VietNam Hanoi August 5 to August 11, 2004

Hanoi, VietNam 2004Antonio Dobado2 Extra dimensions and Brane Worlds The Dark Matter problem

Hanoi, VietNam 2004Antonio Dobado3 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

Hanoi, VietNam 2004Antonio Dobado4 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 as non-perturbative strings, dualities, branes and string theories unification, i.e. the so called M-theory

Hanoi, VietNam 2004Antonio Dobado5 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 = GeV

Hanoi, VietNam 2004Antonio Dobado6 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 D=4+  dimensional space (the bulk space) being the extra dimensions compactified to some small volume (Brane World).

Hanoi, VietNam 2004Antonio Dobado7 In this picture the Standard model particles are confined to the 3-brane but gravitons can propagate along the whole bulk space. graviton

Hanoi, VietNam 2004Antonio Dobado8 Now the fundamental scale of gravity is not the Planck scale any more but another scale M D 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.

Hanoi, VietNam 2004Antonio Dobado9 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 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

Hanoi, VietNam 2004Antonio Dobado10 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

Hanoi, VietNam 2004Antonio Dobado11 Is our universe a 3-brane?

Hanoi, VietNam 2004Antonio Dobado12 First we have the Newton’s Law modified at short distances

Hanoi, VietNam 2004Antonio Dobado13

Hanoi, VietNam 2004Antonio Dobado14 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 3+1 dimensional coordinates extra dimensions coordinates M(n)= n /R KK tower of gravitons  M= 1 /R

Hanoi, VietNam 2004Antonio Dobado15 We expect two kind of effects from this KK tower of massive gravitons Graviton productionVirtual effects

Hanoi, VietNam 2004Antonio Dobado16 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

Hanoi, VietNam 2004Antonio Dobado17 To compute the total cross-section we sum (integrate) over all the KK gravitons The total cross-section is suppressed by powers of M D which is supposed to be of the order of 1 TeV The signature of these events is missing energy with continuous spectrum ( Mirabelli, Perelstein and Peskin)

Hanoi, VietNam 2004Antonio Dobado18 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

Hanoi, VietNam 2004Antonio Dobado19 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).

Hanoi, VietNam 2004Antonio Dobado20 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 << M D the KK modes decouple from the SM particles on the brane

Hanoi, VietNam 2004Antonio Dobado21 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

Hanoi, VietNam 2004Antonio Dobado22 SM particles branons The conclusion is that for flexible branes ( f << M D ) the only relevant degrees of freedom at low energies in the ADD scenario are the SM particles and the 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

Hanoi, VietNam 2004Antonio Dobado23 Lower dimensional example

Hanoi, VietNam 2004Antonio Dobado24 Branon fields Killing vectors corresponding to translations on B Induced metric on the brane Bulk metric

Hanoi, VietNam 2004Antonio Dobado25 Thus the induced metric is Where the coset metric is branon fields and

Hanoi, VietNam 2004Antonio Dobado26 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

Hanoi, VietNam 2004Antonio Dobado27 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.)

Hanoi, VietNam 2004Antonio Dobado28 In addition, for non factorizable spaces, which are the generic ones, we can generate branon masses

Hanoi, VietNam 2004Antonio Dobado29 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.

Hanoi, VietNam 2004Antonio Dobado30 From the corresponding Feynman rules it is possible to compute any cross section for branon production in terms of 3 parameters For example: LC N: number of branons M: branon mass f: brane tension scale The experimental signature would be one single photon (or Z) and missing energy and momentum since branons will not be detected

Hanoi, VietNam 2004Antonio Dobado31 For hadron colliders: Photon and Z productionQuark production

Hanoi, VietNam 2004Antonio Dobado32 The experimental signature would be one single photon (or Z) or one monojet plus missing energy and momentum Gluon production

Hanoi, VietNam 2004Antonio Dobado33 PRESENT COLLIDER CONSTRAINTS LEP II (L3) TEVATRON I

Hanoi, VietNam 2004Antonio Dobado34 TEVATRON II EXPECTED ACCESIBLE REGIONS IN FUTURE HADRON COLLIDERS LHC

Hanoi, VietNam 2004Antonio Dobado35 Branons are stable, weakly interacting and massive Natural WIMP candidates

Hanoi, VietNam 2004Antonio Dobado36 COSMOLOGICAL STANDARD MODEL Homogeneity and isotropy : ds 2 = dt 2 - a 2 (t) [dr 2 /(1-kr 2 ) + r 2 (d  2 + sin 2  d  2 )] Einstein equations: H 2 (t) =  (a’/a) 2 = (8  G/3)  k / a 2 k = -1,0,+1   k = - k /(a’) 2  m =  m /  c   =  /  c  c = 3H 2 (t) / 8  G    0.73±0. 04      <  Non Baryonic  <  0.23 ± 0.04 Spatial curvature:  k  =  0.02 ± 0.02  H     S     tot = 1.02±0.02    0.73±0. 04  DM = 0.23±0. 04  BaryonicMatter ±0. 004

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Hanoi, VietNam 2004Antonio Dobado38 Solar System ROTATION CURVES Fritz Zwicky found a “little” deficit of the 98% in the mass by observing orbital speeds around galaxies (1933) Centripetal Gravitational acceleration

Hanoi, VietNam 2004Antonio Dobado39 DARK HALO

Hanoi, VietNam 2004Antonio Dobado40 RELIC DENSITY Thermal equilibrium density: n i eq =g/(2  ) 3  f(p) d 3 p When  = n i <H, the DM is frozen out dn i /dt = -3Hn i - [(n i ) 2 - (n i eq ) 2 ] WIMPs are produced when T>> m i ; annihilation/pair creation maintain thermal equilibrium When interaction rates are high enough, the density drops as exp(- m i /T) and as T drops below m i : annihilation continues and production becomes suppressed freeze out Cold DM relic density:  i h 2  m i  A v i  T FO ~m i / 20

Hanoi, VietNam 2004Antonio Dobado41 THE PARAMETER SPACE FOR COSMOLOGICAL BRANONS

Hanoi, VietNam 2004Antonio Dobado42 DIRECT DM SEARCHES WIMPs scatter elastically with nuclei nuclear recoil v/c  Direct interaction of the DM halo WIMPS with the detector could make a nucleus recoil with E K ~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 spectrum in the target

Hanoi, VietNam 2004Antonio Dobado43 WIMP SEARCHES CONSTRAINTS ON BRANON PARAMETERS

Hanoi, VietNam 2004Antonio Dobado44 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 >> 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

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