Cold Dark Matter beyond the MM Beyond the MM inglet Extended MM inglet Extended tandard Model
References V. Barger, P. Langacker, M. McCaskey, M. J. Ramsey-Musolf and G. haughnessy, LHC Phenomenology of an Extended tandard Model with a Real calar inglet, arxiv:76.43 [hep-ph]. V. Barger, P. Langacker, I. Lewis, M. McCaskey, G. haughnessy and B. Yencho, Recoil detection of the lightest neutralino in MM singlet extensions, Phys. Rev. D 75, 52 (27) [arxiv:hepph/7236]. V. Barger, P. Langacker and G. haughnessy, Neutralino signatures of the singlet extended MM, Phys. Lett. B 644, 36 (27) [arxiv:hep-ph/6968].
Motivations for (TeV-cale) upersymmetry Incorporation of gravity (But M UY could be very large) tabilization of electroweak scale But landscape ideas (anthropically-motivated fine tuning); variants (e.g., split supersymmetry) Alternatives: LED, DB, Little Higgs Gauge unification (many variations, compensations possible) Cold dark matter (LP) if R P MM) conserved (strongly constrained in Z-pole: any new physics decouples
Minimal upergravity MM (minimal supersymmetric extension of standard model): M gauge group/spectrum plus second Higgs doublet, sparticles, < 5 new parameters Minimal supergravity: UGRA mediation + five (real) parameters (at M P ) m, M /2, A, B, }{{}}{{} µ universal soft breaking Why small? m, M /2, A, tan β, M Z, sign(µ) pecific models (e.g., dilaton) further relations RGE to electroweak scale Usually assume R P conservation LP candidate χ for CDM
8 m [GeV] 7 6 g t 2 5 ũ L, d R ũ R, d L b2 b 4 H, A H ± χ χ 4 3 χ ± 2 t 3 2 ll ν l τ 2 χ 2 χ ± h lr τ χ
Minimal upergravity and Beyond Minimal UGRA is simple, but Poorly motivated theoretically FCNC, diagonal CP violation (EDM s) Tightly constrained by M H, m χ ±, cold dark matter, b sγ, g µ 2 Mass matrix (M χ ) in basis { B, W 3, H, H 2 }: M g v /2 g v 2 /2 M 2 g 2 v /2 g 2 v 2 /2 g v /2 g 2 v /2 µ g v 2 /2 g 2 v 2 /2 µ H i v i 2, p v 2 + v2 2 v 246 GeV
red: bino, varying l R ; blue: Higgsino; green: wino Arkani-Hamed et al., hep-ph/64
Ellis et al, hep-ph/52
Alternatives Minimal UGRA unlikely to be full story, but many alternatives Universal gaugino and universal scalar within each sector (Q, U, D, L, E, N) Non-universal gaugino masses (e.g., anomaly mediation (slepton problem)) Phases Expanded parameter space, e.g., non-bino LP
Gauge mediation FCNC better, but µ? LP Goldstino g 3/2 NLP may decay promptly, in detector, or outside detector (Goldstino CDM prefers fast decays) NLP decay: χ γg 3/2 or l R lg 3/2 R P violation L violating: W LH u, LLĒ, LQ D B violating: W ŪŪ D No missing energy signature Multi jets or leptons No CDM candidate (axion?)
Beyond the MM Even if supersymmetry holds, MM may not be the full story Most of the problems of standard model remain (hierarchy of electroweak and Planck scales is stabilized but not explained) µ problem introduced Could be that all new physics is at GUT/Planck scale, but there could be remnants surviving to TeV scale pecific string constructions often have extended gauge groups, exotics, extended Higgs sectors Important to explore alternatives/extensions to MM
Higgs singlets i tandard model singlets extremely common in string constructions Needed to break extra U() gauge symmetries olution to µ problem (U(), NMM, nmm) W hh u H d µ eff = h Relaxed upper limits, couplings, parameter ranges (e.g., tan β can be close to ), singlet-doublet mixing Large A term and possible tree-level CP violation electroweak baryogenesis
Models with Dynamical µ Model ymmetry uperpotential CP-even CP-odd MM µĥ u Ĥ d H, H 2 A 2 NMM Z 3 h s ŜĤ u Ĥ d + κ 3 Ŝ3 H, H 2, H 3 A, A 2 nmm Z R 5, ZR 7 h s ŜĤ u Ĥ d + ξ F M 2 nŝ H, H 2, H 3 A, A 2 UMM U() h s ŜĤ u Ĥ d H, H 2, H 3 A 2 smm U() h s ŜĤ u Ĥ d + λ s Ŝ Ŝ 2 Ŝ 3 H, H 2, H 3, A, A 2, A 3, A 4 H 4, H 5, H 6 MM: gaugino unification but general µ NMM ( cubic ): may be domain wall problems (Z R 2 ) nmm ( tadpole ): no domain walls; tadpoles from high order UMM: additional Z (µ eff, M Z generated by single ) smm: stringy NMM w. decoupled µ eff, M Z (Ĥ u, Ĥ d, Ŝ reduces to nmm in i decoupling limit n/smm)
tan β NMM n/smm 5 M h
CP-Even Higgs Mass Range CP-Odd Higgs Mass Range MM can NMM 2 can n/smm 2 LEP 92 Th. 35 Th. 64 Th. 7 LEP MM 94 Th. tate Crossing NMM 632 Th. tate Crossing n/smm 7 can 685 UMM LEP & α ZZ 9 Th. 73 LEP & α ZZ UMM 93 can 367 5 5 2 Higgs Mass (GeV) 2 4 6 Higgs Mass (GeV) Charged Higgs Mass Range LEP MM 79 LEP NMM 83 LEP n/smm 8 LEP UMM 8 can 48 can 359 can 6873 can 684 2 4 6 Higgs Mass (GeV) FIG. 2: Mass ranges of the lightest CP-even and CP-odd and the charged Higgs bosons in each
Lightest Neutralino Mass matrix (M χ ) in basis { B, W 3, H, H 2,, Z }: M g v /2 g v 2 /2 M 2 g 2 v /2 g 2 v 2 /2 g v /2 g 2 v /2 µ eff µ eff v 2 /s g Z Q H v g v 2 /2 g 2 v 2 /2 µ eff µ eff v /s g Z Q H 2 v 2 µ eff v 2 /s µ eff v /s 2κs gz Q s g Z Q H v g Z Q H 2 v 2 g Z Q s M ( s 2, H i v i 2, p v 2 + v2 2 v 246 GeV, Q φ = φ U() charge) (black = MM; blue= extensions; cyan = NMM; magenta = UMM)
M χ e, e Z = 2 ± g Q s. (3) 7 5 Neutralino Mass (GeV) 6 5 4 3 2 M χ6 ~.9 TeV B W 3 H H 2 Z Neutralino Mass (GeV) 4 3 2 B W 3 H H 2 Z MM NMM n/smm UMM MM NMM n/smm UMM (a) (nearly) decoupled singlino (b) strongly mixed singlino FIG. : Illustrative neutralino composition for the models in (a) a decoupled singlino scenario and (b) a strongly mixed singino scenario. Here, the MM contains a light Bino and Wino and heavy Higgsinos. The NMM has a similar spectrum, but contains an additional heavy neutralino while the n/smm has a very light extra neutralino. The UMM has two additional neutralinos that can intermix; their masses are strongly dependent on the singlet Higgs charge under the U() symmetry and the corresponding gaugino mass value. Common parameters used for this
N 5 2 NMM N 25 2 NMM.8 N 5 2 n/smm N 5 2 UMM.8 N 25 2 n/smm N 25 2 UMM.6 N 6 2 UMM.6 N 26 2 UMM N i 2.4 N 2i 2.4.2.2 5 5 2 25 3 χ Mass (GeV) (a) 5 5 2 25 3 35 4 45 5 χ 2 Mass (GeV) (b) singlino and gaugino fractions of χ,2 N 35 2 NMM N 55 2 NMM.8 N 35 2 n/smm N 35 2 UMM.8 N 55 2 n/smm N 65 2 UMM N 3i 2.6.4 N 36 2 UMM N 5,6i 2.6.4 N 66 2 UMM.2.2
.8 MM NMM n/smm UMM.8 MM NMM n/smm UMM Bf(χ 2 --> Z χ ).6.4 Bf(χ 2 --> H χ ).6.4.2.2 2 3 4 5 χ 2 Mass (GeV) 2 3 4 5 χ 2 Mass (GeV) (a) branching fractions of χ 2 (Z, H ) χ (b).8 MM NMM n/smm UMM.8 MM NMM n/smm UMM Bf(χ 3 --> χ 2 Z).6.4 Bf(χ 3 --> χ 2 H ).6.4.2.2
MM NMM WMAP WMAP Ω χh Ω χh 2 2....... 5 2 5 Mχ (GeV) 25. 3 5 5 Mχ (GeV) 2 n/smm 3 UMM WMAP WMAP Ω χh 2 2 Ω χh 25....... 2 3 Mχ (GeV) 4 5 6. 5 5 Mχ (GeV) 2 25 3 FIG. : Neutralino relic density versus the lightest neutralino mass. The relic density is constrained Relic.23 densities squarks sleptons) to be in the region > ΩDM(heavy h2 >.99 provided and that the model is solely responsible for the observed dark matter. The efficient annihilations through the Higgs boson pole in the MM, NMM and UMM are evident at mχ MH /2 6 GeV and of the Z boson pole at mχ MZ /2 in the n/smm.
MM NMM. Ω χh 2 >.23. Ω χh 2 >.23 e-5 Ωχh 2 <.99.99<Ω χh 2 <.23 e-5 Ωχh 2 <.99.99<Ω χh 2 <.23 e-6 EDELWEI CDM 25 e-6 EDELWEI CDM 25 (pb) σ χp I e-7 e-8 e-9 CDM 27 upercdm 25kg (pb) σ χp I e-7 e-8 e-9 CDM 27 upercdm 25kg e- WARP 4 kg e- WARP 4 kg e- e- e-2 5 5 2 25 3 M χ (GeV) (a) e-2 5 5 2 25 3 M χ (GeV) (b) n/smm UMM. Ω χh 2 >.23. Ω χh 2 >.23 e-5 Ωχh 2 <.99.99<Ω χh 2 <.23 e-5 Ωχh 2 <.99.99<Ω χh 2 <.23 e-6 EDELWEI CDM 25 e-6 EDELWEI CDM 25 (pb) σ χp I e-7 e-8 e-9 CDM 27 upercdm 25kg (pb) σ χp I e-7 e-8 e-9 CDM 27 upercdm 25kg e- WARP 4 kg e- WARP 4 kg e- e- e-2 5 5 2 25 3 M χ (GeV) (c) e-2 5 5 2 25 3 M χ (GeV) (d) FIG. 8: pin independent detection cross sections Expected I direct detection cross-section for (a) MM, (b) NMM (c) n/smm DUELand meeting, (d) UMM. November The 27 expected sensitivities of the EDELWEI, CDM II (25), Paul Langacker CDM 27, (IA) upercdm (25 kg) and WARP (2.3L) experiments are shown. Over most of the neutralino mass
A Variant: Add stable real scalar to standard model Minimal Higgs extension of standard model: (e.g., O Connell, Ramsey-Musolf, Wise,hep-ph/64) add real singlet V = m2 2 H H + λ 4 (H H) 2 + δ 2 H H + δ 2 2 H H 2 ( δ m 2 ) + + κ 2 2λ 2 2 + κ 3 3 3 + κ 4 4 4 Already shifted so that = δ, κ 3 :, H mixing, decays Z 2 symmetry (δ = κ 3 = ): is stable, CDM candidate
h h h V f h h h h h h V f FIG. 6: Annihilation processes that contribute to the thermally averaged cross section. All processes are mediated via the Higgs boson. The thermally averaged annihilation cross section is determined from the contributions of the processes shown in Fig. 6. ince all of the processes involve the M Higgs boson, h, the key parameters in obtaining the observed relic density are δ 2 and λ. The s-channel Higgs couples to the usual M final states. The h hh diagram is mediated by the Higgs self coupling, although this diagram is expected to be suppressed since the intermediate s-channel Higgs boson is far off-shell. We calculate the relic density of singlet dark matter in this model for the parameter ranges given in Eq. (). Ω h 2 <.99.99 < Ω h 2 <.23.23 < Ω h 2 EWPO consistent Ω h 2 <.99.99 < Ω h 2 <.23.23 < Ω h 2 Ω h 2. Ω h 2..
s-channel Higgs boson is far off-shell. We calculate the relic density of singlet dark matter in this model for the parameter ranges given in Eq. (). Ω h 2 <.99.99 < Ω h 2 <.23.23 < Ω h 2 EWPO consistent Ω h 2 <.99.99 < Ω h 2 <.23.23 < Ω h 2 Ω h 2. Ω h 2...... 2 3 4 5 M (GeV). 2 3 4 5 M (GeV) FIG. 7: Relic density of singlet dark matter versus the singlet mass with (right) and without (left) EWPO constraints on the Higgs boson mass applied. The relic density of the singlet DM is shown in Fig. 7 versus the singlet mass with (right) and without (left) EWPO consistency, which for the M higgs boson implies M h < 5 GeV 7. Imposing this bound can severely restrict the space of models. Fewer points are DUEL 7 In themeeting, LEP Electroweak November 27 Working Group fit that does not include low-energypaul EWPO, Langacker the upper (IA) limits
M = GeV M = 2 GeV M = 3 GeV M = 4 GeV M = 5 GeV 3 3 EWPO consistent M = GeV M M = 3 GeV M = 4 GeV M = 5 GeV = 2 GeV 2 2 δ 2 M = GeV δ 2 M = GeV - - -2 Ω h 2 <.99.99<Ω h 2 <.23-3 -3-2 - 2 3 4 5 ign(κ 2 ) κ 2 /2-2 Ω h 2 <.99.99<Ω h 2 <.23-3 -3-2 - 2 3 4 5 ign(κ 2 ) κ 2 /2 FIG. 8: Predicted relic density values in the plane of κ 2 and δ 2 with (right) and without (left) EWPO constraints on the Higgs boson mass applied. ince the DM mass scales with κ 2 for large κ 2 δ 2 v 2, we show the parameter κ 2 to illustrate the dependence of the relic density on the singlet mass. inglet DM masses are given by contours. The open region with small δ 2 and large κ 2 correspond to models (not shown explicitly) yielding an overdensity of relic DM. shown in the observed range and appear to be non-uniform after imposing the EWPO constraint on the Higgs mass, but these are due to the small window of Ω DM h 2 and the limitations of the scan. The observed region of the relic density allows a wide range of
independent and spin-dependent scattering using both cryogenic and non-cryogenic methods [78, 79]. Limits on the spin-independent scattering cross sections have recently been reported by CDM [8 83], EDELWEI [84], WARP [85] and Xenon [86]. The latter uses a 5 kg h h q g g q q FIG. 9: Feynman diagrams for elastic scattering of the singlet DM particle off a proton. The Higgs boson mediates the interaction. some other non-standard cosmological scenario [72 75]. 23
. e-5 σi DM scaled Ω h 2 <.99.99 < Ω h 2 <.23. e-5 Ω h 2 <.99.99 < Ω h 2 <.23.23 < Ω h 2 e-6 e-6 XENON ~ σ I DM (pb) e-7 e-8 XENON CDM 27 uper CDM σ I DM (pb) e-7 e-8 e-9 CDM 27 uper CDM e-9 e- e- e- 2 3 4 5 6 M (GeV). e-5 EWPO consistent, σi DM scaled Ω h 2 <.99.99 < Ω h 2 <.23 e- 2 3 4 5 6 M (GeV). e-5 EWPO consistent Ω h 2 <.99.99 < Ω h 2 <.23.23 < Ω h 2 e-6 XENON e-6 XENON ~ σ I DM (pb) e-7 e-8 CDM 27 σ I DM (pb) e-7 e-8 CDM 27 e-9 uper CDM e-9 uper CDM e- e- e- 2 3 4 5 6 M (GeV) e- 2 3 4 5 6 M (GeV) FIG. : pin-independent cross section scaled (left) and not scaled (right) with the local density of dark matter for various DM masses. The current best limit on the scattering cross section is from Xenon (solid). It is expected that upercdm will cover most of the scanned parameter
Conclusions imple singlet extensions of the standard model or MM are wellmotivated theoretically and can significantly modify the possibilities for collider searches and CDM Expanded neutralino sector/possibilities in xmm calar CDM candidate in xm Most ranges detectable in I searches Will need complementary program of direct searches and collider experiments to sort out