Dark Matter Francesco Riva (CERN)
Many slides and material from: Marco Cirelli, Andrea deSimone, Neil Weiner and many more… we don’t know anything
we know something (see later how this cake is made) (we don’t know (almost) anything)
we know (almost) everything PART 1 Gravitational Evidence for Dark Matter 1. Rotational Curves of Galaxies
In the solar system: 1. Rotational Curves of Galaxies
(Kepler law) 1. Rotational Curves of Galaxies
Observed
Expected
1/2 Expectation: v(r) R at large R / Observations: v(r) const. at large R '
What can the reason be? 1. Rotational Curves of Galaxies Lessons from the past:
1) Anomaly in Uranus orbit = existence of Neptun
2) Anomaly in Mercury orbit = failure of Newtonian dynamics (birth of general relativity) 1. Rotational Curves of Galaxies Lessons from the past: On galactic scales:
1) Anomaly in Uranus orbit = 1) New matter existence of Neptun DARK MATTER
2) Anomaly in Mercury orbit = 2) modification of GR on failure of Newtonian dynamics galactic scale (birth of general relativity - GR) MOND (modified newtonian dynamics) 1. Rotational Curves of Galaxies
2) MOND - Theoretically not as firm as GR - Experimentally disfavored (see next) 1. Rotational Curves of Galaxies
1) New matter DARK MATTER
R GN M(R) at large R: const v(R)= ,M(R)=4⇡ ⇢(r)r2dr R ' r Z0 G M(R) R v(R)= N ,M(R)=4⇡ ⇢(r)r2dr R r Z0 More matter than visible, and distributed differently (in the halo)!
2
M R requires ⇢DM 1/r DM / / proposed by F. Zwicky (1933) who measured proper motion of galaxies in ( Coma cluster (~1000 galaxies within radius ~ 1 Mpc) 2 calculated using virial2R theoremv M M ( M = N m h i = 300h large h i⇠ GN ) L ⇠ L measured 1. Rotational Curves of Galaxies
How large/heavy/dense is the (milky way) DM Halo?
From simulations:
here
(300’000 ly) (compared to Rmilky way= 30-50 kpc) Abell NGC 2218 GR: Lightbentby(invisible)massiveobjectinforeground 2. Gravitational lensing Reconstruction ofDM distribution 3. Bullet Cluster Two colliding clusters of galaxies
NASA 1E 0657-558 “bullet cluster” astro-ph/0608247 3. Bullet Cluster
NASA 1E 0657-558 “bullet cluster” astro-ph/0608247 3. Bullet Cluster
NASA 1E 0657-558 “bullet cluster” astro-ph/0608247 3. Bullet Cluster
This observation disfavors MOND and confirms Dark Matter NASA 1E 0657-558 “bullet cluster” astro-ph/0608247 4. Cosmic Microwave Background (CMB)
Big Bang Nucleosynthesis(BBN)
CMB
Large Scale Structure 4. Cosmic Microwave Background (CMB)
Big Bang Nucleosynthesis(BBN)
BBN:all neutrons captured in charged nuclei ➙Universe opaque 4. Cosmic Microwave Background (CMB)
CMB
CMB is a last picture of this opaque universe at the moment when N+e combine 4. Cosmic Microwave Background
Baryons interact with photons, DM doesn’t ➙ they leave a different imprint in CMB 5. Baryon Acoustic Oscillations(BAO) The same “picture” can be taken at later times, by studying distributions of galaxies Gravitational DM evidence
Einstein equation+isotropy+homogeneity = Friedman equation
scale factor of the universe total density curvature
Hubble parameter
2 ⇢DM 3H 5 2 3 ⌦DM ⇢c 1.05 10 h GeV cm ⌘ ⇢c ⌘ 8⇡GN ' ⇥ Critical density so that the universe has no curvature k=0 What is this?
Summary: within the assumption that universe has cold DM and a cosmological constant (ΛCDM model), gravitational evidence for DM is striking PART 2 What else do we know on Dark Matter? Can DM be a Baryon?
Ratio baryons/photons very well constrained by CMB and BBN
CMB: BBN:
Baryons cannot collapse as long as photons are coupled - DM can collapse ➙the perturbations we see in CMB imply that some gravitational collapse has taken place
➙DM cannot be a baryon Can DM be a neutrino?
Lower bound on mDM set by the number of particles that can be confined within a given cell of phase space unlimited for bosons (see later) depends on spin statistics of the particle 1 for fermions (Pauli)
velocity set by virial theorem (given the potential it gives the phase-space integral average kinetic energy) (up to maximal velocity v) v
DM Halo volume
& keV (Gunn-Tremaine bound)
DM cannot be a neutrino, or generally a fermion with m ( m ⌫ . 0 .3eV ) X Can DM be a neutrino? On a more practical level, light DM can be relativistic (HOT) when structure forms, while heavier DM is non-relativistic (COLD) EARLY UNIVERSE Cold DM forms hierarchical structures HOT WARM COLD NOW Hot DM constrained by structure formation at small scales (there can be very light DM that doesn’t thermalize, like axions) (notice that these constraints depend on thermal history, while previous ones only on Halo formation) How light/heavy can DM be? For a boson (a Lorentz scalar): large occupations number possible (in fact it behave more like a field, see Jaeckel/Barbieri lectures) Heisenberg principle still sets bound on m: MACHO=MAssiveCompactHaloObjects Heavy DM mass constrained from MACHO searches (they would cause 57 67 lensing when passing in front of bright stars) 10 GeV . mDM . 10 GeV MACHO excluded (Plank) 1057GeV Can it interact with us? (So far we have observed only Gravitational DM interactions) It must be stable on cosmological scales It cannot be charged electrically or under the strong interaction, otherwise we would have seen it already More information can be extracted under specific circumstances/assumptions… ➙Particle DM See Barbieri/Jaeckel ➙Field DM (very light boson, like the axion) ➙Astrophysical object (primordial black holes) (Primordial Black Holes?) LIGO Gravitational Wave Signal LIGO Gravitational Wave How solid is this bound? Can it be that LIGO has detected DM? Even if mass known, it will be difficult to know distribution and confirm DM hypothesis Particle DM (the most popular scenario) DM can in principle interact with the SM only gravitationally, and its abundance be fixed by initial conditions after inflation… (in this case we won’t learn more) ..it might however couple to the SM: Particle DM - production 28 Chapter 4. What is Dark Matter? If the SM-DM interaction is sizable, DM is in thermal equilibrium in early universe: all information on initial conditions lost! 10 2 10 8 - initially, in thermal equilibrium X=DM SM SM 10 4 $ eq Y - Universe cools, less and less X Y 10 6 Y / SM SM 10 9 ! abundance 8 10 equilibrium DM - Universe expands, reaction slows down Y smaller ⇤ of and X abundance “freezes out” of the Out 10 expansion 10 ⇥ Y bigger ⇤ / Y eq / SM SM 12 10 10 ⇥ 10 ! 10 1 1 10 102 103 1 10 102 103 z ⇥ M T z ⇥ M T DM abundance depends only on (measurable) SM-DM interaction!⇤ Figure 4.4: Sample of DM freeze-out. Left:sampleoftheevolutionoftheDMabundanceY = n/s as function of z = T/M. Right:sampleoftheevolutionofthenon-equilibriumabundance Y Yeq,comparedtotheanalyticapproximationofeq.(4.48)(dashed,validforz zf )andof ⇧ of eq. (4.50)(dot-dashed,validforz zf ) ⌃ We can define zf by imposing that the last two terms are equal, obtaining the equation 2 Yeq(1) zf =ln (4.49) zf which can be iteratively solved stating from zf ln Yeq(1) 1/25. ⌅ ⌅ 2 Long after freeze-out, i.e. at late z zf 25,wecanneglecttheY term in eq. (4.46) • ⌃ ⌅ eq obtaining the integrable approximated equation dY/dz = fY 2 with solution z 1 1 z zf 3⌅1 f(z) dz = (1 + ) (4.50) Y Y (z) ⌥ z z⌅0 ⇥ ⇥ Since Y (zf ) Y we have the approximate solution ⌃ ⇥ zf 45/⇥gSM Y = . (4.51) ⇥ MPlM⇥(⌅0 +3⌅1/zf ) The DM abundance is 3 3 ⇤DM s0Y M 688⇥ T0 Y M 0.110 Y M ⇥ ⇥ ⇥ DM = 2 = 2 2 = 2 (4.52) ⇤ ⇤cr 3H0 /8⇥GN 1485MPlH0 h ⇥ 0.40 eV 3 2 having inserted the present entropy density (s0 = gs0T0 2⇥ /45 with gs0 =43/11), the present Hubble constant H0 = h 100 km/sec Mpc,andthepresenttemperatureT0 =2.725 K.Inserting ⇥ the solution (4.51)leadstotheresultannouncedineq.(4.42). Particle DM - production T 2 H = during radiation domination MPl when annihilation rate becomes smaller than H n T 2/M expansion H, X decouples from the SM plasma . () h i . P For heavy DM this is determined by Boltzman distribution: 3/2 m T m /T n = n = g e at T~mX/20 DM particles decouple ¯ 2⇡ f ✓ ◆ (too heavy to be produced) 2 number density of X remains ~ constant n Tf /(MP ) 1 1 3 n ⇠ Tf ⇠ MP Tf ⇠ MP m ⇢ m n 1 the energy density of X today (wrt photons) is: ⇢ ⇠ T0 n ⇠ MP T0 26 3 2 (n (T0)m ) 3 10 cm / sec 1pb ⌦ h = 2 = 0.1 ⇥ 0.1 ⇢c/h ···' v ' v ➙typical weak-scale interactions provide thermal relic with the “right” relic abundance, independently of mass and initial conditions (REMARKABLE COINCIDENCE, a.k.a. “WIMP MIRACLE”) Particle DM - production There are other possible mechanisms for DM production, beside freeze-out (non-thermal production mechanisms) Asymmetric DM: intriguing coincidence SM explained by possible shared SM-DM conserved charge, so that SM and DM are produced together Freeze-in: if interactions very small particles never thermalize, but can freeze in (FIMP), also independently of initial conditions Axions: If DM is a boson (scalar), and is very light, it behaves effectively like a field that oscillates and stores energy (how much depends on initial conditions) (see Jaekel/Barbieri) PART 3 How can DM-SM interactions be tested (detected)? Direct Detection (See Baudis) DD: looking for the scattering of galactic halo DM on heavy nuclei in underground labs. DM Nucleus DM Nucleus ! Xenon, CDMS, CRESST, CoGeNT, Edelweiss.. . DM DM ~q 2 =2µ2 v2(1 cos ✓) ,µ= m M /(m + M ) | | A A A A ~q 2 =2µ2 v2(1 cos ✓) ,µ= m M /(m + M ) | | A A A A ~q 2 2 2 µ Av O(10)keV ER = E|max| =2 Detectable DM: ⇠ 2MR A . (experimental MA sensitivity) m & 8GeV Recoil target nuclei mass Direct Detection (See Baudis) Z-mediated 2 2 4 39 2 ↵ m /M 10 cm ⇠ W p Z ⇡ Excluded done Higgs-mediated projected m & 8GeV loop-mediated ⇢DM Heavier DM is more rare nDM = m ➙ less events, less constraints DM Indirect Detection + DM DM e e ,... + ! e , p¯ AMS-02, Pamela, Fermi, HESS ATIC, Fermi ⌫ IceCube, Antares, Km3Net d¯ GAPS, AMS-02 8 kpc Indirect Detection DM SM evolution ` , q,¯ W ,Z, ,... primary e±, ,⌫,⌫¯,p,p,¯ . . . channels + + stable DM ` ,q,W ,Z, ,... species astrophysical propagation DM annihilations in galactic halo/center e±, ,⌫,⌫¯,p,p,¯ . . . fluxes at detection Indirect Detection model for DM interactions radiation/hadronization/decay ( )) (QCD, QED, EW) LL DM SM evolution ` , q,¯ W ,Z, ,... primary e±, ,⌫,⌫¯,p,p,¯ . . . channels stable `+,q,W+,Z, ,... DM particle physics species astrophysical propagation DM annihilations in galactic halo/center e±, ,⌫,⌫¯,p,p,¯ . . . fluxes at detection 22 -28 -26 ] ] 2 10 2 10 ATLAS 90% CL DAMA/LIBRA, 3% ATLAS 90% CL COUPP 90% CL -30 -1 CRESST II, 2% -28 µ 5 5 -1 =8s TeV, 20.3 fb D8: '& ' &q' ' q =8s TeV, 20.3 fb SIMPLE 90% CL 10 D1: && qq CoGeNT, 99% CL 10 µ D5: '& µ&q' q ! CDMS, 1% D9: µ! q q PICASSO 90% CL µ C1: & & qq %& & %µ! -32 µ! ! µ! CDMS, 2% -30 Super-K 90% CL D11: && G G C5: & &G G truncated, coupling = 1 + - 10 µ! µ! CDMS, low mass 10 IceCube W W 90% CL truncated, coupling = 1 LUX 2013 90% CL truncated, max coupling CMS 8TeV D8 -34 -32 truncated, max coupling Xenon100 90% CL 10 CMS 8TeV D5 10 CMS 8TeV D11 10-36 10-34 10-38 10-36 10-40 10-38 10-42 10-40 WIMP-nucleon cross section [cm WIMP-nucleon cross section [cm 10-44 10-42 spin-independent spin-dependent 10-46 10-44 1 10 102 103 1 10 102 103 WIMP mass m& [GeV] WIMP mass m& [GeV] Indirect(a) Detection (b) -1 /s] -18 95% CL =8s TeV, 20.3 fb 3 ATLAS 10 -19 2 $ ( Fermi-LAT dSphs ( && ) " uu, 4 years) Majorana 10 2 $ (HESS 2011 ( && ) " qq, Einasto profile) > [cm -20 Majorana 10 2 $ (HESS 2011 ( && ) " qq, NFW profile) rel Majorana -21 µ v D5: '& &q' q " (&&) 10 µ qq µ Dirac -22 D8: '& ' 5&q' ' 5q " (&&) µ Dirac "&10 & -23 truncated, coupling = 1 % 10 truncated, max coupling < 10-24 thermal relic 10-25 10-26 10-27 10-28 Fermi-Lat 10-29 telescope 10-30 LHC LHC 10-31 q DM 1 10 102 103 WIMP mass m& [GeV] (c) [arXiv:1502.01518] Fig. 12 Inferred 90% CL limits on (a) the spin-independent and (b) spin-dependent WIMP–nucleon scattering cross section ID as aq function of DM mass mχDMfor different operators (see Sect. 1). Results from direct-detection experiments for the spin- independent [127–133]andspin-dependent[134–138]crosssection,andtheCMS(untruncated)results[14]areshownfor comparison. (c) The inferred 95% CL limits on the DM annihilation rate as a function of DM mass. The annihilation rate is defined as the product of cross section σ and relative velocity v,averagedovertheDMvelocitydistribution(σ v ). Results from gamma-ray telescopes [125, 126]arealsoshown,alongwiththethermalrelicdensityannihilation rate [⟨25, 26⟩ ]. of the ADD and WIMPs models. This is done separately for the different selections, and the one with the most stringent expected limit is adopted as the nominal result. In the region with squark/gluino masses below 800 GeV, SR7 provides the best sensitivity while SR9 provides the most stringent expected limits for − heavier squark/gluino masses. Figure 14 presents the final results. Gravitino masses below 3.5 10 4 eV, − − × 3 10 4 eV, and 2 10 4 eV are excluded at 95% CL for squark/gluino masses of 500 GeV, 1TeV,and × × 1.5 TeV, respectively. The observed limits decrease by about9%–13%afterconsideringthe 1σ uncertainty − from PDF and scale variations in the theoretical predictions. These results are significantly better than previous results at LEP [54]andtheTevatron[15], and constitute the most stringent bounds on the gravitino mass to date. For very high squark/gluino masses, the partialwidthforthegluinoorsquarktodecayintoa gravitino and a parton becomes more than 25% of its mass and thenarrow-widthapproximationemployed is not valid any more. In this case, other decay channels for the gluino and squarks should be considered, leading to a different final state. The corresponding region ofvalidityofthisapproximationisindicatedin the figure. Finally, limits on the gravitino mass are also computed in the case of non-degenerate squarks and gluinos (see Fig. 15). Scenarios with mg˜ =4 mq˜, mg˜ =2 mq˜, mg˜ =1/2 mq˜,andmg˜ =1/4 mq˜ have × × × × − been considered. In this case, 95% CL lower bounds on the gravitino mass in the range between 1 10 4 eV − × and 5 10 4 eV are set depending on the squark and gluino masses. × LHC •Could be the only test for light DM •Dark Matter in a collider is like a neutrino (missing Energy) transverse • if stabilizedPRODUCTION PbyRODUCTION a Z2 symmetry OF OF D ARK D ARK DM MATTER producedMATTER AT in ATCMS pairs CMS p DM • • Search%for%evidence%of%pair[produc=on%of%Dark%MaAer%par=cles%(Search%for%evidence%of%pair[produc=on%of%Dark%MaAer%par=cles%(χ) χ) p DM • Difficult search,Direct unlessDirect Detection Detection correlating (t-channel) (t-channel) missingColliderCollider Searches E SearchesT with (s-channel) (s-channel)other handles • Dark%MaAer%produc=on%gives%missing%transverse%energy%(MET) [ jets/photons• Dark%MaAer%produc=on%gives%missing%transverse%energy%(MET) from initial state radiation? pp DM + X displaced• Photons%(or%jets%from%a%gluon)%can%be%radiated%from%quarks,%giving%monophoton%• Photons%(or%jets%from%a%gluon)%can%be%radiated%from%quarks,%giving%monophoton%vertices? ! 4 (or%monojet)%plus%MET4 4accompanying(or%monojet)%plus%MET particles?4 ] q¯ q¯ q¯ q¯ ¯ ¯ ¯ ¯ q q q q Like DD, probes DM couplings 3 3 MonophotonMonophoton + MET + MET MonojetMonojet + MET + MET with quarks and gluons FigureFigure 1: Dark 1: matter Dark matter production production in association in association withFigure a singlewithFigure 1: Dark a jet single 1: matter in Dark a jet hadron matterproduction in a hadron collider. production in collider. association in association with a single with a jet single in a hadronjet in a collider. hadron collider. 3.1. 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Eventsthe leading with| more jet| is than ⇤(j two,j jets) < with2.0 radians.p > 30 Events GeV are with more than two jets with p > 30 GeV are the leading jet is1 ⇤2 (j ,j ) < 2.0 radians. Eventsthe leading with more jet is1 than 2⇤(j two,j jets) 3 3 Both3 ATLAS and CMS impose additional isolation cuts,Both which ATLAS3 we do and not CMS mimic impose in our additional analysis forisolation simplicity cuts, and which we do not mimic in our analysis for simplicity and since theyBoth would ATLAS not and have CMS a large impose impact additional on our results. isolationsince theycuts,Both would which ATLAS not we do have and not CMS a mimic large impose impact in our additional onanalysis our results. forisolation simplicity cuts, and which we do not mimic in our analysis for simplicity and since they would not have a large impact on our results.since they would not have a large impact on our results. LHC Main background from Z ⌫⌫ ¯ , so this must be stronger… (but recall from direct detection! that Z-mediated interactions are excluded) ➙need a resonant peak or a different distribution LHC So far LHC observed no signal associated with missing ET …yet it’s important to assess what we have learned from this! (remember that most of what we know on DM is about negative results) Difficulty: LHC collisions explore a wide unexplored range of energy few GeV - few TeV if DM is there, it might not be alone specific Exemple: explicit SUSY DM model (neutralino) assumptions MET + many jets (+ leptons) Many new particles involved in process ➙ many parameters! (and many explicit models) LHC Physical information better captured by generic assumptions that encompass broad classes of models Simplified Models Effective Field Theories (EFTs) There is only mediator(s) Assumption: one mediator are much heavier than LHC energies Good modeling Simple and identifies very few Pro: of missing E (relevant) parameters With present sensitivity, Still many Contra: this hypothesis is not testing parameters/models weakly coupled models LHC Example: DM-SM interaction mediated by new vector Z’ ‘ ‘ E mZ0 ⌧ g g ⇤ ⇤ 1 Q¯ Q ¯ µ M 2 µ ⇤ Only one parameter: M = mZ /g ⇤ 0 ⇤ Racco,Wulzer,Zwirner’15 = g ⇤ LHC LHC best for light DM (below direct detection threshold) LHC reach DM-SM coupling g* Simplif. Mod. better EFT better ~TeV Mediator Mass For weakly coupled (light) new physics: EFT For strongly coupled (heavy) new physics: EFT (Moreover pion-like DM doesn’t have a simplified model, only EFT) Bruggisser,Riva,Urbano’16 ➙For maximally strongly coupled DM, mediators up to ~6 TeV are excluded CONCLUSIONS • Gravitational evidence for DM striking Moreover: not baryon, not neutrino (➙BSM), not hot, not SM charged, stable • If couples also non-gravitationally: • freeze-out (or asymmetric DM) provide suggestive production “miracles” • Direct(indirect) detection or the LHC might provide further evidence… …or they might not Direct Detection If (scalar) DM is so light (axion) that it behaves like a field (=large occupation numbers), a sizable signal can still be detected, searching for coherent* effects: *=Coherence is not guaranteed, even if the initial state is, since the cosmological history of different patches of these field might differ. Nevertheless the coherence time is set by the maximal frequency available to DM, which is determined by the virial velocity and for typical Axion masses is long enough