Dark Matter and its Detection— a concept introduction 毕效军 (Bi Xiao-Jun) 中国科学院高能物理研究所 (IHEP) International summer Institute on Particle physics, Astrophysics and Cosmology 16 August 2005, HangZhou

Outline Evidences of dark matter Related problems on dark matter  Astrophysics  Particle physics Thermal production Detection of dark matter  Direct detection of WIMP  Indirect detection of WIMP Other candidates Conclusion

Outline Evidences of dark matter Related problems on dark matter  Astrophysics  Particle physics Thermal production Detection of dark matter  Direct detection of WIMP  Indirect detection of WIMP Other candidates Conclusion

Evidences — cluster scale 1933, Zwicky found the first evidence for the presence of dark matter in the Coma cluster. A system at dynamical equilibrium obeys the virial theorem: K+U/2=0. Zwicky found that the kinetic term estimated by measuring the proper velocities of the individual galaxies was much larger than the potential term due to luminous galaxies: M/L=300M ⊙ /L ⊙ Coma cluster

Evidences — cluster scale Cluster contains hot gas which is at hydro static equilibrium. It’s temperature follows, However, X-ray emission measures the temperature and M/M visible =20

Evidences — cluster scale Weak lensing measures the distortion of images of background galaxies by the foreground cluster, which measures the cluster mass. Sunyaev-Zeldovich distortion measures the distortion of CMB passing through cluster, which measure the temperature of the gas and therefore the mass of the cluster. …other measurements

Evidences — galaxy scale From the Kepler’s law, for r much larger than the luminous terms, you should have v ∝ r - 1/2 However, it is flat or rises slightly. The most direct evidence of the existence of dark matter. Corbelli & Salucci (2000); Bergstrom (2000)

Evidences — cosmological scale WMAP measures the anisotropy of CMB, which includes all relevant cosmological information. A global fit combined with other measurements gives the cosmological paramters precisely.  m h 2 =  m = Spergel et al 2003

Non-baryonic DM From BBN and CMB, it has  B h 2 = Therefore, most dark matter should be non-baryonic.  DM h 2 = Non-baryonic dark matter dominates the matter contents of the of the Universe.

Evidences — not from the gravitational effects Up to now no solid experimental evidences other than the gravity effects indicate the existence of dark matter. There are hints from DAMA, HEAT, EGRET and HESS experiments which may implies the existence of dark matter. However, all the result are not definite. We will introduce these results later.

Outline Evidences of dark matter Related problems on dark matter  Astrophysics  Particle physics Thermal production Detection of dark matter  Direct detection of WIMP  Indirect detection of WIMP Other candidates Conclusion

Outline Evidences of dark matter Related problems on dark matter  Astrophysics  Particle physics Thermal production Detection of dark matter  Direct detection of WIMP  Indirect detection of WIMP Other candidates Conclusion

Nature of the dark matter — Hot or cold Hot dark matter is relativistic at the collapse epoch and free-streaming out the galaxy-sized over density. Larger structure forms early and fragments to smaller ones. Cold DM is non-relativistic at de-coupling, forms structure in a hierarchical, bottom-up scenario. HDM is tightly bound from observation and LSS forma- tion theory

Distribution of the dark matter N-body simulation is extensively adopted to study the evolution of structure with non-linear gravitational clustering from the initial conditions. The reliability of an N-body simulation is measured by its mass and force resolution. Simulations suggest a universal dark matter profile, same for all masses, epochs and initial power spectra.

Distribution of the dark matter Two widely adopted density profiles are the NFW and Moore: Both profiles have the same behavior at large radius, however, they are different at small radius

Distribution of the dark matter Figure shows the profiles of the Milky Way. The density profiles agree with each other at large scales. Large uncertainty at the small scale.

Local density of dark matter Determined by measurement of the rotation curves of the Milky Way. However large uncertainties are introduced due to our special position. Velocity is also determined by the rotation curves. Bahcall (83), ρ 0 =0.34GeV/cm 3, Caldwell (81)ρ 0 =0.23GeV/cm 3, Turner(86)ρ 0 = GeV/cm 3

Some recent developments The slope at the inner most radius is under debate. The most recent simulations seem indicate that the slope is between the NFW and Moore profiles [Navarro, , Reed, ]. The slope may even be not universal, depending on the mass scale [Reed]. The central super massive black hole will affect the central cusp heavily depending on the its initial mass and adiabatic growth.

Distribution of the dark matter The profile is specified by the two scale parameters ρ s, r s. They are determined by the virial mass of the structure and the concentration parameter by c=r vir /r s. The concentration parameter represents how the dark matter centrally concentrated. The larger concentration the more centrally concentrated. The concentration parameter is determined by the evolution of the structure.

How does structure form? For CDM, structure form hierarchically bottom up ， i.e., smaller object forms earlier (at smaller scale, the fluctuation is larger), they merges to form bigger and bigger structures. The smaller object have larger concentration parameter, since earlier epoch has greater density. δρ/ρ δρ/ρ threshold threshold

How does structure form? Objects at each mass scale corresponds to a collapse epoch z c. The collapsing epoch is determined by the condition as σ (M)=δ sc, where σis the rms density fluctuation at the comoving scale encompassing M and δ sc is the critical over density for collapse. A semi-analytic model is described by two free parameters: the collapse epoch is determined by the collapsing time of a fraction of the object mass, σ (M * =FM)=δ sc ; The concentration parameter is determined by another free parameter c(M,z)=K(1+z c )/(1+z). The model is determined completely by the cosmological parameters.

Concentration parameter via the virial mass From the figure, the concentration parameter decreases with the virial mass. It is determined once the cosmological parameters are specified.

Substructure Will the smaller objects formed earlier survive today in the dark halo? A wealth of subhalos exist due to high resolution simulations. The number density is as: Moore et al

Problems of CDM on sub-galactic scale The simulation over-predicts the number of subhalos. 11 dwarf satellites of the MW are observed, which is an order of magnitude smaller than predicted. Solutions are proposed, including inflation potential suppressing the small scale fluctuation, star formation suppressed in small subhalos, and new form of dark matter candidates, such as self- interacting dark matter, non-thermal production, warm dark matter and so on. Milli-lensing by halo substructure seems favor the CDM scenario. It is still controversial.

The first generation object Diemand, Moore & Stadel, 2005: Depending on the nature of the dark matter: for neutralino-like dark matter, the first structures are mini-halos of M ⊙. There would be zillions of them surviving and making up a sizeable fraction of the dark matter halo. The dark matter detection schemes may be quite different!

Outline Evidences of dark matter Related problems on dark matter  Astrophysics  Particle physics Thermal production Detection of dark matter  Direct detection of WIMP  Indirect detection of WIMP Other candidates Conclusion

Candidates of the dark matter Good candidates which independently motivated in particle physics, such as neutralino, axion.

Other subjects What theory is responsible for dark matter? SUSY, extra-dimension, little Higgs, mirror world How to discriminate the nature of DM among a large amount of candidates? How does the dark matter produced? Thermally or non-thermally? How to detect WIMP dark matter other than the gravitational effect? Direct or indirect? How to detect superWIMP particles? Can we produce the DM particles at the colliders?

Outline Evidences of dark matter Related problems on dark matter  Astrophysics  Particle physics Thermal production Detection of dark matter  Direct detection of WIMP  Indirect detection of WIMP Other candidates Conclusion

Thermal production of dark matter Assuming a new, stable particle ， its mass and weak interaction with the SM particles. At the early Universe of temperature T, is at thermal equilibrium through, for the number density is, while for the number density is As the cooling of the Universe, when the reaction rate equates to expanding rate ， the particle decouples from the thermal equilibrium. Dark matter as thermal relics freeze in. the comoving number density is then a contant. Introducing ， with s the entropy density 。

Hot dark matter At decoupling, if is relativistic, both number density of and s are, the ratio is independent of temperature, therefore. The relic density of hot dark matter is porp to its mass. the mass is therefore constrained by cosmology. Neutrino is hot dark matter, its abundance and it mass are constrained by SDSS and WMAP (Tegmark et al 2003)

Cold dark matter The CDM is non-relativistic at decoupling, its number density is exponentially suppressed, therefore the ratio to S depends strongly on its decoupling temeperature, applying the relations we get Here determines the strength of the interaction.

Density via interaction strength We have to solve the Boltzmann equation numerically, taking into account the threshold and co- annihilation

Why WIMP (Weak interacting massive particles) From ， we have for Therefore, WIMP is the most nature dark matter candidate if we take DM as thermal relics of the big bang. Conversely, precise cosmological measurements of the dark matter abundance constrain the particle physics model strong.

Constrains on the SUSY parameter space The blue stripe is allowed by WMAP J. Ellis et al (2004)

mSUGRA or CMSSM: simplest (and most constrained) model for supersymmetric dark matter R-parity conservation, radiative electroweak symmetry breaking Free parameters (set at GUT scale): m 0, m 1/2, tan  A 0, sign(  ) 4 main regions where neutralino fulfills WMAP relic density: bulk region (low m 0 and m 1/2 ) stau coannihilation region m   m stau hyperbolic branch/focus point (m 0 >> m 1/2 ) funnel region (m A,H  2m  ) (5th region? h pole region, large m t ?) However, general MSSM model versions give more freedom. At least 3 additional parameters: , A t, A b (and perhaps several more…) H. Baer, A. Belyaev, T. Krupovnickas, J. O’Farrill, JCAP 0408:005,2004 From the talk given by Bergstrom at SUSY 2005

Outline Evidences of dark matter Related problems on dark matter  Astrophysics  Particle physics Thermal production Detection of dark matter  Direct detection of WIMP  Indirect detection of WIMP Other candidates Conclusion

Outline Evidences of dark matter Related problems on dark matter  Astrophysics  Particle physics Thermal production Detection of dark matter  Direct detection of WIMP  Indirect detection of WIMP Other candidates Conclusion

Direct detection of WIMP Detect the signal when a WIMP collides with the nuclei. The interaction is related with annihilation via a cross symmetry. Therefore we expect small but non-zero interaction between the WIMP and nuclei. The scattering includes elastic and inelastic. The inelastic process is extremely weak and radiation from excited nuclei is hard to distinguish from the background. At present the experiments measure the elastic scattering. The energy deposited in the detector is measured. For typical and velocity of the WIMP, the energy is at the order of KeV.

Elastic scattering The effective coupling between and quark can be divided to the scalar, pseudo-scalar, vector, axial- vector and tensor types. For the extreme non- relativistic Majorana neutralino, the interaction is simplified to two cases: spin-dependent and spin- independent coupling. For the SD coupling WIMP couples to the spin of the nucleus; while the SI coupling WIMP couples to the mass of the nucleus.

SD coupling SD coupling induced by the axial-vector coupling in the quark level The SD coupling depends on the spin of the nucleus The cross section if given by ， F is the form factor and

SI coupling Similarly we get the cross section of the SI scattering The cross section is proportional to the mass square, therefore the cross section is greatly enhanced for heavy nucleus, in general it is greater the SD cross section for Most experiments try to detect the SI interaction

Dependence on the distribution of the velocity The energy deposit rate for elastic scattering It is, but not can be measured. The deposit energy depends on the velocity distribution near the earth, the lower limit depends on the material of the detector It should be noted that the detector adopting different material may be sensitive to different WIMP velocity space. Additionally there are uncertainties associated with the wave function of the nucleus, it is generally difficult to compare between different experiments.

Annual modulation signal in DAMA A model independent way for direct detection of WIMP is to measure the annual modulation effect. A 6.3 σ modulation signal has been observed at the DAMA experiment. However, the interpretation as SI interaction with EM has not been confirmed.

Sensitivity of direct detection experiments Actually the parameter space due to DAMA has been excluded by new CDMS result. As the convention, all the experimental results are normalized to SI WIMP- proton cross section assuming Maxwellian velocity distribution Due to some special velocity distribution form or special DM model there is narrow space for DAMA to reconcile with other experiments.

Outline Evidences of dark matter Related problems on dark matter  Astrophysics  Particle physics Thermal production Detection of dark matter  Direct detection of WIMP  Indirect detection of WIMP Other candidates Conclusion

Outline Evidences of dark matter Related problems on dark matter  Astrophysics  Particle physics Thermal production Detection of dark matter  Direct detection of WIMP  Indirect detection of WIMP Other candidates Conclusion

Indirect detection of WIMP Indirect detection detects the annihilation products of the dark matter. The annihilation rate is proportional to the square of the dark matter density. For the average density of DM in the Universe the annihilation is negligible. However the DM density at somewhere is very high the annihilation rate is also high. According to the source the experiments are divided in to: detection of neutrinos from the sun or the earth; cosmic rays from the MW or extra-galaxies; products near the black hole in the halo center or from the subhalos.

Flux of the annihilation products Flux is determined by the products of two factors The first factor is the strength of the interaction, determined completely by particle physics The second by the distribution of DM The flux depends on both the astrophysics and the particle aspects.

Uncertainties due to the SUSY parameter space The uncertainty is small. The annihilation is correlated with the early decoupling process.

Uncertainties from the distribution of the DM

Gamma rays Monoenergetic line Continuous spectrum A smoking gun of DM ann. The flux is suppressed due to loop production. Larger flux. Need careful analysis of the background

Gamma ray detection experiments ground space cherenkov EAS angular reso exce （ <0.1 o ) good(1 o ) exce(~0.1 o ) obser time short (10%) long (~90%) long(~100%) effective area large(10 4 M ) large(10 4 M 2 ) small(~1M 2 ) field of view small( 2π ） bkg good （ ~99.9% ） bad(<70%) good energy reso good(~20%) not bad (~100%) good(<10%, small syst error ）

Simulation on the GLAST GLAST Science Brochure

Gamma lines at the GLAST Brgstrom et al, 97

Neutrinos from the sun or the earth Density at the solar center is determined by the scattering, insensitive to the local density The present data gives constraints on the parameter space IceCube can cover most paramter space

Constraints from the neutrino detection From the Sun and the Earth Gondolo 2000 Ahrens et al. 2002

Cosmic rays from the halo of the MW — some weak hints on DM Some astrophysics observations can not be explained by the canonical physics. They may indicate the signal of DM, however, no conclusion can be drawn now. One of such experiments is the HEAT. (The HEAT signal may indicate the non-thermal production or the subhalo nearby) Baltz et al. 2002

Excess of gamma rays beyond 1 GeV by EGRET Cesarini et al. 2003

High energy gamma rays from the GC by HESS and CANGROO Horns 2004

From the central black hole The SMBL of mass will affect the distribution of DM at the GC. The annihilation flux can be either enhanced or decreased. Synchrotron radiation from the GC excludes the central spike

Flux from the subhalos 2sigma uppermedian ARGO sensitivity

Outline Evidences of dark matter Related problems on dark matter  Astrophysics  Particle physics Thermal production Detection of dark matter  Direct detection of WIMP  Indirect detection of WIMP Other candidates Conclusion

Some other candidates superWIMP Its interaction strength is much smaller than the weak scale, such as gravitino, quintessino They can not be generated efficiently through the thermal interaction, however they be produced through non-thermal production, such as via decay of heavy relics If the decay is later than BBN, it will affect the BBN and CMB observations In SUSY model, the NLSP can be either the neutralino or the stau, they have long life time (as long as 10 7 sec due to suppression) This kind of dark matter can not be detected as WIMP, there are some interesting prediction of this kind of models and can then be tested

SUSY partner of Quintessence as DM The quintessence interacts with matter, its super partner can be the dark matter In order not to destroy the flatness of the potential of quintessence, we introduce the derivative coupling and its supersymmetric form It is produced non-thermally

Effects of Quintessino DM Due to large velocity of non- thermal production, the matter power spectrum at subgalactic scales is suppressed Affect BBN ， suppress 7 Li abundance Predicts a massive, long life time and charged particel Lin, Huang, Zhang, Brandberg 01 Bi, Li, Zhang, 2004

production by cosmic rays High energy cosmic neutrinos interacts with the earth matter, the supersymmetric particle and finally the NLSP particle is produced L3+C or IceCube can detect the Bi, wang, zhang, zhang 04

production at collider If is the NLSP, all the susy particle will finally decay to it and leave a track of charged particle Collect and study its decay, we can learn gravity even in the laboratory At LHC/ILC at most is produced in one year Buchmuller et al 2004 Kuno et al., 2004 Feng et al., 2004

Conclusion The existence of dark matter has been firmly established. CDM is favored. Almost a hundred of DM models have been built, however the nature of the DM is still unclear. DM is a interdisciplinary field where its astrophysics and its particle physics aspects are closely related. Both direct and indirect detection of DM as well as the relic density measurement are complementary to colliders to constrain the parameter space of new physics strongly. Some may even reach deeper parameter space than LHC. Maybe the DM problem is near its solution.