Light relic neutralinos. Stefano Scopel. Università di Torino & INFN, Sezione di Torino ITALY

Transcription

1 International Workshop on Astroparticle and High Energy Physics, AHEP 2003, Valencia, Spain, October 2003 Light relic neutralinos Stefano Scopel Università di Torino & INFN, Sezione di Torino ITALY S. Scopel Page 1 Valencia, october 2003

2 Based on work made in collaboration with: Alessandro Bottino Fiorenza Donato Nicolao Fornengo Università di Torino & INFN, Sezione di Torino ITALY S. Scopel Page 2 Valencia, october 2003

3 Introduction ost analysis of the SUSY model assume that gaugino masses are unified at the GUT-scale: 1 = 2 at GUT GeV Gaugino mass unification implies a lower bound on the neutralino mass: m > 50 GeV However the assumption of gaugino mass unification at the GUT scale might not be justified (for instance, the gaugino unification scale may be much lower than the standard GUT-scale, see E. Gabrielli, S. Khalil, C. unõz and E. Torrente-Lujan, PRD63, (2001)) S. Scopel Page 3 Valencia, october 2003

4 Previous papers with 1 2 include... J. Ellis, K. Enqvist, D.V. Nanopoulos and K. Tamvakis, PLB155, 381 (1985);. Drees, PLB158, 409 (1985); PRD33, 1486 (1986);. Drees and X. Tata, PRD43, 2971 (1991); K. Griest and L. Roszkowski, PRD (1992); S. izuta, D. Ng and. Yamaguchi, PLB300, 96 (1993); A. Gabutti,. Olechowski, S. Cooper, S. Pokorski and L. Stodolsky, Astrop. Phys. 6, 1 (1996); G.Bélanger, F.Boudjema, F.Donato, R.Godbole and S.Rosier-Lees, NPB581, 3 (2000); A. Corsetti and P. Nath, PRD64, (2001); R. Arnowitt, B. Dutta and Y.Santoso, arxiv:hep-ph/ ; D.G. Cerdeño, S. Khalil, C. uñoz, arxiv:hep-ph/ ; V.A. Bednyakov and H.V. Klapdor-Kleingrothaus, PRD63, (2001); H. Baer, C. Balazs, A. Belyaev, R. Dermisek, A. afi, and A. ustafayev, JHEP 0205, 061 (2002); V. Bertin, E. Nezri and J. Orloff, JHEP0302, 046 (2003) A. Birkedal-Hansen and B. D. Nelson, PRD67, (2003); PRD64, (2001); G. Bélanger, F. Boudjema, A. Pukhov and S. Rosier Lees, arxiv:hep-ph/ ; D. Hooper and T. Plehn, PLB562, 18 (2003). S. Scopel Page 4 Valencia, october 2003

5 Effective SS scheme (effss) - Independent parameters 1 U(1) gaugino soft breaking term 2 SU(2) gaugino soft breaking term m q soft mass common to all squarks m l soft mass common to all sleptons µ Higgs mixing mass parameter tan β ratio of two Higgs v.e.v. s m A mass of CP-odd neutral Higgs boson (the extended Higgs sector of SS includes also the neutral scalars h, H and the charged scalars H ± ) all defined at the Electro-Weak scale A common dimensionless trilinear parameter for the third family (A b = A t Am q ; A τ Am l) R 1 / 2 SUGRA R = 0.5 S. Scopel Page 5 Valencia, october 2003

6 Experimental constraints accelerators data on supersymmetric and Higgs boson searches (CERN e + e collider LEP2 and Collider Detector CDF at Fermilab) measurements of the b s + γ decay measurements of the muon anomalous magnetic moment a µ (g µ 2)/2 (we use: 160 a µ ) S. Scopel Page 6 Valencia, october 2003

7 The neutralino The neutralino is defined as the lowest mass linear superposition of bino B, wino W (3) and of the two higgsino states H 1, H 2: a 1 B + a 2 W (3) + a 3 H 1 + a 4 H 2 neutral, colourless, only interactions of the weak type stable if R parity is conserved, thermal relic non relativistic at decoupling Cold Dark atter (required by CB data+structure formation models) Relic density can be compatible with cosmological observations: < Ω h 2 < IDEAL CANDIDATE FOR COLD DARK ATTER S. Scopel Page 7 Valencia, october 2003

8 LOWER LIIT ON THE NEUTRALINO ASS FRO :! " # # %$ $ $ %$ & $ &$ '! ( ) ) * + " -, / / /98 4 :<; :>= /? 300 /3. A 2 / B C D GFE H I1 J K / K 71 / J. /? 4 A / ? J L 7N 23 /3 6 OQP /9 A 1 65 R J S 3.? U0 VE U VE U VE U VE E O L W W / 28 3J X. K1 Y13 [Z \ D \ ] ^ $ & = \ ] ^ $ % Z a`_ cb d e a f hg e ib jc lk g ck e j he i i jc k mn o mn o mn o mn o Vp E rq X r P N E r s N R tu 5 00 \ mn wve Vp L r q xq yn xz, rr s tu 5 [00 \ mv H I1 u 5 00 \ mn ve Vp n r Xq {N z s }R 2 65 ~t E u \ ] mn H I1 mn nvl Vp G V r Xq {N z s }R tu 5 [00 \ u 5 00 \ mn VvL Vp w r U U rx X X x ns 2 65 t m v o u [ \ mn H I1 u 5 00 \ ƒ 71 / J /8 Y/ /8 9 K u 2. u u 21? Z o r q q, P P Fp z ˆ ] ^Š E ] ^ L mg E Vp F r q N Fp U z ˆ ] ^Š E ] ^ L: m > 31 GeV Warning: this limit is model dependent! S. Scopel Page 8 Valencia, october 2003

9 Lower limits on the neutralino mass from accelerators Indirect limits from chargino production (e + e + ): m ± > 100 GeV m > 50 GeV if R 1 2 = 5 3 tan2 θ w Direct limits from e + e i 0 j 0 ( 1 0, m 1 0 < m 2 0 < m 3 0 < m 4 0 ) : Invisible width of the Z boson (upper limit on number N ν of neutrino families) issing energy + photon(s) or f f from i> decay Direct limits from t c and b b at Tevatron small production cross sections light squark masses (< 100 GeV) required No absolute direct lower bounds on m S. Scopel Page 9 Valencia, october 2003

10 ass matrices: Neutralino vs. chargino Neutralino 1 0 m Z sin θ W cos β m Z sin θ W sin β 0 2 m Z cos θ W cos β m Z cos θ W sin β m Z sin θ W cos β m Z cos θ W cos β 0 µ m Z sin θ W sin β m Z cos θ W sin β µ 0 1 appears only in neutralino mass. Limits on chargino mass affect 2 Chargino 2 m W 2 cos θw m W 2 sin θw µ Pure higgsino m m ± µ Pure bino m 1 ; m ± 2 S. Scopel Page 10 Valencia, october 2003

11 Dark matter density from WAP New CB data, used in combination with other cosmological observations, are narrowing down the range of the matter abundance Ω m h 2 and some of its constituents, Ω ν h 2 and Ω b h 2 : < Ω CD h 2 < (2 σ range) The upper bound (Ω CD h 2 ) max establishes a strict upper limit for any specific cold species The lower bound (Ω CD h 2 ) min fixes the value of the average abundance below which the halo density of a specific cold constituent has to be rescaled as compared to the total CD halo density Rescaling factor: ξ ρ /ρ 0 min(1, Ω h 2 /(Ω CD h 2 ) min ) (ρ = local neutralino density; ρ 0 =total local dark matter density) S. Scopel Page 11 Valencia, october 2003

12 Neutralino relic abundance Ω h 2 = x f cm 2 g (x f ) 1/2 <σ ann v> < σ ann v > x f σ ann v int, σ ann v int x 0 x f < σ ann v > dx < σ ann v > = thermally averaged product of the annihilation cross-section times the relative velocity of a pair of neutralinos x f,0 m T f,0, T f =freeze-out temperature; T 0 =today s temperature g (x f ) =# of relativistic degrees of freedom of the thermodynamic bath at x f Standard expansion in S and P waves for σann v : σann v ã + 1 2x f b S. Scopel Page 12 Valencia, october 2003

13 f f annihilation cross section - Diagrams (low m ) A f h f H f f f f f f f f f f Z f f S. Scopel Page 13 Valencia, october 2003

14 Light neutralinos and WIP direct searches, A. Bottino, F. Donato, N. Fornengo and S. Scopel, hep-ph/ ; Lower Bound on the Neutralino ass from New Data on CB and Implications for Relic Neutralinos, A. Bottino, F. Donato, N. Fornengo and S. Scopel, Phys. Rev. D 68, (2003); Light relic neutralinos, A. Bottino, N. Fornengo and S. Scopel, Phys. Rev. D 67, (2003). S. Scopel Page 14 Valencia, october 2003

15 Approximate analytic expressions at small m By diagonalizing the usual neutralino mass matrix in the approximation 1 << 2, µ: B deviation from pure bino composition due to a mixture with H 1, i. e. a 1 >> a 3 >> a 2, a 4 For the ratio a 3 /a 1 one finds: a 3 a 1 sin θ W sin β m Z µ a 3 < a sin β taking into account the experimental lower bound µ > 100 GeV S. Scopel Page 15 Valencia, october 2003

16 Approximate analytic expressions at small m The dominant terms in σ ann v int are the contributions due to Higgs-exchange in the s channel and sfermion-exchange in the t, u channels of the annihilation process + f + f. For m A < 200 GeV Higgs exchange contribution due to S-wave annihilation into down-type fermions dominates: σ ann v Higgs f ã Higgs f 2πα2 e.m. c f a 2 sin 2 θ W cos 2 θ W 1a 2 3 tan 2 β (1 + ɛ f ) 2 m 2 f m 2 W m 2 [1 m2 f /m2 ]1/2 [(2m ) 2 m 2 A ]2 c f = 3 for quarks, c f = 1 for leptons m f = fermion running mass evaluated at the energy scale 2m m f = fermion pole mass ɛ f = one loop correction to the relationship between a down type fermion running mass and the corresponding Yukawa coupling (m = h v (1 + ɛ)) S. Scopel Page 16 Valencia, october 2003

17 Cosmological lower bound on m (low m A mass) Ω h 2 < < σ ann v > is an increasing function of m The maximal value ( < σ ann v >) max at fixed m is obtained by inserting into < σ ann v > the product a 2 1a 2 3 tan 2 β for maximal bino higgsino mixing: a 3 < a sin β for m A 90 GeV, tan β < 45 (CDF) (a 2 1a 2 3 tan 2 β) max 260 Keeping only the dominant contribution to b b final state: m [1 m 2 b /m2 ] 1/4 > 5.3 GeV ( m ) A 2 90 GeV S. Scopel Page 17 Valencia, october 2003

18 Cosmological lower bound on m (low m A mass) Observational range for Ω CD h 2 full calculation lower bound (approximate calculation, T QCD = 300 ev) lower bound (approximate calculation, T QCD = 100 ev) lower bound (approximate calculation, T QCD = 500 ev) S. Scopel Page 18 Valencia, october 2003

19 Sfermion-exchange contribution Important if m A > 200 GeV Both S-wave and P-wave contributions have to be taken into account in the expression: σ ann v sfermion f ã sfermion f + 1 2x f bsfermion f Lowest Ω h 2 obtained for τ exchange. Lightest τ (m τ 87 GeV) if mixing is maximal σ ann v sfermion σ ann v sfermion τ ( σann v sfermion ) max maximized by: πα2 m 2 e.m. [1 m2 τ /m2 ]1/2 8 cos 4 θ 4 W m τ [ ( ) ] 2 m τ m x f S. Scopel Page 19 Valencia, october 2003

20 Cosmological lower bound on m (high m A mass) Driven by τ exchange in the annihilation cross section: m [1 m 2 τ/m 2 ] 1/4 > 22 GeV ( m τ 90 GeV ) 2 Observational range for Ω CD h 2 full calculation lower bound (approximate calculation) S. Scopel Page 20 Valencia, october 2003

21 Variation with m A of the lower bound on m lower bound on m, (Ω CD h 2 ) max = lower bound on m, (Ω CD h 2 ) max = 0.3 S. Scopel Page 21 Valencia, october 2003

22 Cosmological lower bound on m The bottom line: m > 6 GeV for light m A m > 22 GeV for heavy m A see, for instance: G. Bélanger, F. Boudjema, A. Pukhov and S. Rosier Lees, arxiv:hep-ph/ ; D. Hooper and T. Plehn, arxiv:hep-ph/ S. Scopel Page 22 Valencia, october 2003

23 Neutralino direct detection N Elastic recoil of non relativistic halo neutralinos off the nuclei of an underground detector Recoil energy of the nucleus in the kev range Yearly modulation effect due to the rotation of the Earth around the Sun (the relative velocity between the halo, usually assumed at rest in the Galactic system, and the detector changes during the year) Sun v 0 = 232 km/sec v = 30 km/sec Earth S. Scopel Page 23 Valencia, october 2003

24 Neutralino nucleon cross section - Diagrams h Z q q q q q q q q q q S. Scopel Page 24 Valencia, october 2003

25 Detectability of light s by WIP direct measurements Very light m, m A < 200 GeV ❶ nucleon elastic cross section σ (nucleon) scalar the t-channel dominated by h-exchange in ❷ annihilation cross section σ ann dominated by A-exchange in the s-channel (Ω h 2 ) σ (nucleon) scalar cm 2 T ( ) 2 ms N ss N GeV ev m 2 [1 m2 b /m2 ]1/2 ( ma m h ) 4 T = (a 3 sin α+a 4 cos α) 2 (a 4 cos β a 3 sin β) 2 (sin α+ɛ s cos(α β) sin β) 2 sin 2 β (1+ɛ b ) 2 = O(1) N ss N = s-quark density matrix element over the nucleonic state α = Higgs fields mass-eigenstates rotation angle S. Scopel Page 25 Valencia, october 2003

26 Detectability of light s by WIP direct measurements Ω h 2 (Ω CD h 2 ) max σ (nucleon) scalar > cm 2 GeV 2 (Ω CD h 2 ) max for m m 2 < [1 m2 b /m2 ]1/2 20 GeV The elastic cross section is bounded from below funnel at low mass S. Scopel Page 26 Valencia, october 2003

27 DAA: 7 years of annual modulation ( kg day) (Bernabei et al., Riv.N.Cim.26 n. 1 (2003) 1-73, astro-ph/ ) Residuals (cpd/kg/kev) Residuals (cpd/kg/kev) Residuals (cpd/kg/kev) Residuals: 2-4 kev I II III IV V VI VII kev Time (day) I II III IV V VI VII kev Time (day) I II III IV V VI VII Time (day) Power spectrum of residuals in the (2 6) kev energy range: Normalized Power Frequency (d -1 ) Frequency=1/ d 1 S. Scopel Page 27 Valencia, october 2003

28 The DAA annual modulation result The DAA/NaI experiment shows an annual-modulation effect at the 6.3 σ C.L. after a 7-years running with a total exposure of kg day. DAA analysis extended to a large class of possible phase space distribution functions (DF) for WIPs in the galactic halo. The full set of experimental data analyzed in terms of a spin independent effect over an unconstrained range for the mass of a generic WIP. S. Scopel Page 28 Valencia, october 2003

29 Neutralino nucleon cross section (A.Bottino, F.Donato, N.Fornengo and S.Scopel, hep-ph/ ) DAA modulation region, Riv.N.Cim.26 n. 1 (2003) 1-73, astro-ph/ Ω h 2 < Ω h Contour line delimits region of the m ξσ (nucleon) scalar plane where the likelihood-function values are distant more than 4σ from the null (absence of modulation) hypothesis. S. Scopel Page 29 Valencia, october 2003

30 Neutralino nucleon cross section (A.Bottino, F.Donato, N.Fornengo and S.Scopel, hep-ph/ ) Upper limits from direct searches Ω h 2 < Ω h CDS, without neutron statistical subtraction (arxiv:hep-ex/ ) Edelweiss, A. Benoit et al., Phys. Lett. B 545, 43 (2002) Assumptions: isothermal sphere, v 0 =220 km/sec, ρ 0 =0.3 GeV/cm 3 S. Scopel Page 30 Valencia, october 2003

31 Uncertainty due to velocity distribution (P. Belli, R. Cerulli, N. Fornengo and S. Scopel, PRD66(2002)043503) S. Scopel Page 31 Valencia, october 2003

32 Uncertainty on ρ 0 due to velocity distribution (P. Belli, R. Cerulli, N. Fornengo and S. Scopel, PRD66(2002)043503) (0.17< ρ 0 < 1.68) (v 0 galactic rotational velocity at the Earth s position) S. Scopel Page 32 Valencia, october 2003

33 Uncertainty due to velocity distribution Sodium Iodide m W IP =50 GeV σscalar nucleon =10 8 nbarn v 0 = 220 km/sec Each curve corresponds to a different halo model: dr/de (cpd/kg/kev) dr/de (june-dec) (cpd/kg/kev) Energy (kev) Time independent component Energy (kev) odulation amplitude S. Scopel Page 33 Valencia, october 2003

34 Uncertainty due to velocity distribution Germanium m W IP =50 GeV σscalar nucleon =10 8 nbarn v 0 = 220 km/sec Each curve corresponds to a different halo model: dr/de (cpd/kg/kev) dr/de (june-dec) (cpd/kg/kev) Energy (kev) Time independent component Energy (kev) odulation amplitude S. Scopel Page 34 Valencia, october 2003

35 Distortion of the signal time dependence (N. Fornengo and S. Scopel, hep-ph/ ) Triaxial system described by a multivariate gaussian: (Galaxy rest frame) f( v) = N exp ( v2 x 2σ 2 x v2 y 2σ 2 y Rate=F(v min ) v2 z 2σ 2 z ) Each curve corresponds to a different value of v min : σ x /σ y = 0.2 σ z /σ y = 0.8 v min minimal WIP incoming velocity at fixed recoil energy (Earth rest frame) Departure from sinusoidal behavior at low v min ( low recoil energies) S. Scopel Page 35 Valencia, october 2003

36 To set a solid constraint on theoretical predictions it is necessary to derive from the experimental data the upper bounds on ξσ (nucleon) scalar a large variety of DFs and of the corresponding astrophysical parameters (with their own uncertainties) for Only the intersection of these bounds would provide an absolute limit to be used to possibly exclude a subset of supersymmetric population. A combined investigation of all experiments along these lines is not available at the moment. S. Scopel Page 36 Valencia, october 2003

37 Conclusions - 1 Relic neutralinos with masses m < 45 GeV are allowed in SS models without gaugino-mass unification at the GUT scale. The cosmological lower bound on the neutralino mass from WAP CB data combined with other measurements is m > 6 GeV. For m < 20 GeV the neutralino nucleon elastic cross section is bounded from below (low mass funnel ). These neutralinos, mainly a B H 1 mixture, are compatible with the final modulation result presented by the DAA Collaboration ( kg day exposure). WIP direct experiments with cryogenic detectors with improved sensitivities may potentially provide useful constraints on low mass neutralinos. Astrophysical uncertainties must be taken into accont when comparing different experimental results. S. Scopel Page 37 Valencia, october 2003

38 Conclusions - 2 Current data from experiments of WIP indirect searches ( p s, γ s, up going µ s), if interpreted conservatively, do not yet set significant constraints. S. Scopel Page 38 Valencia, october 2003