GOLDSTONE FERMION DARK MATTER Phys. Rev. D83, 073002 arxiv:1004.2037 Cornell University In collaboration with B. Bellazzini, C. Csáki, J. Hubisz, and J. Shao SUSY, 31 August 2011 1 / Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 1/25 25
The WIMP Miracle Contains factors of M Pl, s 0, Ω DM h 2 0.1 ( ) x ( f g ) 1 2 20 80 σv 0 3 10 26 cm 3 /s α 2 v (100 GeV) 2 Within orders of magnitude! 2 / Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 2/25 25
Reality: direct detection vs Ωh 2 σ ann. 0.1 pb σ SI 7.0 10 9 pb 50 GeV WIMP Typical strategy: pick parameters such that σ SI is suppressed, then use tricks to enhance σ ann.. Tune the neutralino composition ( B vs. W, H) Coannihilations (accidental slepton degeneracy) Resonant annihilation 3 / Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 3/25 25
Reality: direct detection vs Ωh2 CMSSM 10 42 Ruled out σ SI in cm2 10 43 Well tempered neutralino 10 44 h0 resonance 10 45 slepton co-annihilations 10 A0 resonance 46 stop co-annihilations 10 47 0 200 1104.3572 Flip Tanedo pt267@cornell.edu 400 600 800 M DM in GeV Goldstone Fermion Dark Matter 4/ 25 4/25
MSSM Dark Matter and Tuning 10 43 insensitive to parameters σsi [cm2 ] 10 44 10 45 10 46 10 47 10 48 10 sensitive to parameters 49 10 1107.5048 Flip Tanedo pt267@cornell.edu 50 100 500 1000 5000 Tuning Goldstone Fermion Dark Matter 5/ 25 5/25
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 6 / Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 6/25 25
Motivation I: a natural WIMP Annihilation: p-wave decay to Goldstones 1 f χγµ γ 5 χ µ a σv ( ) ( ) m 2 χ Tf 1 pb f 4 m χ Direct detection: CP-even Goldstone mixing with Higgs mixing m χv f 2 0.01 σ SI = ( mχ v f 2 ) 2 σ MSSM SI O(10 45 cm 2 ) 7 / Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 7/25 25
Motivation II: Buried Higgs Idea: Light Higgs buried in QCD background Global symmetry at f 500 GeV with coupling 1 h 2 ( a) 2 f 2 h a a jet jet 0906.3026, 1012.1316, 1012.1347 Can we bury the Higgs through a decays, but dig up dark matter in χ? 8 / Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 8/25 25
The Goldstone Supermultiplet sgoldstone Goldstone boson Goldstone fermion A = 1 2 ( s + i a ) + 2θ χ + θ 2 F Carries the low-energy degrees of freedom of the UV fields, Φ i = f i e q i A/f f 2 = i q 2 i f 2 i Neglecting terms which simultaneously break SUSY and U(1): SUSY explicit s mass, m χ q i F i /f, a massless a mass through small supersymmetric explicit U(1) terms 9 / Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 9/25 25
Interactions: Kähler potential Our non-linear realization of the global U(1) leads to interactions of the Goldstone fields in through the kinetic (Kähler) terms: 2 K A A = 1 + b q 1 f (A + A ) + b 1 = 1 q 3 qf 2 i fi 2 Note the manifest shift-invariance. This leads to: ( ) (1 2 L = 1 + b 1 s + f 2 ( s)2 + 1 2 ( a)2 + i ) 2 χγµ µ χ + 1 ( ) 2 1 2 b 1 2 f + b 2 f s + ( χγ µ γ 5 χ) 2 µ a + i Phys. Lett. B 87 (1979) 203 b 1 controls the annihilation cross section. 10 / Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 10/25 25
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: K = 1 f ( A + A ) (c 1 H u H d + ) + 1 2f 2 ( A + A ) 2 (c2 H u H d + ) The new scalar interactions take the form [ 1 L 2 ( a)2 + 1 ] 2 χ v / χ 1 + c h f h + Where c h is a function of the c i and the Higgs mixing angles. c h (m h /m s ) 2 in the large m s limit. We neglect mixing with the heavy higgses. 11 / Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 11/25 25
Interactions: kinetic mixing The higher order terms in K also induce kinetic H χ mixing. L iɛ u χγ µ µ H 0 u + iɛ d χγ µ µ H 0 d + h.c. where ɛ v/f. In the large µ limit, χ has a small H component on the order of vm χ /f µ. Mixing with other MSSM fields is suppressed. Assuming MFV, K = 1 f ( ) ( ) A + A Y u QH u U + M u where the scalse M u,d,l are unrelated to f or v and can be large and dependent on the UV completion 12 / Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 12/25 25
Interactions: anomaly Fermions Ψ charged under global U(1) and Standard Model L an c ( an f ag a G ) µν µν a + 2 χg µνσ a µν γ 5 λ a 2 c an = α ( ) N Ψ yi f 2 = α 8π 8π q ΨN Ψ i m Ψi Where we have assumed degeneracy of m Ψ and Yukawas y = m Ψ q Ψ /f 2 Integrating out λ a generates χ couplings to gluons L ( ) c 2 an 2M λ f 2 χχ GG i ( c 2 an 2M λ f 2 ) a χγ 5 χ G G This contributes to direct detection and collider operators. g g U(1) SU(3) 2 c U(1) U(1) 2 QED 13 / Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 13/25 25
Interactions: explicit breaking Include explicit U(1) spurion R α = λ α f with λ α 1 W U(1) = f 2 α R α e aa/f Perserve SUSY at least two spurions with opposite charge. This generates m a = m χ = m s and couplings m a L 2 (α + β) i a χγ 5 χ + m a 2f 8f 2 (α2 + αβ + β 2 ) a 2 χχ }{{}}{{} δ ρ By integration by parts this is equivalent to a shift in the b 1 coefficient from the Kähler potential 14 / Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 14/25 25
Parameter space scan Abundance: σv b 1 4 mχ 2 8π m χ f 1 pb 4 p-wave: b 1 1, all other parameters take natural values T f Parameter Description Scan Range f Global symmetry breaking scale 500 GeV 1.2 TeV m χ Goldstone fermion mass 50 150 GeV m a Goldstone boson mass 8 GeV f /10 b 1 χχa coupling [0, 2] c an Anomaly coefficient 0.06 c h Higgs coupling [ 1, 1] δ Explicit breaking ia χγ 5 χ coupling 3/2 L [ 1 2 ( a)2 + 1 ] 2 χ/ χ v c h f h + b 1 2 2f ( χγ µ γ 5 χ ) µ a + c an f 2 ag G + iδa χγ 5 χ 15 / Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 15/25 25
Contours of fixed Ω Coupling b1 3.5 3.0 2.5 2.0 Ωh 2 = 0.11 m a m χ 10 % Dominant contribution Kähler, anomaly, U(1) χ g χ a χ a χ g Subleading Mixing with Higgs χ h χ a 1.5 1.0 40 % 70 % 60 80 100 120 140 m χ [GeV] χ h χ Negligible χχ s aa, χχ t,u hh h 16 / Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 16/25 25
Direct Detection Relevant couplings from EWSB and anomaly: L c hv 2f χ χ/ χh c an 2 2M λ f χχgg ic 2 an 2 2M λ f 2 χγ5 χg G h N χ a g χ N χ g Effective coupling to nucleons: L = G nuc NN χχ, ( ) λ N G nuc = c h 2 mχ m N 2 mh 2f + 4πc an 2 m N 1 2 9α s M λ f f (N) i i=u,d,s 17 / Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 17/25 25
Direct Detection Higgs exchange typically dominates by a factor of O(10 3 ). σ H SI 3 10 45 cm 2 c 2 h ( ) 4 ( ) 4 115 GeV 700 GeV ( m χ ) 2 ( µχ ) ( ) 2 2 λn f 100 GeV GeV 0.5 m h Compare this to the MSSM Higgs with L = 1 cg χχh: 2 σsi MSSM c 2 g 2 λ 2 Nµ 2 mn 2 2π mh 2v c 2 10 42 cm 2 2 Natural suppression: (m χ v/f 2 ) 2 due to Goldstone nature Is it enough to avoid current direct detection bounds? 18 / Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 18/25 25
Parameter space scan Direct Detection -43 σ [cm2 ] 1 x 10-44 5 x 10 Ruled out XENON -43 1 x 10-44 5 x 10-43 1 x 10-44 5 x 10 ev 700 G < f 0 GeV < 80 500 < f ev < 900 G 700 < f 800 < 900 < f < 1000 GeV -46 1 x 10 100 150 mχ [GeV] Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 19 / 19/2525
Indirect detection: p flux vs. PAMELA f = 700 GeV, Q Ψ = 2, δ = 3 2, N Ψ = 5 dφ/dk [GeV m 2 s sr] 1 0.01 0.001 10-4 10-5 10-6 Einasto Max Einasto Min.1.5 1 5 10 50 100 Kinetic energy [GeV] m a m χ = 0.5 Dotted: mχ = 150 GeV, b1 = 1 Dashed: mχ = 100 GeV, b1 = 1.5 Solid: mχ = 50 GeV, b1 = 3 Using Einasto DM Halo profile in 1012.4515, 1009.0224 20 / Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 20/25 25
Indirect detection: Fermi-LAT γ-ray line search: 30 200 GeV Upper bound σv γγ < 2.5 10 27 cm 3 /s χχ a γγ via anomaly For SU(5) fundamentals, σv γγ 2 10 3 σv gg O(10) smaller than bound even for extreme parameters Diffuse γ-ray spectrum: 20 100 GeV Bounds χχ to charged particles, π 0 s χχ a gg via anomaly O(10) smaller than bound Photo-production from DM annihilation: spheroidal galaxies Low mass DM m χ 60 GeV, constrains bb decays GF: annihilation σ always at least a factor of 3 lower http://fermi.gsfc.nasa.gov/science/symposium/2011/program 21 / Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 21/25 25
Collider production Collider production through gluons. ISR monojet signature is sensitive to σ N SI 10 46 cm 2 at the LHC with 100 fb 1. The dim-7 anomaly operators are too small: L c an 2 2M λ f χχgg ic 2 an 2 2M λ f 2 χγ5 χg G gg a χχ may be within 5σ reach with 100 fb 1 1005.1286, 1005.3797, 1008.1783, 1103.0240, 1108.1196 Cascade decays: LOSP χ through χgλ anomaly χ H kinetic mixing Decays typically prompt, a reconstruction is difficult for light masses. Heavy fermions Ψ in anomaly may appear as fourth generation quarks 22 / Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 22/25 25
Non-standard Higgs decays Hard to completely bury the Higgs. LEP: Br(SM) 20% m h 110 GeV 1.0 f = 500 GeV, m a = 45 GeV, m χ = 100 GeV, c h = 2 Higgs branching ratio 0.8 0.6 0.4 0.2 aa b b WW ZZ 0.0 100 110 120 130 140 150 160 Higgs mass m h [GeV] 23 / Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 23/25 25
Non-standard Higgs decays Partially buried & invisible: Suppressed SM channels, MET, Γ tot < 1 1.0 f = 400 GeV, m a = m χ = 60 GeV, c h = 2 Higgs branching ratio 0.8 0.6 0.4 0.2 b b aa χχ ZZ WW 0.0 100 110 120 130 140 150 160 Higgs mass m h [GeV] 24 / Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 24/25 25
Conclusions Executive summary: Goldstone Fermion dark matter SSB: global U(1) Goldstone boson a and fermion χ χ is LSP and DM, a gives buried Higgs channel Simple extension of MSSM with natural WIMP dark matter Kähler χχa interaction controls abundance Higgs mixing, anomaly controls direct detection Novel collider signature: partially buried/invisible Higgs Further directions: p-wave Sommerfeld enhancement (can push m a, m χ to 10 GeV) Non-abelian generalization 25 / Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 25/25 25
Extra Slides 25 / Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 25/25 25
Examples of Linear Models Simplest example: W = ys ( NN µ 2) + N φφ + SH }{{} u H d + W }{{} explicit }{{} anomaly mixing explicit U(1) Example with b 1 1: W = λxyz µ 2 Z + λ 2 Y 2 N µ NN q Z = 0, q N = q N = 2q Y = 2q X. Goldstone multiplet: A = i q i f i ψ i f = q Y f ( YfY Xf X + 2 NF N) b 1 = f 2 X + f 2 Y + 8f 2 N f 2 X + f 2 Y + 4f 2 N 25 / Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 25/25 25
Tamvakis-Wyler Theorem Phys. Lett B 112 (1982) 451; Phys. Rev. D 33 (1986) 1762 Global symmetry: W [Φ i ] = W [e iαq i Φ i ] so that 0 = W [eiαq i Φ i ] α = j W j q j Φ j, Taking a derivative / Φ i gives: 0 = Φ i j W j q j Φ j = Φ j W ij q j f j + W i q i 25 / Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 25/25 25
SUSY NLΣM Phys. Lett. B 87 (1979) 203 Expand Kähler potential, drop total derivatives, integrate out F : L = K ( i 2 χσ χ + φ 2 ) + K 4 iχσ χ (φ φ ) + 1 ( K (K ) 2 ) χ 2 χ 2 4 K These terms can be understood in terms of geometric properties of the vacuum manifold, see e.g. hep-th/0101055. 25 / Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 25/25 25
SUSY Breaking and χ mass We assume that soft SUSY terms that also explicitly break the global U(1) are negligible. Neglect D-term mixing with λ a, then fermion mass matrix is W ij. Tamvakis-Wyler: W ij q j f j = q i W i = q i F i j so that χ = i q i f i ψ i /f mass depends on how U(1)-charged F -terms in the presence of soft SUSY terms. If W has an unbroken R symmetry, then R[χ] = 1 which prohibits a Majorana mass. However, while soft scalar masses preserve R, A-terms are holomorphic and generally break R symmetries to contribute to m χ. 25 / Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 25/25 25
SUSY Breaking and χ mass The A-term contribution to m χ is equivalent to F -term mixing between U(1) charged fields and the SUSY spurion, X. This was recently emphasized in 1104.0692 as an irreducible O(m 3/2 ) contribution to the Goldstone fermion For concreteness, consider gravity mediation with m soft F /M Pl. K = i Z(X, X )Φ i Φ i Analytically continue into superspace hep-ph/9706540 ( Φ Φ Z 1/2 1 + ln Z ) X F θ2 Φ Canonical normalization generates A-terms: L soft = W ( Z 1/2 Φ Φ=φ ln Z ln X ) F M 25 / Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 25/25 25
SUSY Breaking and χ mass L soft = W Φ ( Z 1/2 Φ=φ ln Z ln X ) F M Completely incorporates F -term mixing of the form FF i Φ i. The χ mass is determined by the induced F i obtained by minimizing W 2 V = φ i + A i W φ i φ i + h.c. + m 2 i φ i 2 Assuming A i, m i < f i, generic size is F i A i f i so that m χ A i q i. Often the A-terms are suppressed relative to other soft terms, so it s reasonable to expect χ to be the LSP. Contributions from soft scalar masses are on the order of m 2 i /f i which can easily be suppressed. 25 / Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 25/25 25
Direct detection: nucleon matrix elements Nucleon matrix elements can be parameterized via Phys. Rev. D38 2869, Phys. Lett. B219 347, 0801.3656, 0907.417 m i N q i q i N = f (N) i m N The heavy quark contribution via gluons can be calculated by the conformal anomaly, Phys. Lett. B78 433 f (N) j m N = 2 27 1 = f q (N) q=u,d,s j = c, b, t Relevant quantity in Higgs exchange: c q, diagonalized Yukawa λ N = q=u,d,s c q f (N) q + 2 27 1 = f q (N) c q q=u,d,s q =c,b,t 25 / Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 25/25 25
Direct Detection Some details: G χn = c h λ N 2 2 ( ) mχ m N mh 2f + 4πc an 2 2 9α s For reduced mass µ χ = (m 1 χ m N M λ f + m 1 N ) 1, 1 i=u,d,s f (N) i σ Higgs SI = 4µ2 χ A 2 π [G χpz + G χn (A Z)] σ H SI 3 10 45 cm 2 c 2 h σ glue SI ( ) 4 ( ) 4 115 GeV 700 GeV ( m χ ) 2 ( µχ ) ( ) 2 2 λn f 100 GeV 1 GeV 0.5 m h 2 10 48 cm 2 ( 700 GeV M λ using c an = α s q Ψ N Ψ /8π ) 2 ( ) 4 ( ) 4 700 GeV (qψ NΨ f 5 2 ) 4 ( µ ) 2 1 GeV 25 / Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 25/25 25
Why are the χχ aa annihilations p-wave? If the initial state is a particle-antiparticle pair with zero total angular momentum and the final state is CP even, then the process must vanish when v = 0. Under CP a particle/antiparticle pair picks up a phase ( ) L+1. When v = 0 momenta are invariant and thus the initial state gets an overall minus sign. Since final state is CP even, the amplitude must vanish in this limit. For Dirac particles P is sufficient, but for Majorana particles CP is the well-defined operation. This is why χχ G G is s-wave while χχ aa is p-wave. 25 / Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 25/25 25
Nuclear matrix element and matching The nucleon matrix element at vanishing momentum transfer: M N = Θ µ µ = N i=u,d,s m i q i q i + β(α) 4α G a αβg a αβ N from: Shifman, Vainshtein, Zakharov. Phys. Lett 78B (1978) β = 9α 2 /2π + contains only the light quark contribution, M N is the nucleon mass. The GG matches onto the nucleon operator NN. M N f (N) i=u,d,s = N m i q i q i N f (N) g = 1 i=u,d,s f (N) i 25 / Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 25/25 25
Nuclear matrix element and matching β(α) 4α G αβg a αβ a M N 1 i=u,d,s f (N) i NN Where f (N) u,d f s (N) 0.25. For a detailed discussion, see 0801.3656 and 0803.2360. 25 / Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 25/25 25
Image Credits and Colophon Zombie arm illustration from http://plantsvszombies.wikia.com Beamer theme Flip, available online http://www.lepp.cornell.edu/~pt267/docs.html All other images were made by Flip using TikZ and Illustrator 25 / Flip Tanedo pt267@cornell.edu Goldstone Fermion Dark Matter 25/25 25