FERMION DARK MATTER Accepted to JHEP [arXiv:1106.2162] Cornell - PowerPoint PPT Presentation

GOLDSTONE FERMION DARK MATTER Accepted to JHEP [arXiv:1106.2162] Cornell University In collaboration with B. Bellazzini, C. Csáki, J. Hubisz, and J. Shao SUSY , 29 August 2011 1 / 23 Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 1/23

The WIMP Miracle Contains factors of M Pl , s 0 , · · ·   � x f � − 1 � � g ∗ � σ v � 0   Ω DM h 2 ≈ 0 . 1 2       3 × 10 − 26 cm 3 / s 20 80   � � α 2 v ∼ ( 100 GeV ) 2 ❲✐t❤✐♥ ♦r❞❡rs ♦❢ ♠❛❣♥✐t✉❞❡✦ 2 / 23 Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 2/23

Ω h 2 vs direct detection Tension between annihilation cross section and direct detection bounds σ SI ∼ 7 . 0 × 10 − 9 pb σ ann. ∼ 0 . 1 pb 50 GeV WIMP Typical strategy: pick parameters such that σ SI is suppressed , then use tricks to enhance σ ann. . 3 / 23 Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 3/23

Ω h 2 vs direct detection CMSSM 10  42 Ruled out 10  43 Well tempered neutralino h 0 resonance 10  44 σ SI in cm 2 slepton co-annihilations 10  45 A 0 resonance 10  46 stop co-annihilations 10  47 0 200 400 600 800 M DM in GeV 1104.3572 4 / 23 Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 4/23

Motivation I: a natural WIMP Typical MSSM WIMP: σ SI too large Want to naturally suppress direct detection while maintaining ‘miracle’ of successful abundance. If LSP is part of a Goldstone multiplet , ( s + ia , χ ) , additional suppression from derivative coupling. • Like a weak scale axino, but unrelated to CP • Like singlino DM, but global symmetry broken in SUSY limit 5 / 23 Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 5/23

Motivation I: a natural WIMP Annihilation : p -wave decay to Goldstones � 2 � T f � � m χ 1 χγ µ γ 5 χ∂ µ a f ¯ ⇒ � σ v � ≈ ≈ 1 pb f 2 m χ Direct detection : CP-even Goldstone mixing with Higgs � m χ v � 2 m χ v ≈ O ( 10 − 45 cm 2 ) σ MSSM ∼ 0 . 01 ⇒ σ SI = SI f 2 f 2 6 / 23 Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 6/23

Motivation II: Buried Higgs Idea : Light Higgs buried in QCD background ✭✭✭✭✭✭✭✭ ✭ f 2 h 2 ( ∂ a ) 2 1 Global symmetry at f ∼ 500 GeV with coupling jet a h a jet 0906.3026, 1012.1316, 1012.1347 Can we bury the Higgs through a decays, but dig up dark matter in χ ? 7 / 23 Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 7/23

The Goldstone Supermultiplet sGoldstone Goldstone boson Goldstone fermion √ A = 1 � � 2 θ χ + θ 2 F √ s + i a + 2 Carries the low-energy degrees of freedom of the UV fields, � f 2 = Φ i = f i e q i A / f q 2 i f 2 i i ✘✘✘ ✘ SUSY ⇒ explicit s mass, m χ ≈ q i � F i � / f , a massless 8 / 23 Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 8/23

Interactions: Overview coupling to a coupling to H coupling to g , γ Kähler potential scalar NL Σ M Mixing Kähler kinetic Goldstone coupling to a MSSM Fermion interactions Explicit Anomaly breaking Superpotential 9 / 23 Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 9/23

Interactions: NL Σ M Kähler potential Non-linear realization of the global U(1) ⇒ Kähler interactions of the Goldstone multiplet: ∂ 2 K q 1 � f ( A + A † ) + · · · q 3 i f 2 ∂ A ∂ A † = 1 + b 1 b 1 = i qf 2 i Note K = K ( s ) , manifest shift-invariance. √ � � � 1 � 2 2 ( ∂ s ) 2 + 1 2 ( ∂ a ) 2 + i χγ µ ∂ µ χ L = 1 + b 1 f s + · · · 2 ¯ √ � � 1 1 2 √ χγ µ γ 5 χ ) ∂ µ a + · · · + b 1 f + b 2 f 2 s + · · · (¯ 2 2 b 1 controls the annihilation cross section. Phys. Lett. B 87 (1979) 203 10 / 23 Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 10/23

Interactions: scalar mixing MSSM fields are uncharged under the global U(1), but may mix with the Goldstone multiplet through higher-order terms in K : � A + A † � � A + A † � 2 ( c 2 H u H d + · · · ) K = 1 ( c 1 H u H d + · · · ) + 1 2 f 2 f The new scalar interactions take the form �   � 1 2 ( ∂ a ) 2 + 1 v χ/  1 + c h  L ⊃ f h + · · · 2 ¯ ∂χ c h depends on c i and the Higgs mixing angles. c h controls direct detection 11 / 23 Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 11/23

Interactions: kinetic mixing The higher order terms in K also induce kinetic � H – χ mixing. χγ µ ∂ µ � χγ µ ∂ µ � H 0 H 0 L ⊃ i ǫ u ¯ u + i ǫ d ¯ d + h.c. where ǫ ∼ v / f . For large µ , χ has a small � H of order vm χ / f µ . Mixing with other MSSM fields is suppressed. Assuming MFV, A + A † � � Y u � � K = 1 ¯ QH u U + · · · f M u where the scales M u , d ,ℓ are unrelated to f or v and can be large and dependent on the UV completion 12 / 23 Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 12/23

Interactions: anomaly Fermions Ψ charged under global U(1) and Standard Model g � � L an ⊃ c an aG a µν � G a χ G a µν σ µν γ 5 λ a √ µν + 2 ¯ f 2 a � y i f � √ N Ψ c an = α � = α 2 8 π q Ψ N Ψ 8 π m Ψ i g i √ Also γγ Assumed: degenerate m Ψ and y = m Ψ q Ψ / f 2 Integrating out λ a generates χ couplings to gluons � � � � c 2 c 2 χχ GG − i ¯ χγ 5 χ G � an an L ⊃ − ¯ G 2 M λ f 2 2 M λ f 2 These contribute to collider and astro operators. 13 / 23 Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 13/23

Interactions: explicit breaking ✟ Include explicit ✟✟ U ( 1 ) spurion R α = λ α f with λ α ≪ 1 U ( 1 ) = f 2 � R − α e aA / f W ✟✟ α Perserve SUSY ⇒ at least two spurions with opposite charge. This generates m a = m χ = m s and couplings m a χγ 5 χ + m a 8 f 2 ( α 2 + αβ + β 2 ) a 2 ¯ √ i a ¯ L ⊃ − 2 f ( α + β ) χχ 2 � �� � � �� � ρ δ By integration by parts this is equivalent to a shift in the b 1 coefficient from the Kähler potential 14 / 23 Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 14/23

Main parameters coupling to a coupling to H coupling to g , γ Kähler potential c h scalar NL Σ M b 1 Mixing Kähler σ SI σ ann kinetic Goldstone coupling to a MSSM Fermion m χ ; SSB at f m a collider, astro Explicit c an δ Anomaly breaking Superpotential 15 / 23 Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 15/23

Parameter space scan Abundance : � σ v � ≈ b 14 m 2 T f χ f 4 ≈ 1 pb 8 π m χ p -wave: b 1 � 1, all other parameters take natural values Parameter Description Scan Range f Global symmetry breaking scale 500 GeV − 1 . 2 TeV ✘ m χ Goldstone fermion mass ( ✘✘ SUSY) 50 − 150 GeV m a Goldstone boson mass 8 GeV – f / 10 b 1 χχ a coupling [ 0 , 2 ] c an Anomaly coefficient 0 . 06 c h Higgs coupling [ − 1 , 1 ] χγ 5 χ coupling δ Explicit breaking ia ¯ 3 / 2 � 1 � � � 2 ( ∂ a ) 2 + 1 v b 1 ∂ µ a + c an χγ µ γ 5 χ aG � χ/ χγ 5 χ L ⊃ 2 ¯ ∂χ f h + √ ¯ √ G + i δ a ¯ c h 2 2 f 2 f 16 / 23 Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 16/23

Contours of fixed Ω Dominant contribution Ω h 2 = 0 . 11 ✟ Kähler, anomaly, ✟✟ U(1) 3.5 g χ m a χ a m χ 3.0 Coupling b 1 χ χ g a 2.5 Subleading Mixing with Higgs 10 % 2.0 χ χ a h 1.5 40 % χ χ h h 70 % 1.0 Negligible 60 80 100 120 140 t , u χχ → s → aa , χχ → hh m χ [GeV] 17 / 23 Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 17/23

Direct Detection Higgs exchange typically dominates by a factor of O ( 10 3 ) . � 115 GeV � 4 � � 2 · 700 GeV 100 GeV · µ χ m χ GeV · λ N SI ≈ 3 · 10 − 45 cm 2 c 2 σ H h 0 . 5 m h f Compare this to the MSSM Higgs with L = 1 2 cg ¯ χχ h : ∼ c 2 g 2 λ 2 N µ 2 m 2 ≈ c 2 × 10 − 42 cm 2 σ MSSM N SI m 2 2 π h v 2 Natural suppression : ( m χ v / f 2 ) 2 due to Goldstone nature 18 / 23 Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 18/23

Parameter space scan Direct Detection 1 x 10 -43 5 x 10 -44 Ruled out XENON 1 x 10 -44 σ [cm 2 ] 5 x 10 -45 500 < f < 700 GeV 700 < f < 800 GeV 800 < f < 900 GeV 1 x 10 -45 5 x 10 -46 900 < f < 1000 GeV 1 x 10 -46 150 100 m χ [GeV] 19 / 23 Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 19/23

Indirect detection & Colliders p spectrum : below PAMELA ¯ • (Einsasto DM Halo profile) 1104.3572 γ -ray line search : O ( 10 ) smaller than bound • χχ → a → γγ Diffuse γ -ray spectrum : O ( 10 ) smaller than bound • χχ → a → gg → π ′ s Photo-production from annihilation : σ 3x lower than bound • Low mass DM m χ � 60 GeV, constrains bb decays ISR monojets at colliders : dim-7 operators too small L ⊃ − c an2 χχ GG − ic an2 χγ 5 χ G � 2 M λ f 2 ¯ 2 M λ f 2 ¯ G 20 / 23 Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 20/23

Non-standard Higgs decays Hard to completely bury the Higgs. LEP: Br(SM) � 20% ⇒ m h � 110 GeV f = 500 GeV, m a = 45 GeV, m χ = 100 GeV, c h = 2 1.0 Higgs branching ratio 0.8 WW ∗ aa 0.6 0.4 b ¯ b ZZ ∗ 0.2 0.0 100 110 120 130 140 150 160 Higgs mass m h [GeV] 21 / 23 Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 21/23