LHC and the Cosmos. Fawzi BOUDJEMA. Dark Matter at Colliders and from the Sky. LAPTH, CNRS, Annecy-le-Vieux, France

Transcription

1 LHC and the Cosmos Dark Matter at Colliders and from the Sky Fawzi BOUDJEMA LAPTH, CNRS, Annecy-le-Vieux, France F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 1/1

2 Most cited papers of 2008 and ,3,4) Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation. By WMAP Collaboration Cited ) Review of Particle Physics. By Particle Data Group (C. Amsler et al.) ) An anomalous positron abundance in cosmic rays with energies GeV. PAMELA 274 7) Improved Cosmological Constraints from New, Old and Combined Supernova Datasets. By Supernova Cosmology Project 196 8) An excess of cosmic ray electrons at energies of GeV.ATTIC 9) A Theory of Dark Matter Nima Arkani-Hamed et al., ) Search for Weakly Interacting Massive Particles with the First Five-Tower Data from the Cryogenic Dark Matter Search at the Soudan Underground Laboratory. By CDMS Collaboration 12) Model-independent implications of the e+-, anti-proton cosmic ray spectra on properties of Dark Matter Cirelli, Kadastik, Raidal and Strumia 150 F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 2/1

3 Most cited papers of 2008 and ,3,4,7) CMB, Supernova, LSS 6,8) PAMELA, ATTIC (HESS, Fermi-LAT,..) Indirect Detection 10) CDMS (DAMA, COUPP,Edelweiss,..) Direct Detection 9,12) Theory of DM Particle Physics: New Physics 2) Review of Particle Physics. Particle Physics: SM F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 3/1

4 Most cited papers of 2008 and ,3,4,7) CMB, Supernova, LSS relic density 6,8) PAMELA, ATTIC (HESS, Fermi-LAT,..) Indirect Detection Astro (prop.) uncertainties 10) CDMS (DAMA, COUPP,Edelweiss,..) Direct Detection (astro) Nuclear uncertainties 9,12) Theory of DM Particle Physics: New Physics 2) Review of Particle Physics. Particle Physics: SM F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 3/1

5 Most cited papers of 2008 and ,3,4,7) CMB, Supernova, LSS relic density 6,8) PAMELA, ATTIC (HESS, Fermi-LAT,..) Indirect Detection Astro (prop.) uncertainties 10) CDMS (DAMA, COUPP,Edelweiss,..) Direct Detection (astro) Nuclear uncertainties 9,12) Theory of DM Particle Physics: New Physics 2) Review of Particle Physics. Particle Physics: SM F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 3/1

6 LHC Dark Matter Connection F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 4/1

7 LHC Dark Matter Connection: The new paradigm no mention of a connection, despite a SUSY WG There is a mention of LSP to be stable/neutral because of cosmo reason, but no attempt at identifying it or weighing the universe at the LHC LHC: Symmetry breaking and Higgs New Paradigm, Dark Matter is New Physics. Dark Matter is being looked for everywhere New Paradigm, Particle Physics to match the precision of recent cosmological measurements F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 5/1

8 Plan I Cosmology in the era of precision measurements Dark Matter is New Physics Evidence for and Precision on the matter content of the universe New Paradigm: can LHC/ILC match the precision of the upcoming cosmo/astro experiments and indirectly probe the history of the early universe? Indirect and direct detection overview, uncertainties PAMELA, ATTIC, Fermi-LAT, HESS,...results The new view: symmetry breaking, dark matter and missing energy at LHC Relic density and precision annihilation cross sections Need for efficient cross border tools micromegas an overview MSSM as prototype, beyond tree-level S LOOP S γ ray line and relic at one-loop Automatisation, modularity, GF, Gram s, results and simulation, Sommerfeld enhancement F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 6/1

9 Plan II (?) Non conventional scenarios and history of the universe Requirements on particle physics experiments to match upcoming cosmological measurements summary F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 7/1

10 The need for Dark Matter Newton s law v 2 rot. /r = G NM(r)/r 2 We are not in the centre of the universe F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 8/1

11 The need for Dark Matter Newton s law v 2 rot. /r = G NM(r)/r 2 (tracer star at a distance r from centre of mass distribution ) We are not in the centre of the universe we are not made up of the same stuff as most of our universe F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 8/1

12 The need for Dark Matter Newton s law v 2 rot. /r = G NM(r)/r 2 (tracer star at a distance r from centre of mass distribution ) We are not in the centre of the universe Dark Matter= New Physics we are not made up of the same stuff as most of our universe F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 8/1

13 The need for Dark Matter, old story F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 9/1

14 Cosmology in the era of precision measurement: from various constraints 3 No Big Bang 2 observed luminosity and redshift exploits the Supernovae different z dependence of vacuum energy density (cosmological constant) Clusters Maxima SNAP Target Statistical Uncertainty CMB Boomerang open expands forever recollapses eventually flat closed matter/energy density bullet experiment: disfavours alternative explanations through modification of mass density gravity F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 10/1

15 The new paradigm why? Cosmology in the era of precision: CMB observed temperature anisotropies (related to the density fluctuations at the time of emission) is 10 5 F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 11/1

16 Cosmology in the era of precision measurement 1. Pre-WMAP and WMAP vs Pre-LEP and LEP F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 12/1

17 Cosmology in the era of precision measurement sin 2 θ w VBM (m Z ) ν - q e - q ν - e (Ellis-Fogli) m W / m Z m t (GeV) M H [GeV] sin 2 θ eff M W GigaZ (1σ errors) SM@GigaZ 100 now 50 angular power spectrum of the CMB, pre-wmap m t [GeV] and WMAP Planck+SNAP will do even better (per-cent precision) like from LEP to LHC+LC F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 13/1

18 Pre-WMAP and WMAP vs Pre-LEP and LEP power spectrum of anisotropies, WMAP vs Pre-WMAP.242 sin 2 θ w VBM (m Z ) ν - q e - q ν - e (Ellis-Fogli) m W / m Z m t (GeV) M H [GeV] sin 2 θ eff M W GigaZ (1σ errors) SM@GigaZ 100 now 50 Planck+SNAP will do even better (per-cent precision) improvement like going from LEP to LHC+ILC LHC, PLanck 2007 ILC,SNAP m t [GeV] F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 14/1

19 F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 15/1

20 Matter Budget and Precision 1. Dark Matter 73% 23% ν(ω Stars ν < 0.01) 4% Baryons Dark Energy t 0 = 13.7 ± 0.2 Gyr (1.5%) Ω tot = 1.02 ± 0.02 (2%) Ω DM = 0.23 ± 0.04 (17%) F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 16/1

21 Matter Budget and Precision 2. Dark Matter 73% 23% ν(ω Stars ν < 0.01) 4% Baryons Dark Energy t 0 = 13.7 ± 0.2 Gyr (1.5%) α 1 = 10t 0 (10 7 %) Ω tot = 1.02 ± 0.02(2%) ρ = Ω tot ( 0.1%) Ω DM = 0.23 ± 0.04(17%) sin 2 θ eff = Ω DM (0.08%) We should then be able to match the present WMAP precision!... once we discover susy dark matter F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 17/1

22 Matter Budget and Precision 2. Dark Matter 73% 23% ν(ω Stars ν < 0.01) 4% Baryons Dark Energy t 0 = 13.7 ± 0.2 Gyr (1.5%) α 1 = 10t 0 (10 7 %) Ω tot = 1.02 ± 0.02(2%) ρ = Ω tot ( 0.1%) Ω DM = 0.23 ± 0.04(17%) sin 2 θ eff = Ω DM (0.08%) We should then be able to match the present WMAP precision!... once we discover susy dark matter F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 18/1

23 Symmetry breaking and DM: The new view The SM Higgs naturalness problem has been behind the construction of many models of New Physics: at LHC not enough to see the Higgs need to address electroweak symmetry breaking and naturalness DM is New Physics, most probable that the New Physics of EWSB provides DM candidate, especially that All models of NP can be made to have quite easily and naturally a conserved quantum number, Z 2 parity such that all the NP particles have Z 2 = 1 (odd) and the SM part. have it even Then the lightest New Physics particle is stable. If it is electrically neutral then can be a candidate for DM This conserved quantum number is not imposed just to have a DM candidate it has been imposed for the model to survive F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 19/1

24 New Physics provides DM Symmetry breaking and DM Survival evade proton decay indirect precision measurements (LEP legacy) Examples: R-parity and LSP in SUSY (majorana fermion) KK parity and the and LKP in UED (gauge boson) T-parity in Little Higgs with the LTP (gauge boson) LZP (warped GUTs) (actually it s a Z 3 here) (Dirac fermion) even modern technicolour has a DM candidate so New Physics even if not cosmological DM has an invisible signature at the colliders F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 20/1

25 Matter Budget and Precision 3. Testing the cosmology/astrophysics Present measurement at 2σ < ω = Ω DM h 2 < (6%) future (SNAP+Planck) < 1% Particle Physics Cosmology through ω is wholly New Physics But will LHC, ILC see the same New Physics? New paradigm and new precision: change in perception about this connection ω used to: constrain new physics (choice of LHC susy points, benchmarks) Now: if New Physics is found, what precision do we require on colliders and theory to constrain cosmology? (Allanach, Belanger, FB, Pukhov JHEP 2004) strategy/requirements on theory and collider measurements to match the present/future precision on ω and gives clue on the distribution of DM F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 21/1

26 direct and indirect Direct and Indirect Searches p, e +, γ, ν,... χ 0 1 χ χχ ν ν ν CDMS, Edelweiss, DAMA, Genuis,.. Amanda, Antares, I cecube,.. F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 22/1

27 Indirect Detection F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 23/1

28 Indirect Detection F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 23/1

29 Indirect Detection p,e +,γ do not scan the same amount of space F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 23/1

30 Annihilation into photons: Particle Physics and Astro dφ γ dωde γ = i dn i γ 1 σ i v de γ 4πm 2 χ }{{} Physique des Particules ρ 2 dl }{{} Astro γ s: Point to the source, independent of propagation model(s) continuum spectrum from χ 0 1 χ0 1 f f,..., hadronisation/fragmentation ( π 0 γ ) done through isajet/herwig Loop induced mono energetic photons,γγ,zγ final states ACT: HESS, Magic, VERITAS, Cangoroo,... Space-based: AMS, Egret,... GLAST, F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 24/1

31 indirect detection: DM density distributions, profiles rρ kpc GeV cm Moore Einasto NFW Isothermal r kpc «γ 1 + (ro /a) «( β γ α ) ρ o 0.3GeV/cm 3 atr o = 8.5kpc ρ(r) = ρ o ro r 1 + (r o /a) (α, β, γ, a(kpc)) = (2,2,0,4) Isothermal (α, β, γ, a(kpc)) = (1,3, 1,20) NFW cusped (α, β, γ, a(kpc)) = (1.5,3,1.5,28) Moore,cusped and there might be clumps!...boost factors F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 25/1

32 indirect detection: modelling propagation 1 F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 26/1

33 indirect detection: modelling propagation 2 F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 27/1

34 PAMELA controversy TeV WIMP ( χ χ W W HEAT AMS 98 Background ) Background + Signal ) PAMELA 08 + e + / ( e - e B = Energy [GeV] 2 10 F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 28/1

35 PAMELA controversy TeV WIMP ( χ χ W W HEAT AMS 98 Background ) Background + Signal ) PAMELA 08 + e + / ( e - e B = Energy [GeV] 2 10 F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 28/1

36 DM annihilation to W + W with M = 150GeV, Strumia et al., pre FermiLAT/HESS F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 29/1

37 DM annihilation to W + W with M = 150GeV, Strumia et al., with FermiLAT/HESS F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 30/1

38 DM annihilation to W + W with M = 1TeV F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 31/1

39 DM annihilation to W + W with M = 10TeV F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 32/1

40 PAMELA, just a pulsar? F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 33/1

41 Direct detection ingredients: dark matter density and modulation, velocity distribution Nuclear form factors,...(uncertainties...) F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 34/1

42 Underground direct detection (pb) σ S.I Edelweiss II Zeplin II Zeplin IV Xenon Genius within WMAP (pb) σ S.I Edelweiss II Zeplin II Zeplin IV Xenon Genius m χ tan β = 10 tan β = m χ F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 35/1

43 New Physics or DM Physics and E T miss...so New Physics even if not cosmological DM has an "invisible" signature at the colliders...easy to shed light on DM at LHC? F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 36/1

44 New Physics or DM Physics and E T miss Is it necessarily DM candidate? stable at the scale of LHC detectors, 1ms, not age of the Universe... F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 37/1

45 in 1998 we were told to expect an early SUSY discovery F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 38/1

46 Discovery of miss Et L dt = 100 fb -1 A 0 = 0, tanβ = 2, µ < 0 g ~ (3000) m1/2 (GeV) ISAJET CMSJET 4.5 q ~ (2500) miss E T g ~ (2500) h(95) 1l 1000 no leptons q ~ (2000) TH g ~ (2000) 800 2l OS 2l SS g ~ (1500) 600 3l q ~ (1500) Ωh 2 = 1 g ~ (1000) g ~ (500) q ~ (1000) Ωh 2 = 0.4 h(80) q ~ (500) 0 EX m 0 ( GeV) F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 39/1

47 But fake miss Et: Not even SM physics! Miss Et pointing along jets All machine garbage ends up in Et miss trigger F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 40/1

48 ATLAS TDR (same with CMS) ATLAS TDR 98 (msugra point, PreWMAP) F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 41/1

49 ATLAS TDR (same with CMS) ATLAS TDR 98 (msugra point, PreWMAP) ATLAS 2006 F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 41/1

50 ATLAS TDR (same with CMS) ATLAS TDR 98 (msugra point, PreWMAP) ATLAS 2006 What happened? Real Et miss from neutrinos Complex multi-body final states: can not rely on MC alone. Need data and MC. Improve NLO multilegs, matching,... F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 41/1

51 F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 42/1

52 Next step: Properties of DM, example SPIN?? Couplings F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 43/1

53 Synergy Collider-Cosmology-Astrophysics What does it take to prove it is a DM candidate the right relic density has to confirm the rate of Dark Matter Direct Detection has to confirm Indirect Detection rates: annihilations into anti-matter, photons, neutrinos But all three items carry substantial assumptions or drastic differences in the modelling of astrophysics one is assuming detection is assured in DD and Ind. Detection Important to extract as precise as possible the microscopic properties of DM, interaction constrain the cosmological models constrain the astrophysics models: DM distribution, clumping, perhaps propagation may even use some hints from astrophysics to input at colliders F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 44/1

54 Collider Inputs SUSY Parameters Annihilation N Interaction Relic Density Indirect Detection Direct Detection Astrophysical and Cosmological Inputs F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 45/1

55 Constraining Power of the relic density Orders of magnitude, DM cross sections orders of magnitude also (same for direct and indirect detection) F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 46/1

56 formation of DM: Very basics of decoupling At first all particles in thermal equilibrium, frequent collisions and particles are trapped in the cosmic soup universe cools and expands: interaction rate too small or not efficient to maintain Equil. (stable) particles can not find each other: freeze out and get free and leave the soup, their number density is locked giving the observed relic density from then on total number (n a 3 ) = cste Condition for equilibrium: mean free path smaller than distance traveled: l m.f.p < vt l m.f.p = 1/nσ t 1/H or Equilbrium: Γ = nσv > H freeze ou/decoupling occurs at T = T D = T F : Γ = H and Ω χ 0 1 h 2 1/σ χ 0 1 F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 47/1

57 Relic Density: Boltzman transport equation based on L[f] = C[f] dilution due to expansion Boltzmann Suppression Exp(-m/T) Freeze-out dn/dt = 3Hn < σv > (n 2 n 2 eq ) χ 0 1 χ0 1 X X χ 0 1 χ0 1 at early times Γ H n n eq T m X not enough energy to give T f 20GeV t 10 8 s X χ 0 1 χ0 1 T f m/25 n drops and so does Γ Ω χ 0 1 h 2 1/σ χ 0 1 F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 48/1

58 Thermal average must calculate all annihilation, co-annihilation processes. Each annihilation can consist of tens of cross sections... χ 0 i χ0 j X SMY SM, χ 0 1 f 1 X SM Y SM,... < σv >= P R g i g j ds sk 1 ( s/t) p 2 ij σ ij(s) i,j (m i + m j ) 2 2T ` P g i m 2 i K, 2(m i /T) 2 i p ij is the momentum of the incoming particles in their center-of-mass frame.» (s (mi + m j ) 2 )(s (m i m j ) 2 1 ) 2 v p ij = 1 2 s v = 0 v σv F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 49/1

59 All in all... Ω χ 0 1 h M P x f g 1 <σ χ 0 1 v> Ω χ 0 1 h < σ χ 0 1 v > 1pb order of magnitude of LHC cross sections < σ χ 0 1 v >= πα 2 /m 2 Ω χ 0 1 h 2 (m/tev ) 2 m G 1/2 F 300GeV but with the precision on the relic that we have now (6%) and the many possibilities from the particle physics perspectives, need more than just an order of magnitude calculation. need to efficiently calculate within many models of NP As we saw need to calculate relic, direct, indirect and collider observables at the heart is the microscopic properties of DM and the New Physics (with good control of background) F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 50/1

60 Recap: Collider,Relic, Indirect, Direct For indirect need σ χ 0v for v for Ω χ 0h 2 1 σ χ 0v for v = with σ χ 0v = a + bv 2 if a dominant usually measures indirect. 1 At collider process not necessarily inverse of DM DM annihilation No need underlying parameters. F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 51/1

61 Tools from particle physics Need powerful, modular and versatile tools F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 52/1

62 micromegas: Tools for DM/ Collider Physics/ Flavour for a general NP F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 53/1

63 micromegas given any set of parameters it can identify LSP, NLSP, generate and calculate ω Model defined in Lanhep (more later) Fed into CalcHEP...tree-level, some 3000 processes could be needed. Higgs sector (SUSY): improved Higgs masses/mixings (read from FeynHiggs, for example) but interpreted in terms of an effective scalar potential (GI), following FB and A. Semenov (PRD 02) Effective Lagrangian also includes important RC (Higgs couplings, m b effects,..) Interfaced with Isajet, Suspect, SoftSUSY parameters at high scale run down to the ew scale (g 2) µ, b sγ, B s µ µ +,.. NMSSM (with C. Hugonie), CP violation (with S. Kraml), UED, Dirac, host of others open source : procedure to define your own model, soon powerful generalised direct detection module indirect detection cross sections, interface with propagation, polarisation completed SLHA compliant, MCMC interface (Ritesh) F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 54/1

64 Need to go beyond tree-level: Need percent level Higgs funnel with and without Higgs higher order effective couplings taking WMAP for example, for heavy A only loop result makes model survives F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 55/1

65 S LOOP S N. Baro, FB, G. Chalons, S. Hao, A. Semenov, (D. Temes) Need for an automatic tool for susy calculations handles large numbers of diagrams both for tree-level and loop level able to compute loop diagrams at v = 0 : dark matter, LSP, move at galactic velocities, v = 10 3 ability to check results: UV and IR finiteness but also gauge parameter independence for example ability to include different models easily and switch between different renormalisation schemes Used for SM one-loop multi-leg: new powerful loop libraries (with Ninh Le Duc) F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 56/1

66 SloopS F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 57/1

67 Non-linear gauge implementation L GF = 1 ξ W ( µ ie αa µ igc W βzµ )W µ + + ξ W g 2 (v + δ h h + δ H H + i κχ 3 )χ ξ Z (.Z + ξ Z g (v + ǫ h h + ǫ H H)χ 3 ) 2 1 (.A) 2 2c W 2ξ γ quite a handful of gauge parameters, but with ξ i = 1, no unphysical threshold more important: no need for higher (than the minimal set)for higher rank tensors and tedious algebraic manipulations F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 58/1

68 ÜÔÐÓ Ø Ò Ò ÒØ Ö Ò ÑÓ ÙÐ ËØÖ Ø Ý «Ö ÒØ Ó ÖÓÑ Ó Ø ÑÓ Ð Ä Ö Ò Ò Ò Ä ÒÀ È Ò Ô ÖØ Ð ÓÒØ ÒØ ¹ ÒØ Ö Ø ÓÒ Ø ÖÑ ¹ Ø Ò Ð Ò Ô Ö Ñ Ø Ö ¹ Ó Ø Ø ÖÑ ÓÒ ØÖÙØ Ý ÊËÌ ¹ Ú Ú ÐÙ Ø ÓÒ ÝÒ ÖØ ¹ ÓÖÑ Ð ÑÓ ÄÓÓÔÌÓÓÐ Ö ÙØ ÓÒ Ò ÔÔÖÓÔÖ Ø ÓÖ Ñ ÐÐ Ö Ð Ø Ú Ú ÐÓ Ø Ø Ò ÓÖ Ò Ø ÓÒ Ó Ö ÒÓÖѺ ÓÒ Øº Ò Ø Ð ÑÓ Ð ¹ Ù ¹ Ü Ò ÓÒ ØÖ ÒØ Ù Ô Ö Ñ Ø Ö Ô Ò Ò ÆÓÒ¹Ä Ò Ö Ò Ö ÅÓ Ð Ð ÅÓ Ð ¹ Ò Ñ Ø Ð ØÖÙØÙÖ ¹ ÝÒÑ Ò ÖÙÐ ÒÐÙ Ò Ì ÖÓ Ö Ñ Ø ÖÑ Ò ÒØ µ Ê ÒÓÖÑ Ð Ø ÓÒ Ñ F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 59/1

69 From the Lagrangian to the Feynman Rules vector A/A: (photon, gauge), Z/Z:( Z boson, mass MZ = , gauge), W+ / W- : ( W boson, mass MW = MZ*CW, gauge). scalar H/H:(Higgs, mass MH = 115). transform A->A*(1+dZAA/2)+dZAZ*Z/2, Z->Z*(1+dZZZ/2)+dZZA*A/2, W+ -> W+ *(1+dZW/2), W- -> W- *(1+dZW/2). transform H->H*(1+dZH/2), Z.f -> Z.f *(1+dZZf/2), W+.f -> W+.f *(1+dZWf/2), W-.f -> W-.f *(1+dZWf/2). let pp = { -i* W+.f, (vev(2*mw/ee*sw)+h+i* Z.f )/Sqrt2 }, PP=anti(pp). lterm -2*lambda*(pp*anti(pp)-v**2/2)**2 where lambda=(ee*mh/mw/sw)**2/16, v=2*mw*sw/ee. let Dpp^mu^a = (deriv^mu+i*g1/2*b0^mu)*pp^a + i*g/2*taupm^a^b^c*ww^mu^c*pp^b. let DPP^mu^a = (deriv^mu-i*g1/2*b0^mu)*pp^a -i*g/2*taupm^a^b^c*{ W- ^mu,w3^mu, W+ ^mu}^c*pp^b. lterm DPP*Dpp. Gauge fixing and BRS transformation let G_Z = deriv*z+(mw/cw+ee/sw/cw/2*nle*h)* Z.f. lterm -G_A**2/2 - G_Wp*G_Wm - G_Z**2/2. lterm - Z.C *brst(g_z). RenConst[ dmhsq ] := ReTilde[SelfEnergy[prt["H"] -> prt["h"], MH]] RenConst[ dzh ] := -ReTilde[DSelfEnergy[prt["H"] -> prt["h"], MH]] RenConst[ dzzf ] := -ReTilde[DSelfEnergy[prt["Z.f"] -> prt["z.f"], MZ]] RenConst[ dzwf ] := -ReTilde[DSelfEnergy[prt["W+.f"] -> prt["w+.f"], MW]] M$CouplingMatrices = { Output of Feynman Rules with Counterterms!! (* H H *) C[ S[3], S[3] ] == - I * { { 0, dzh }, { 0, MH^2 dzh + dmhsq } }, (* W+.f W-.f *) C[ S[2], -S[2] ] == - I * { { 0, dzwf }, { 0, 0 } }, (* A Z *) C[ V[1], V[2] ] == 1/2 I / CW^2 MW^2 * { { 0, 0 }, { 0, dzza }, { 0, 0 } }, (* H H H *) C[ S[3], S[3], S[3] ] == -3/4 I EE / MW / SW * { { 2 MH^2, 3 MH^2 dzh -2 MH^2 / SW dsw - MH^2 / MW^2 dmwsq }, (* H W+.f W-.f *) C[ S[3], S[2], -S[2] ] == -1/4 I EE / MW / SW * { { 2 MH^2, MH^2 dzh + 2 MH^2 dzwf -2 MH^2 / SW dsw - MH^2 / }, (* W-.C A.c W *) C[ -U[3], U[1], V[3] ] == - I EE * { { 1 }, { - nla } }, F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 60/1

70 SloopS for SUSY at tree-level F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 61/1

71 Gram determinant for small velocity ¾ ½¼ ¾ ½¼ F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 62/1

72 All annihilations and co-annihilations: 1-loop EW and QCD, Baro+FB (PL 2008) F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 63/1

73 SloopS, bino co-annihilation F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 64/1

74 SloopS, bino annihilation F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 65/1

75 SloopS, wino co-annihilation F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 66/1

76 SloopS, wino co-annihilation F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 67/1

77 Ø ÖÓ ¹ Ø ÓÒ ÓÑÔÙØ Ò Ø Ò Ø ÓÙ Ò Ö Ñ ÒÐÙ Ò ÅÓÖ Application to χ 0 1 χ0 1 γγ, Zγ, gg (FB, A. Semenov, D. Temes,hep-ph/ , PRD...) χ 0 1 χ + i γ χ 0 1 W γ χ 0 1 χ + i χ 0 1 W χ + j χ + i χ + i Z χ 0 1 W W W a) b) c) Z χ 0 1 γ Z χ 0 1 γ χ 0 1 W γ χ 0 1 W γ A, H, h, Z χ + i χ + i χ + i H, h χ 0 1 χ + j Z W Z χ 0 1 χ 0 1 d) e) f) W Z Æ Û ÓÒØÖ ÙØ ÓÒ ÓÙÒ Ò Zγ χ 0 1 γ χ 0 i χ 0 1 Z ÓÒØÖ ÙØ ÓÒ ÓÙÒØ ÖØ ÖÑ Ç Ø Ò ÖÓÑ ØÖ ¹Ð Ú Ð χ 0 1 χ 0 1 ZZ Ò δz ¹ Zγ ¹ Ë Ò δz Zγ (1 α) Ì Ò ÔÙØ ØÓ Þ ÖÓ α = 1 ÓÓ Ò ÔÖÓÔ Ö Ù ÑÔÐ Ø ÓÑÔÙØ Ø ÓÒ 1 2 F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 68/1

78 Sommerfeld Enhancement and matching Å Ø Ò Û Ø ÒÓÒ¹Ô ÖØÙÖ Ø Ú ÓÑÔÙØ Ø ÓÒ À ÒÓ Ø Ðº³¼ ÁÒ Ø ÜØÖ Ñ ÒÓ Ò Û ÒÓ Ð Ñ Ø ÓÒ ¹ÐÓÓÔ ØÖ ØÑ ÒØ Ö ÙÒ Ø Ö ØÝ ÒÓÒ¹Ô ÖØÙÖ Ø Ú ÒÓÒ¹Ö Ð Ø Ú Ø ÔÔÖÓ... ÓÑÔÙØ Ø ÓÒ Ò ÓÒ ¹ÐÓÓÔ Ö ÙÐØ ÆÓÒ¹Ô ÖØÙÖ Ø Ú (v = 0) ÒÓ m f = m A = 100 TeV, M 2 = 2M 1 = 50 TeV, tan β = 10, A = 0, δm = 0.1 GeV Ê ÓÒ Ò Ò Ò Ò Ö ÙÐØ Ú Ö Ð ÓÖ Ö Ó Ñ Ò ØÙ Å Ø Ò Û ÐÐ Ø ÔÐ ÖÓÙÒ Î F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 69/1

79 Relic Density: Loopholes and Assumptions At early times Universe is radiation dominated: H(T) T 2 Expansion rate can be enhanced by some scalar field (kination), extra dimension H 2 = 8πG/3 ρ(1 + ρ/ρ 5 ), anisotropic cosmology,... Entropy conservation (entropy increase will reduce the relic abundance Wimps (super Wimps) can be produced non thermally, or in addition produced in decays of some field (inflaton,...) F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 70/1

80 Almost Wimps: Swimps, Feng et al; Assuming that each WIMP decay produces one swimp, the inherited density is simply WIMP superwimp Ω swimp = m swimp Wimp Ω Wimp beware though: If couplings very weak, decays may be very late and would directly impact on BBN, CMB, diffuse γ flux (energy released in visible decay products serious stopper!) F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 71/1

81 History of the Universe, WIMP density depends on the history of the Universe before BBN (0.8MeV) (abundance of light elements), large time scale between freeze-out and BBN for BBN to hold it is enough that the earliest and highest temperature during the radiation era T RH > 4MeV T RH is to be understood as the temp. which after a period of rapid inflationary expansion the Universe reheats (defrosts) and the expanding plasma reaches full thermal equilibrium F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 72/1

82 History of the Universe, T RH > Density may be decreased by reducing rate of thermal production, possibility to have tiny T RH < T f.o or by production of radiation after freeze-out increased by injecting Wimps from decays or/and increasing the expansion rate Open up more possibilities, constrain Physics at the Planck scale?? F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 73/1

83 Non Standard Cosmo Prototype: A scalar field decaying not long before BBN (Giudice, Kolb; Gelmini and Gondolo,...) dρ φ dt dn dt ds dt = 3Hρ φ Γ φ ρ φ = 3Hn σv (n 2 n 2 eq) + b m φ Γ φ ρ φ = 3Hs + Γ φρ φ T where m φ, Γ φ, and ρ φ are respectively the mass, the decay width and the energy density of the scalar field, and b is the average number of neutralinos produced per φ decay. Notice that b and m φ enter into these equations only through the ratio b/m φ (η = b(100tev/m φ ) and not separately. Finally, the Hubble parameter, H, receives contributions from the scalar field, Standard Model particles, and supersymmetric particles, H 2 = 8π 3M 2 P (ρ φ + ρ SM + ρ χ ). T RH = 10MeV (m φ /100TeV ) 3/2 (M P /Λ) Γ φ m 3 φ /Λ2 F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 74/1

84 Non Standard Cosmo, Figs Gelmini and Gondolo 1e-02 1e-04 1e-06 1e-08 1e-10 Standard Equlibrium T RH =10 MeV T RH =100 MeV T RH =1 GeV T RH =10 GeV Y=n χ /s 1e-12 1e-14 1e-16 1e-18 1e-20 1e-22 1e Temperature (GeV) M 1/2 = m 0 = 600GeV, A 0 = 0, tan β = 10, and µ > 0, m χ = 246 GeV T f.o = 10GeV. Ω std h η = 0 msugra parameters F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 75/1

85 Non Standard Cosmo 1e-02 1e-04 1e-06 T RH Standard Equlibrium η = 0 η=1e-8 η =1e-6 η =1e-4 η =1e-2 Y=n χ /s 1e-08 1e-10 1e-12 1e-14 1e Temperature (GeV) F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 76/1

86 Non Standard Cosmo Ωh e Reheating Temperature (GeV) η = 0 η = η = 10-8 η = 10-6 η = 10-4 η = 10-2 Note that different cosmological models may look standard! F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 77/1

87 Important Message The bulk region can be correct, good news for parameter extraction at LHC Large Wino cross sections that are good for Indirect Detection not ruled out F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 78/1

88 reconstruct Properties of DM measure masses and all important relevant couplings (bino/wino/ components,..., mixing) that enter the relic calculation Most often this is also what enters the indirect detection, for s-wave if no Sommerfeld enhancement strive to measure the coupling of the Higgs to the DM, often enters in the direct detection calc. F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 79/1

89 Case studies, the msugra inspired regions, requirements from colliders 800 tan β = 10, µ < 0 Bulk region: bino LSP, l R exchange, (small m 0, M 1/2 ) m 0 (GeV) b sγ m h = 114 GeV τ 1 co-annihilation: NLSP thermally accessible, ratio of the two populations exp( M/T f ) small m 0, M 1/2 : GeV Higgs Funnel: Large tan β, χ 0 1 χ0 1 A b b,(τ τ), (exc.) Pre-WMAP (bulk) τ 1 / χ 0 1 co-annihilation strip m τ1 < m χ 0 1 M 1/2 : GeV, m 0 : GeV Focus region: small µ M 1, important higgsino component, WMAP m 1/2 (GeV) requires very large TeV m 0 derived accuracies refer to obtaining 10% precision o n WMAP F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 80/1

90 τ 1 co-annihilation region: The Spectrum 1400 χ χ 0 3 mass (GeV) χ 0 4 ~ er ~ e L ~ τ 2 µ > 0,tan β = 10, A 0 = 10 m 0 = M 1/ M 2 1/ M 0 (GeV) χ 1 At ILC will produce ( τ 1, µ R,ẽ R ), 500GeV, a window for ẽ L and χ 0 1 χ0 2. F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 81/1

91 τ 1 co-annihilation region: The Landscape annihilation (%) χ 1 χ1 0 ~ χ 1 τ ~ ~ τ τ 0 ~ χ 1 l ~ ~ l~ (τ /l ) ~ ~ ~ l =µ or e M (GeV) M cos2θ τ cos2θ τ m~ τ m~ τ Different co-annihilation channels are important M = m τ1 m χ 0 1 from 10GeV to 1GeV. τ 1 mixing angle small. Other relevant parameters µ tanβ F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 82/1

92 τ 1 co-annihilation region: accuracy within msugra a a(m 1/2 ) a(m 0 ) A 0 - a(tanβ) A 0 - (GeV) accuracy on m 0, M 1/2 demanding: 3% : 1% may be achievable at LHC for tgb require 10percent m~ (GeV) τ since spectrum has decay chain similar to bulk (unless mass difference too small), LHC might match WMAP But more study is needed. LHC/LC obviously helps F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 83/1

93 τ 1 co-annihilation region: Model Independent M must be measured to less than 1GeV cos2θ τ - required, a(m) cos2θ τ - required δm required a(m χ ) m~ τ (GeV) 1 δm required (GeV) mixing angle accuracy should be feasible at ILC accuracy on LSP mass not demanding but this is because we have constrained M. other slepton masses need also be measured in terms of physical parameters residual µ tan β accuracies not demanding Preliminary studies indicate these accuracies will be met for the lowest m χ δ - ( M) Ωh 2 /Ωh tanβ= µ=µ m~ τ (GeV) GeV m~ (GeV) e F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 84/1

94 Focus: The Landscape, m 0, m f > 1TeV,tan β = 50 annihilation (%) coannihilation annihilation tt - bb - WW/ZZ Zh,hh mass (GeV) M χ1 0 χ 2 0 χ 3 0 µ χ 4 0 M 1 M M 0 (GeV) χ M 0 χ1 (GeV) χ 0 1 χ0 1 Z t t important A exchange small (M A > 1TeV), here it s Goldstone dominance Higgsino component implies WW, ZZ channel co-annihilation not the most important within WMAP. Higgsino component implies µ measurement F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 85/1

95 Focus: Accuracies in relevant parameters M 1, µ m t M 2 tanβ M 1 µ M χ3 0 a M 0 χ1 (GeV) Here a(m t ) 10% accuracies on M 1 (m χ 0 1 ), µ(m χ 0 2 ) 1% F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 86/1

96 LHC+ILC No. MC Experiments (a) / 34 Constant Mean E-04 Sigma E E-04 ISASUGRA v Ω χ h 2 Polesello+Tovey, LHC, bulk Baltz,Battaglia, Peskin and Wisansky F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 87/1

97 Highlights on accuracies and reconstruction Within msugra accuracies on (m 0, M 1/2 ) 1% sometimes less, given enough energy LHC+LC should do the job Within msugra need to control RGE codes some focus scenarios are too tough. May not be able to match WMAP and PLANCK model independent analysis in msugra inspired though gives the edge to LC (if spectrum within sight) plus some help from LHC Need to extend studies to less accidental scenarios (non gaugino unification) what about a study with non standard cosmology? important study to be done beyond tree-level!!! F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 88/1

98 direct and indirect learning and feeding into Direct and Indirect Searches p, e +, γ, ν,... χ 0 1 χ χχ ν ν ν CDMS, Edelweiss, DAMA, Genuis,.. Amanda, Antares, I cecube,.. F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 89/1

99 Annihilation into photons dφ γ dωde γ = i dn i γ 1 σ i v de γ 4πm 2 χ }{{} Particule physics (ρ + δρ) 2 dl } {{ } Astro γ s: Point to the source, independent of propagation model(s) continuum spectrum from χ 0 1 χ0 1 f f,..., hadronisation/fragmentation ( π 0 γ ) done through isajet/herwig Loop induced mono energetic photons,γγ,zγ final states ACT: HESS, Magic, VERITAS, Cangoroo,... Space-based: AMS, Fermi-LAT, Egret,... F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 90/1

100 Propagation SloopS, micromegas,ams/hess SloopS GUT Scale Suspect micromegas PYTHIA Halo model Cosmic Ray Fluxes charged γ m χ =151 GeV.s -1 ] s -1 ] -2 [ GeV.cm γ.φ 2 E bb [ GeV.cm γ E 2.φ 10-7 γγ τ + τ - 0 γz E γ 10 with AMS energy resolution [ GeV ] with a typical ACT energy resolution [ GeV ] E γ 2 SIMULATION: Parameterising the halo profile: (α, β, γ) = (1,3,1), a = 25kpc. (core radius), r 0 = 8kpc (distance to galactic centre), ρ 0 = 0.3 GeV/cm 3 (DM density), opening angle cone 1 o SUSY parameterisation m 0 = 113GeV, m 1/2 = 375 GeV, A = 0, tan β = 20, µ > 0 γ lines could be distinguished from diffuse background F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 91/1

101 Annihilation into e +, p, D dφ f dωde f = i dn ī f 1 σ i v de f 4πm 2 (ρ + δρ) 2 P prop χ }{{}}{{} Particle physics Astro γ s: Model of propagation and background Halo Profile modeling, clumps, cusps,..boost factors,.. If particle Physics fixed, constrain astrophysics ACT: HESS, Magic, VERITAS, Cangoroo,... Space-based: AMS, GLAST, Egret,... F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 92/1

102 Summary Cosmology has entered the era of precision measurements. Particle Physics component of DM must be extracted unambiguously. If large clean and understood signals of Etmiss at LHC there is most probably a link with DM Strive for as much as possible for a model independent reconstruction of the important relevant parameters of DM One may be lucky to be a good region of the New physics parameter space Other hints and constraint can come from observables not necessarily with Etmiss, the rest of the NP spectrum even Higgs In a first stage one can fit to constrained models strategy would also depend on how the astrophysics scene evolves in the most lucky situation an extraordinary synergy between collider physics, astrophysics and cosmology, a glimpse on the history of the Universe, remnants of the Planck scale??? F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 93/1

103 Summary, continued Improve tools both for the NP and the SM Open our...horizons F. BOUDJEMA, Dark Matter and the LHC, Würzburg, Jul 09 p. 94/1