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" ! " MPl m " ! " m e c τ e NTP 2 G mLSP 2 mτe in Cosmology e Colliders g m NLSP = Stau ττ# : NTP 2 $ 0.002 Dark −→ Ω h G Y h Frank (Max-Planck-Institute of Physics, Munich) Matter and at 69 NLSP a e NTP 2 Frank D. D. Steffen Steffen (Max-Planck-Institute of Physics, Munich) Dark Matter in Cosmology and at Colliders 30 NLSP = Stau # : ΩMunich) h $ 0.002 G BBN + Ω h = e 100 GeV 100 GeV Frank D. Steffen (Max-Planck-Institute−→ of Physics, Dark Matter in Cosmology and at Colliders 30 g extremely ... G LSP 100 GeV 100 GeV ρc /s(T0 ) c b b$ # g" ! " ! ! " g g m m ! " ! " e e mLSP mG YNLSP NTP 2 CMB B m # e e NLSP $ Bino B: NTP 2 h ∼ 0.1 −→ Ω (model dep.) B G M = 2.44 ×1 # = ; Bolz, Brandenburg, Buchmüller, Pl−11 e NLSP $ Bino −→ B: h ∼ 0.1 ΩG (model dep.) [... ’01] e 100 GeV GeV 100 100 GeV 3.7 × 10 G 100 GeV 100 GeV a $ FDS, b ’06] c γ rays # [Pradler,

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18

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19

[Pradler, FDS, arXiv:0710.4548]

Gravitino DM with a GeV scale mass (as obtained in gravity med. SUSY breaking) could be very difficult to probe at the LHC

Gravitino DM with a mass < 1 GeV (as obtained in gauge mediated SUSY breaking)

could still be accessible at the LHC Frank D. Steffen (Max-Planck-Institute of Physics, Munich)


19

(10 GeV) = 0.1ρrad (10 GeV) and Tafter = ρXbelow. cay (4) width and the energy density of X. Thus, the temperature web version) for ρthat GeV) = 8ρrad (10 Fig. 7 lines shows mod X (10 inflation after the decay can be expressed in terms of ΓX , FDS, ’07] 9[Pradler, produced gravitino yield (3) as a function of TR for = 10 GeV become allowed in T (5) # Fig. 1. The thermally R mG 100 1 GeV, 10 GeV, 100 GeV, and 1 TeV (solid lines ! = 10 MeV, $ 1/4MeV, % thermally produced gravitin dark the matter for δ = ∆ ≈ 233 100. Here m1/2 F.D. = 500 GeV. The dotted lines Thus, from 10 left to right) and M1,2,3 (MGUT ) = J. Pradler, Steffen / Physics Letters(21) B 648 (2007) 224–235 ≡ Γ M , T Rescuing Thermal Leptogenesis X obtained P n after mass, show the224–235 corresponding yield with the SU(3) result for the collision oflate-time entropy entropy production after NLSP de production in the / Physics Letters B g 648 (2007) 231 c (T )π 2 ∗ after term of Ref. [10]. The dashed (blue in the web version) horizontal line indicates range of NLSP masses cannot be relaxed. With the dilution after thermally gravitino yield are between produced NLSP decoupling and BB the NLSP equilibrium yield the of(T arelaxation relativistic spinT 1/2 Majorana fermion. no yield = 3H ). Indeed, primordial synthesis which satisfies Γ constraints is more decoupling, of the R X rad after c for viability of S(T thermal leptogenesis i pronounced. Here also the cosmologically range of g is can ) given a lower limit on this temperaturedisfavored low imposes [55–58]: !after ) = NLSP masses can be relaxed [27]. However, as can be seen in G ). YG Y(T story & (T & (Tlowprospec yield to the equilibrium abundance. Without the backreactions G > T ) and for collider 6 R panels (b) and (d) of Fig. 7, the Li bound is persistent. With f S(Tafter ) taken into account, the kink position indicates a lower bound , m ) a dilution factor of ∆ = 100, large regions of the (m 1/2 0 Tafter ! 0.7–4 MeV. (22) !remain cosmologically disfavored. For ! ∆ ! 104 , how(6) G G plane In the case of late-time entropy pro n smaller mG decreases to Letters the infor Tf . Towards F.D. Steffendue / Physics B 648 (2007) 224–235 23 ! , TJ.f Pradler, will be shown explicitly ever, the 6 Li bound can be evaded as 3 3 6. Thermal leptogenesis in the Cth In Fig. creasing 6 we the evolution of S,couplings. a ρX , and ρrad forfor pling of the NLSP, we parameterize strength of the gravitino Fora example, d gravitibelow.show dard ! 7 GeV 14 shows that inflation models predicting, forscale example, two exemplary scenarios (22). factor is dark matter upper limit onrespecting TR of 10 can be for 10 aGeV). =Fig. 1 7GeV (10 MeV), we find TfGThe ! problematic 10 GeV (10 mG !An How9 1 TP = 10 GeV become allowed in the CMSSM with gravitino T R −1 TP inflation models andGeV) baryogenesis scenarios. This finding can s normalized reas the initial In the analytical expression (3) we refer to T by a ≡ a(10 = 1 GeV and the temperature R Y (T ) = YG dark Imatter for δ = ∆ ≈ 100. Here it is not necessary to have 0 & & (Tlow ). G thus be important for our understanding of the thermal history ong- (7) δ late-time entropy production in the somewhat window temperature of the radiation-dominated epoch. So far we have taken into account as narrow determined in [59]. dependence of g∗ is 7 GeV of the Universe. The constraint T " 10 between NLSP decoupling and BBN. This is different for the R 1mass −1 considered the (10 phase in which the coherent oscillations sForand therebycoΩ this case,scenarios YNLSP (Tfor GeV) =of0.1ρ GeV) andconsidered Tafter = 6 MeV, S in- of InCMSSM ρX (10not viability thermal in the scenarios 0 ) and radleptogenesis a standard iated ! inflaton field of the Universe, G 5.a (T Constraints on with late-time entropy production R for prospects as energy discussed below. straints remain unaffected. bythe factor of ∆Tφcollider =dominate 100 as the shown bydensity the correspondf > TR ) and s creases dedisfavors thermal leptogenesis. How in terms of the decay width Γ of where one usually defines T R φ gravitino Conversely, in the case of late-time (10shown GeV) = are 8ρrad GeV) andphase, Tafterwe=nuing solid line. For ρXfield constraints applicable for a standard theThe φ. Toinabove account for(10 thegravitino reheating 6.inflaton Thermal leptogenesis the CMSSM with after NLSP decoupling, a dilution f ous val4 as thermal history during the radiation-dominated epoch. Howthe decoupling of the NLSP (and bef shown by the 4.9 MeV, S increases by a factor of ∆ = 10 dark matter merically integrate (1) together with the Boltzmann equations thermal leptogenesis (20) m1/2 = viable for TR " ever, it is possible that a substantial amount of entropy is re(T ), are reduced: and Y corresponding dotted (blue in the web version) line. for the energy densities7 of radiation and the of inflaton field, NLSP 0 t MGUT : leased,Theforconstraint example,TRin" out-of-equilibrium a longStandard thermal leptogenesis 10 GeV obtained in decays the considered d the 10 We restrict our study to entropy production at late times, lived particle X [2,51]. scenarios forspecies a standard cosmological history strongly respondFig. 8. The effect of entropy production after NLSP decoupling for dρCMSSM actor radmassive 1However, Fig. 6. Evolution of S, a 3 ρX , and a 3 ρrad as a function of T for the norGeV ent 13 GeV and ∆ # 4 in the[17]. TP TPfor tan β = 30,late-time T = 10 10 (m , m ) plane A0 = 0, = Γ ρ , + 4Hρ (9) R 1/2 0 disfavors thermal leptogenesis. However, if entropy is released −1 lives sufficiently long, it might decay while φsolid aI If ≡X a(10 GeV) =rad 1 GeVthat .φ Thethe lines are obtained for its rest mass (T ) = (T ), Y Y % T , so thermal production of gravTde-before e= m1/2malization , $ Tlow 0 low R & & The shaded (green in the G web version) bands show µ > 0, and mG 4 can render dt ! = m0 . G decoupling, a=dilution factor of (blue ∆ " in 10the =after 0.1ρNLSP GeV) and Tafter 6 MeV, ρX (10 GeV) ∆ baryon asymmetry which is gener dominates the energy density of the thedotted Universe. The associatedthe region in which rad (10 ature 2 $ 0.126 h for ∆ = 104 (dark) and 2 × 104 0.075 $ Ω 13=GeV. ark mat! itinos isversion) not affected. To work in a model way, G web lines for ρXleptogenesis (10 GeV) = 8ρviable (10 GeV) and T10 4.9 MeV.independent dρ " thermal for T 3 rad after R φ de-(medium). (10) evolution of the entropy per comoving volume, S ≡ sa , is The dot-dashed (red in the web version) 1 lines illustrate the cor9 = −Γleptogenesis + 3Hρ coupling, φthermal φ ρφ , ! 10 Standard usually requires T 6 Li bound. For ∆ = 104 , the regions below the the yield R responding evolution of the we assumescribed that the production of gravitinos and NLSPs in Y (T ) = (Tlow ). by [2,51] dtGeV [17]. However, late-time entropy production dilutes the NLSP 0the right of theYassociated NLSPleftmost associated two rightmost curves and to curve Thus, the thermally produced gravitino yield and—in the case ∆ (blue in (21) !NLSP "see the entropy producing event, such as the direct production in are allowed. For ∆ = 2 × 104 , the region below the line labeled accordingly is baryon asymmetry which is generated well before NLSP de1/3 respectively; for details Appendix F of Ref. [34]. 3 2 of entropy production after decoupling—also the nondS ΓX ρX a 2π 4 −1/3 1 TP um yield cosmologically allowed. NTP become coupling, 11 (20) Γcollision = = g thermally produced gravitino yield are diluted: ∗ the X ρX a S term With our result for (2), we find that the and Ω Accordingly, Ω Moreover, in this section, we decays of X, is negligible. ). η(T η(Tafter ) = G dt T 45 hesis & before G & ∆ ) S(T gravitino yield obtained numerically is in good agreement with 1 low canthebe relaxed. focusYG&on which decoupling (T scenarios ) =η(Tafterwith (Tlow ). ). the together the Boltzmann equation (10) for(23) φ of = Xthe and NLSP thethe webisversion) straints bands indicate region in which 0.075 $ ) =Yin η(T (26) & before G S(T ) (8) afterthe ∆ after 2 13 analytical expression (3) for $ 0.126 for TRIn 10a 3 ρDark GeV and = 104 how (dark) late-time and Frank (Max-Planck-Institute of Physics, Munich) Matter Friedmann equation governing theby evolution of theproduction, scale factorΩG! hi.e., we show e not orD.atSteffen most marginally affected entropy Fig. 6.Gravitino/Axino Evolution of=S,Fig. , and a 3 ρ∆ of T for the20 nor (22) X7 rad as a function

Late-Time Entropy Production

Gravitino DM - with broken R-parity Yesterdays Session Frank D. Steffen (Max-Planck-Institute of Physics, Munich)


21

Gravitino DM @ LHC 2009 LHC particle detector

allowed

proton

The signal: jets + leptons + 2 “stable” charged particles

di

stau

’

sf

av or ed

proton

stau

Stau NLSP Cosmological Constraints

Cosmological Constraints [Steffen, ’06, Steffen, hep-ph/0611027] Frank D. Steffen (Max-Planck-Institute of Physics, Munich)

[Pradler, Steffen, arXiv:0710.4548]

−→ Talk by Josef Pradler (Kosmologie

Very different from the large ETmiss signal of Neutralino DM Frank D. Steffen (Max-Planck-Institute of Physics, Munich)

Dark Matter at the LHC

22

Axino DM @ LHC 2009 LHC particle detector

proton

stau

Stau NLSP Cosmological Constraints

proton

are much weaker stau

The signal: jets + leptons

for axino DM because of a shorter NLSP lifetime

+ 2 “stable” charged particles Very different from the large ETmiss signal of Neutralino DM Frank D. Steffen (Max-Planck-Institute of Physics, Munich)

Dark Matter at the LHC

23

CMS: τ˜1 NLSP: long-lived “Stable” Charged Massive charged Particle @ LHC

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Frank Steffen - Desy

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