Non-SUSY WIMP Candidates

Non-SUSY WIMP Candidates M. Perelstein, Cornell DESY Theory Workshop, Hamburg, Oct 1 2008

Dark Matter Puzzle: About 25% of the energy in the universe is dark, non-relativistic matter Non-particle explanations unlikely χ has to be stable (or at least τ 10 bln. years) χ cannot have strong interactions (otherwise pχ exotic nuclei) or electric charge (dark) χ cannot be a Standard Model neutrino (free streaming) Have to invent (at least one) new particle

χ 2σ constraint using Ωdmh =0.112±0.009 (WMAP) [ignoring coannihilations, resonances] [Plot: Birkedal, Matchev, MP, PRD77:07701(2004)]

Dark Matter-Weak Scale Connection The required annihilation cross section is exactly in the right range to be produced by weak-scale physics: σ 1 pb α (TeV) 2 Hypothesis: dark matter consist of stable, weakly interacting particles with mass~weak scale Massive Weakly Interacting Particles - WIMPs! Two main requirements on new physics models: Weakly-interacting states in the spectrum Symmetry to ensure stability of the WIMP Both are fairly generic in models of weak-scale new physics, motivated independently of DM

Dark Matter-Weak Scale Connection Canonical example: SUSY (MSSM) Double the SM spectrum W3ino, 2 neutral higgsinos gravitino weakly-coupled bino, neutralino, + sneutrinos, Symmetry: R-parity (motivated by the need to avoid proton decay at the susy-breaking scale) Rest of this talk: two alternatives Universal Extra Dimensions [UED] Little Higgs with T Parity [LHT] I will try to highlight similarities to and differences from SUSY and each other

Extra Dimensions String theory: D>4 Extra dimensions compactified, radius R scalar fields ( Calabi-Yau moduli, dilaton ) vev of Naive expectation: R M 1 Pl However the same logic fails for the Higgs vev: H TeV M Pl Compactification radius should be treated as a free parameter Phenomenologically (if SM fields propagate in the extra dimensions): R (TeV) 1

Universal Extra Dimensions Simplest model: all SM fields live in D=5, with Compactified geometry naturally has a discrete symmetry - Kaluza-Klein parity a b b a SM states = KK zero modes, even First level KK states are odd, degenerate with First-level KK states do not contribute to precision EW observables at tree level (KK parity!) PEW constraints are satisfied with [Appelquist, Cheng, Dobrescu, hep-ph/0012100] R (TeV) 1 M = R 1

UED: Spectrum Loop corrections split degeneracy, lightest KK-odd state is the hypercharge GB KK mode B (1) - WIMP! FIG. 6: The spectrum of the first KK level at (a) tree level and (b) one-loop, for R 1 = 500 GeV, ΛR = 20, m h = 120 GeV, m 2 H = 0, and assuming vanishing boundary terms at the cut-off scale Λ. [Cheng, Matchev, Schmaltz, hep-ph/0204342] NB: non-minimal UED (non-zero boundary terms) larger mass splittings, more parameters

UED Dark Matter LKP annihilation dominated by B 1 f B 1 f f 1 f 1 B 1 f B 1 f Couplings 0.6 Y f right-handed leptons dominate! 0.5 Overclosure Limit 0.4 0.4 " h 2 0.3 coannihilations are important!!h 2 0.3 0.2 0.2 0.1!h 2 = 0.16 ± 0.04 0.1 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 m KK (TeV) [Servant, Tait, hep-ph/0206071] 0 0.5 1 1.5 2 2.5 3 3.5! (1) mass (TeV) [Burnell, Kribs, hep-ph/0509118]

UED DM: Direct Detection Elastic scattering Typically (b) and (c) dominate (esp. minimal UED), rates can be large Spin-Dep Spin-Ind. [Cheng, Feng, Matchev, hep-ph/0207125]

UED DM: Positrons WIMP annihilation in the galaxy can result in e + production, providing indirect signature for WIMPs s-annihilation sizeable cross section σv 1 pb 30% direct annihilation B 1 B 1 e + e, 60% muon and tau - HARD positrons! [Cheng, Feng, Matchev, hep-ph/0207125]

UED DM: Photons Leptonic channels dominate annihilation photon signal suppressed fragmentation Brehmstrahlung (final-state radiation) photons: Model-independent shape prediction thanks to factorization: dσ dx = α π 1 + (1 x) 2 x ( ) s(1 x) log m 2 e σ 0 B 1 B 1 l + l γ edge feature! [Bergstrom, Bringmann, Eriksson, Gustafsson, astro-ph/0410359; Birkedal, Matchev, MP, Spray, hep-ph/0507194] Figure 2: Comparison of the photon spectrum obtained by a direct calculation in the UED model with the radius of the extra dimension R = (499.07 GeV) 1 (red histogram) and the

UED DM: Neutrinos Sizeable elastic cross section the Sun! large # of LKPs in 60% of annihilation into muons and taus energetic s! ν lots of minimal UED [Hooper, Kribs, hep-ph/0208261]

Gauge-Higgs Unification A zero-mass photon does not require fine-tuning - mass is protected by gauge symmetry In a 5D theory, the gauge field If the 5th dimension is infinite, A M (x) A µ (x), A 5 (x) A 5 is naturally massless! After compactification, m(a 5 ) 1/R good if 1/R M W A timely merger with the vector saves the Higgs from the instability Higgs mass quadratic divergences are canceled by KK modes:

Little Higgs Quadratic divergence cancellation by same-spin states can also occur in a purely 4D theory - Little Higgs [LH effective theory of the 0th and 1st KK modes in GHU - truncation!] In LH, Higgs is a Goldstone boson arising from a global symmetry breaking [a la pions in QCD] If the global symmetry is exact, naturally! m h = 0 Goldstones only interact derivatively need to break the global symmetry explicitly by gauge and Yukawa interactions Generically explicit breaking reintroduces quadratic divergences Collective breaking pattern in LH avoids quad. div. at one loop [Arkani-Hamed, Cohen, Georgi, 2002]

Littlest Higgs Littlest Higgs model - the first simple, fully realistic implementation of the idea [Arkani-Hamed, Cohen, Katz, Nelson, 2002] Particle content: heavy top T, weak-triplet scalar Φ, heavy gauge bosons W ±, W 3, B Very few parameters predictive! Very strong constraints from precision electroweak fits ( B exchanges, triplet vev) - fine-tuning persists! lower bound on f [TeV] 16 14 12 10 8 6 4 2 68% 95% 99% [Csaki, Hubisz, Kribs, Meade, Terning, 2002] 0 0.1 0.3 0.5 0.7 0.9 c

Littlest Higgs with T Parity (LHT) Solution: introduce a discrete symmetry called T Parity [Cheng, Low, 2003-4] All SM fields are T-even, all non-sm fields are T-odd No tree-level corrections from the BSM sector to SM processes: [forbidden by T-conservation!] The only corrections are loop-level suppressed: etc.

The spectrum of the LHT model Heavy T-odd copies of the electroweak gauge bosons: M(W a H) gf, M(B H ) g f 5 0.16f Heavy T-odd copies of the SM weak-doublet fermions Q a i, Li (i = 1... 3) : LTP! M ab ( Q) = λ Q ab f δ ab M M ab ( L) = λ L abf δ ab M Tquark mass degeneracy motivated by FCNCs T-even heavy top (just like in the original model): M(T ) = 1 2 ( r + 1 r T-odd Higgs triplet: ) f M(Φ) 2m2 h f 2 [Hubisz, Lee, Paz, 05; Buras et al, 05-07] +more stuff at the cutoff scale, Λ 4πf 10 TeV v 2

LHT gives acceptable fits to precision electroweak observables without fine-tuning! <10% tuning F t = m2 h t m 2 h m(h) = 115 GeV [Hubisz, Meade, Noble, MP, hep-ph/0506042]

LHT Dark Matter Typically, the T-odd hypercharge gauge boson is the lightest T-odd particle (LTP): M(B ) 0.16f We will call it a heavy photon - a somewhat inaccurate, but convenient, name The heavy photon LTP is a WIMP - generically has the right relic density to play the role of dark matter! Dominant annihilation processes: [NB coannihilation!]

LTP Relic Density Contours [Hubisz, Meade, hep-ph/0411264] Ω LTP h 2 = 0.111 (100% of WMAP value) [No coannihilations!]

More LTP Relic Density Contours [Birkedal, Noble, MP, Spray, hep-ph/0603077] s-chan. H s-chan. H coan. tail coan. tail mh=300 GeV mh=120 GeV

LHT Dark Matter: Detection? [Birkedal, Noble, MP, Spray, hep-ph/0603077] Direct detection: elastic scattering of WIMPs off nuclei T-odd quark exchange diagrams are suppressed: the vertex B H Qq is g Y/10 Higgs coupling to gluons via top loops gives the dominant contribution (strange coupling subdominant) Rates are small, only the supercdms will have an interesting reach

Direct Detection: Spin- Independent Cross Sections s-chan. H region coannihilation tail [SuperCDMS - stage C, 1000 kg of Ge]

Direct Detection: Spin- Dependent Cross Sections s-chan. H region coannihilation tail

LHT Dark Matter: Detection? Indirect detection: anomalous high-energy gamma rays from WIMP annihilation in the galaxy Fragmentation photons: W/Z q q B H + B H W + W, ZZ q π 0..., π 0 γγ M = 150, 200, 250 GeV J Ω = 1 (Φ J Ω) Galactic models predict J Ω 10 3... 10 2 at Ω 10 3 LHDM ruled out by EGRET if J Ω > 10 ; it will be observable at GLAST if J Ω > 1

LHT Dark Matter: Detection? If a fragmentation signal is observed, will need additional information to eliminate possible astro backgrounds Monochromatic ( line ) photons: B H B H γγ, γz clear signature, but typically small cross section Log 10 s 1 cm 2-14 -15-16 -17-18 J Ω = 1 γz γγ 100 200 300 400 500 M GeV [MP, Spray, hep-ph/0610357] Log 10 s 1 cm 2-10 -11-12 -13-14 J Ω = max GLAST HESS 150 200 250 300 350 400 450 500 M GeV

LHT Dark Matter: Detection? Final-state radiation (FSR) photons: Less numerous than fragmentation photons (cross section down by a power of ) The FSR flux has a sharp feature at the kinematic edge α B H + B H W + W γ E max = M m2 W M Observing the edge would strengthen the case for WIMPs + provide an accurate mass measurement! [Mod.-ind. discussion: Birkedal, Matchev, MP, Spray, hep-ph/0507194]

Indirect Detection: Positrons Positron flux in the LHT model: B H B H W + W, ZZ; Z e + e, W + e + ν e s-annihilation sizeable cross section (like UED) Fairly hard positrons (though softer than in UED) BF (Boost Factor) 8 6 4 2 0.6 m AH(GeV) 100 200 300 PAMELA (95%) AMS!02 (95%) 0.8 1 2 f (TeV) [Asano, Matsumoto,N.Okada, Y.Okada,hep-ph/0610357]

Indirect Detection: Neutrinos [MP, Spray, hep-ph/0610357] WIMPs are gravitationally trapped inside astronomical bodies, eg. Sun, Earth local overdensity! Energetic neutrinos from WIMP annihilation in the Sun/ Earth can be observed e.g. as upward-going muons Neutrino flux in the LHT model B H B H W + W, ZZ; Z ν ν, W lν Need to include effects of neutrino propagation and oscillations [we use the results of Cirelli et al, 2005] Log 10 yr 1 km 2 4 2 0-2 -4-6 -8 IceCube 100 200 300 400 500 M GeV Coan. region Pair-an. region

Direct Detection Rates: MSSM, UED, LHT 0.01 [Hooper, Zaharijas, hep-ph/0612137]! XN (pb) 0.0001 1e-06 1e-08 1e-10 1e-12 1e-14 CDMS (current) minimal UED 1e-16 1e-18 0 200 400 600 800 1000 1200 1400 m X (GeV) UED Little Higgs CDMS Bound [magenta points - MSSM scan]

Neutrino Telescope Rates: MSSM, UED, LHT [Hooper, Zaharijas, hep-ph/0612137] 100 IceCube R! (km -2 yr -1 ) 1 0.01 0.0001 1e-06 0 200 400 600 800 1000 1200 1400 m X (GeV) UED Little Higgs [magenta points - MSSM scan]

Positron Spectra: MSSM, UED, LHT [Hooper, Zaharijas, hep-ph/0612137] M WIMP = 300 GeV M WIMP = 600 GeV Dotted/ data : UED Dot-dash: LHT or wino MSSM (WW) Dash: bino MSSM (bb) Solid: astrophysics BG

A Preliminary Comment on PAMELA Preliminary August 2008 Model A Model B Model C Mass Mode χ 2 /df BF χ 2 /df BF χ 2 /df BF 100 e + e 0.152 3.8 1.459 23 0.555 2.4 100 µ + µ 1.028 6.1 0.175 25 1.577 4.3 100 τ + τ 2.893 12 2.019 45 3.224 9.0 100 W + W 1.758 24 0.728 91 2.259 17 100 ZZ 1.921 34 1.139 100 2.413 24 100 b b 5.154 33 4.692 100 5.107 24 300 e + e 0.182 32 1.132 430 0.439 18 300 µ + µ 0.186 44 0.475 250 0.532 29 300 τ + τ 1.131 57 0.387 240 1.586 39 300 W + W 2.598 66 2.483 240 2.781 47 300 ZZ 3.126 74 2.993 250 3.256 53 300 b b 4.133 57 3.735 180 4.216 42 1000 e + e 0.106 310 1.533 6300 0.210 170 1000 µ + µ 0.128 450 0.902 4200 0.339 270 1000 τ + τ 0.333 430 0.118 2400 0.693 280 1000 W + W 2.243 210 1.757 820 2.515 150 1000 ZZ 2.552 210 2.055 770 2.809 150 1000 b b 2.877 160 2.270 570 3.141 110 TABLE I: The quality of the spectral fit (χ 2 per degree of freedom) and the boost factors required for various dark matter masses (in GeV), annihilation modes, and diffusion parameters to produce the PAMELA positron excess. The column BF contains the boost factors required assuming a local dark matter density of ρ = 0.35. As stated in the text, the χ 2 /df should be interpreted as a qualitative distinction between the scenarios, as the data are still preliminary and errors only statistical. [Cholis, Goodenough, Hooper, Simet, Weiner, 0809:1683] Fits (rate and spectrum) seem to favor direct annihilation of WIMPs into e + e pairs, with σ 1 pb Spin-1/2 Majorana fermions (e.g. neutralinos) cannot do this:. σ(χχ f f) m 2 f at v χ 1 If this persists, could be a hint for non-susy WIMPs (UED?)

WIMPs at Colliders: a Model-Independent Approach [Birkedal, Matchev, MP, hep-ph/0403004] detailed balance soft-collinear (WW) factorization Variables: WIMP mass, spin, s- or p-annihilator, e+e- annihilation fraction " e 1 " e 1 " e 1-1 10-1 10-1 10-2 10-2 10-2 10-3 10 100 120 140 160 180 200 220 240 M! [GeV] -3 10 100 120 140 160 180 200 220 240 M! [GeV] -3 10 100 120 140 160 180 200 220 240 M! [GeV] Figure 3: 3σ observation reach of the ILC for a Spin-1 WIMP in terms of WIMP mass and κ e for three different assumptions on the chirality of the electron-wimp coupling, see text. Full line: P e = P e + = 0, dotted line: P e = 0.8, P e + = 0, dashed line : P e = 0.8, P e + = 0.6. Regions above the curves are accessible. [Batrels, List, 0709:2629 (hep-ex)]

Minimal Dark Matter Does stability of the WIMP require discrete symmetries? No, it may be accidental (i.e. no available decays conserving gauge quantum numbers from d<=5 operators: just like the proton!) Ex: fermionic 5-plet of SU(2) [Cirelli, Strumia, et.al., 2005-08] Quantum numbers DM can DM mass m DM ± m DM Events at LHC σ SI in SU(2) L U(1) Y Spin decay into in TeV in MeV L dt =100/fb 10 45 cm 2 2 1/2 0 EL 0.54 ± 0.01 350 320 510 0.2 2 1/2 1/2 EH 1.1 ± 0.03 341 160 330 0.2 3 0 0 HH 2.0 ± 0.05 166 0.2 1.0 1.3 3 0 1/2 LH 2.4 ± 0.06 166 0.8 4.0 1.3 3 1 0 HH, LL 1.6 ± 0.04 540 3.0 10 1.7 3 1 1/2 LH 1.8 ± 0.05 525 27 90 1.7 4 1/2 0 HHH 2.4 ± 0.06 353 0.10 0.6 1.6 4 1/2 1/2 (LHH ) 2.4 ± 0.06 347 5.3 25 1.6 4 3/2 0 HHH 2.9 ± 0.07 729 0.01 0.10 7.5 4 3/2 1/2 (LHH) 2.6 ± 0.07 712 1.7 9.5 7.5 5 0 0 (HHH H ) 5.0 ± 0.1 166 1 12 5 0 1/2 4.4 ± 0.1 166 1 12 7 0 0 8.5 ± 0.2 166 1 46 [Cirelli, Fornengo, Strumia, hep-ph/0512090]

Conclusions WIMP dark matter candidates are pretty generic in SM extensions at the TeV scale Two examples in this talk: UED and LHT dark matter Other interesting examples exist (e.g. minimal DM) Phenomenology (direct, indirect rates) may be quite different from the neutralino DM Models may be discriminated based on direct+indirect detection rates, in addition to the LHC data Example: positrons in UED - large rate, hard spectrum Some predictions possible based only on gross features of WIMP (mass, spin, annihilation fractions) independent of the details of microscopic model - e.g. FSR photons, ILC radiative production