Neutralino dark matter in the NMSSM

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1 Neutralino dark matter in the NMSSM Ana M. Teixeira (LPT - Orsay) XLII Rencontres de Moriond La Thuile, Italy, 4 March 27 In collaboration with Cerdeño, Gabrielli, Hugonie, López-Fogliani and Muñoz Discussion in JHEP 42 (24) 48 and hep-ph/727 Plan: A good dark matter candidate - WIMPs Introducing the NMSSM NMSSM dark matter: results and discussion

2 A good dark matter candidate No emission/absorption of electromagnetic radiation (any λ) Gravitational interactions on array of scales tiny dwarf galaxies, large spirals (Milky Way), clusters of galaxies... Correct relic density Astrophysical bounds. Ωdark h 2.3 Cosmological observations WMAP:.95 Ωdark h 2.2 ΩTOTAL =ΩΛ +Ωmatter =.2 ±.2 Ωdark 25 % ΩTOTAL Cold dark matter requires candidate from physics beyond SM ν R Arise in well-motivated models (SUSY, Large Extra Dimensions, etc) Phenomenologically viable low-energy scenario compatible with LEP/Tevatron bounds: direct searches, precision measurements, etc Other accelerator constraints: B- and K-decays, (g 2)μ,...

3 Weakly Interacting Massive Particles The most promising (non-baryonic) cold dark matter candidates WIMPs: 8> < > : Heavy 4 th generation neutrino (ruled out for m<.5 TeV) Extra scalar fields (little Higgs model, N=2 SUSY, LEDs,...) SUSY ( ν, χ, G, ã) WIMPs arise in well motivated extensions of the standard model Stable particles, no electromagnetic interactions; WIMP weak matter WIMP masses typically lie in the range GeV up to a few TeV If WIMPs do indeed fulfil above conditions correct relic abundance WIMP direct detection (indirect detection also possible...) WIMP dark matter can be detectable via target crystal observation of WIMP-matter scattering in a detector scattered particle WIMP signal: excess of recoil events above expected background recoiling nucleus

4 SUSY dark matter beyond the MSSM - the NMSSM Add singlet superfield S to the MSSM Next-to-Minimal Supersymmetric Standard Model Elegant solution to the μ-problem of the MSSM μhh2 λshh2 Dynamically generated μ: μeff = λ S Scale-invariant superpotential: EW, SUSY scale only appearing via Lsoft Less severe Higgs - little fine tuning problem of the MSSM Formally... NMSSM=MSSM + ŜŜŜ 2 extra Higgs (CP-even, CP-odd) additional neutralino W = Yu H2 Qu+ Yd H Qd+ Ye H Le λ SHH2 + 3 κs3 L Higgs soft soft = m 2 Hi H i H i + m 2 S S S + ( λaλ λaλshh2 + 3 κaκ κ S 3 + H.c. ) L Higgs soft Richer and more complex phenomenology - extra Higgs, neutralino Important implications for dark matter analysis!

5 Neutralino sector: Neutral Higgs sector: NMSSM neutralino dark matter 8 < : 8 < : 5 Majorana fermions χ = N B + N2 W 3 + N3 H + N4 H 2 + N5 S S S 2 pseudoscalar and 3 scalar bosons h = SH + S2H 2 + S3S Very light singlet-like Higgs and singlino-like χ can escape detection (e.g. reduced coupling to Z boson) experimentally viable Implications for Dark Matter: Neutralino-nucleon cross section σ χ p ~χ ~χ Higgs-exchange + Squark-exchange (spin-independent) σ χ p α 3i h = P 3 a= m 2 h a C i Y Re [C a HL] C a HL = 2{ g (N 2 tan θ W N )(S an 3 S a2n 4 )+ + 2λ [Sa3N 3 N 4 + N 5 (S a2n 3 + S an 4 )] 2κSa3N 5 N 5 } C (2) Y = gm u(d) 2M W sin(cos)β S a2() Exchange of light Higgs (not pure singlet) enhancement to σ χ p.. q h i q..

6 χ. χ. Neutralino sector: Neutral Higgs sector: NMSSM neutralino dark matter 8 < : 8 < : 5 Majorana fermions χ = N B + N2 W 3 + N3 H + N4 H 2 + N5 S S S 2 pseudoscalar and 3 scalar bosons h = SH + S2H 2 + S3S Very light singlet-like Higgs and singlino-like χ can escape detection (e.g. reduced coupling to Z boson) experimentally viable Implications for Dark Matter: Neutralino relic density Ωh 2 h.. q ( l + ) q (l ) New open channels! Additional resonances! Extra Higgs: annihilation via s-channel Higgs resonances Light h,a new annihilation channels Zh, h h, h a,... 8 < : s channel : Z, h, a t channel : χ exchange In general, large σ χ p are associated with Ωh 2 below observed values

7 Exploring the NMSSM parameter space Unconstrained low energy NMSSM λ,κ,μ(= λs),aλ,aκ,m,m2,msusy free Minimisation of the potential [exclusion of over 2/3 of parameter space] Absence of Landau poles for λ, κ, Yt and Yb below MGUT Computation of the NMSSM spectrum Higgs, chargino and neutralino masses and mixings; couplings Experimental constraints Neutralino: Γ inv Z, direct production σ(e+ e χ i χ j ); Bounds on m χ + Neutral Higgs: Constraints on production rates (all LEP channels) and m H + NMHDECAY Rare B- andk-meson decays SUSY contributions to BR(b sγ)! Muon anomalous magnetic moment SUSY contributions to saturate a exp μ Cosmological constraints: Ωh 2 compatibility (astro & WMAP) MicrOMEGAS Neutralino-nucleon cross section - comparison with detector sensitivities Interested in NMSSM-like scenarios (light h, χ ) inducing large σ χ p

8 Looking for NMSSM-like dark matter scenarios Regimes where singlet-singlino components are active Lightest Higgs is not doublet-like (important singlet composition) & lightest neutralino has large singlino component Typically found for Low tan β β, small μ ( M), small Aλ... In the parameter space generated by the new couplings in WNMSSM (λ κ) : Singlino-like χ small κ/λ Singlet-like h small κ In general likely to exhibit large σ χ p! But... to which extent can we find viable DM scenarios in this limit??

9 Constraining the parameter space: b sγ and aμ m H ± =TeV Large σ χ p low tan β, smallaλ... 5 GeV 45 GeV LEP excl. Landau Pole BR(b b sγ) [exp: (3.55 ±.27) 4 ] 8 (λ, κ) < : tan β =3, Aλ = 2 GeV μ = 3 GeV, Aκ = 2 GeV VCKM flavour violation, heavy gluino Dominant contribution from H ± -t loops FM CP-even tachyons m H ± 2μ sin 2β ( μκ λ + A λ) v 2 λ 2 + M 2 W BR(b sγ) exp favours larger Aλ, tan β aμ [exp: a NP μ (2.76 ±.8) 9 ] O( TeV) soft breaking terms negligible SUSY contributions, O( ) 8 Saturating a exp μ < large tanβ; large μlr (AE 2.5 TeV) a SUSY μ O( 9 ) : m 2 GeV; M Ẽ,L 25 GeV light sleptons, bino

10 Cosmological constraints An example: tan β =5, Aλ = 4 GeV, Aκ = 2 GeV, μ = 3 GeV M = 6 GeV [GUT-relation for M i, compatible with BR(b sγ), aμ] m χ = mz m χ = mw Ωh 2 : spectrum of χ, h MSSM-like scenarios (WMAP) doublet-like h, bino-higgsino χ 2m χ = m h m h <m χ FM CP-even tachyons NMSSM-like scenarios: μ M, Higgsino-singlino χ WMAP ( ) / astrophysical ( ) bound: large S S S component, light χ Kinematically forbid χ χ Z, W, h Compatible region close to tachyon border: Light, singlet-like Higgs NMSSM-like dark matter scenarios excellent prospects for direct detection

11 8 < : Prospects for NMSSM dark matter detection tan β =5,μ= 3 GeV,M = 6 GeV Aλ = 2 GeV, Aκ = 2 GeV 8 < : tan β =5,μ= 6 GeV,M = 33 GeV Aλ = 57 GeV, Aκ = 6 GeV Large predictions for σ χ p found! Even within DAMA reach!! t-channel exchange of singlet-like very light h (25-5 GeV), singlino LSP Modify the Bino mass (cannot saturate aμ) Resonances appear as funnels in σ χ p (e.g. m χ = MZ/2, m χ = m h /2)

12 Conclusions Neutralino dark matter in the NMSSM Thourough analysis of the low-energy NMSSM parameter space Include LEP, meson decays, aμ and astrophysical constraints Computed theoretical predictions for σ χ p Stringent constraints on the NMSSM parameter space Enhancing aμ favours small slepton and gaugino masses Potentially large contributions to BR(b sγ) (H ± mediated) Ωh 2 : light neutralinos (kinematically unaccessible channels); singlino-like χ (suppress annihilations) Prospects for direct detection of NMSSM χ dark matter Large values of σ χ p attainable, within reach of present detectors Exchange of light singlet-like Higgses in t-channel (m h 5 GeV) Light, singlino-higgsino-like χ - characteristic of NMSSM

13 Additional slides

14 Minimisation of V Higgs neutral - the NMSSM parameter space Ensuring minimum of V Higgs neutral with respect to the phases of the VEV s: excludes combinations of signs for the parameters Conventions: tan β, λ positive; s, κ, Aλ, Aκ For κ>, minima possible if (i) sign(s) = sign(aλ) = sign(aκ) (ii) sign(s) = sign(aλ) = sign(aκ), with Aκ > 3λvv2 Aλ /( saλ + κ s 2 ) (iii) sign(s) = sign(aλ) = sign(aκ), with Aκ < 3λvv2 Aλ /( saλ + κ s 2 ) For κ<, minima possible if (iv) sign(s) = sign(aλ) = sign(aκ), with Aκ > 3λvv2 Aλ /( saλ κ s 2 ) In addition three minimization conditions for the Higgs VEV s: m 2 H, m2 H2, m2 S = f(λ, κ, Aλ, Aκ, v, v2, s)

15 NMSSM: χ and scalar Higgs mass matrices CP-even Higgs CP-odd Higgs M 2 S, = M2 Z cos2 β + λs tan β(a λ + κs) M 2 S,22 = M2 Z sin2 β + λs cot β(a λ + κs) M 2 P, = sin 2λs 2β `κs + Aλ M 2 S,33 =4κ2 s 2 + κaκs + λ s A λ v v 2 M 2 P,22 2κ = λ + A «λ 2s M 2 S,2 = λ2 v 2 M2 Z 2! sin 2β λs `A λ + κs M 2 P,2 = λv `A λ 2κs v 2 sin 2β 3κAκs M 2 S,3 =2λ2 v s λv 2 `Aλ +2κs M 2 S,23 =2λ2 v 2 s λv `Aλ +2κs a i = P ijp j h a = SabH b Neutralino Sector M χ = B BBB M M Z sin θ W cos β M Z sin θ W sin β M 2 M Z cos θ W cos β M Z cos θ W sin β B M BB@ Z sin θ W cos β M Z cos θ W cos β λs λv 2 M Z sin θ W sin β M Z cos θ W sin β λs λv λv 2 λv 2κs C CCC C CCA

16 On the experimental constraints: LEP: direct bounds on masses of H ±, χ ±, q, l; LEP: Invisible decay width of the Z boson: Z χ i χ j and Z h a ; LEP: neutral Higgs (all LEP channels): e + e h Z (IHDM); e + e h Z (DHDM) [h {b b, τ + τ, 2 jets, γγ, inv} ]; e + e h a (APM) [h a {4b s, 4τ s, 6b s} ]; K-meson decays: Light a indirect contributions: K K mixing; B-meson decays Light a indirect contributions to B B mixing, B μ + μ, B Xsμ + μ, B K ν ν, B K S X ; Direct production (large tan β) viab sa, B Ka, and B πa ; b sγ: NLO contributions (only LO SUSY contributions to Wilson coeffs.); aμ =(gμ 2).