Goldstone Fermion Dark Matter 1/4848

DARK. MATTER JHEP 1109:035,2011 [arXiv:1106.2162] & work in progress

Cornell Flip Tanedo University In collaboration with B. Bellazzini, M. Cliche, C. Csáki, J. Hubisz, J. Shao UC Davis Particle Theory Seminar, 22 Oct 2012 1/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 1/4848 . . The WIMP Miracle

Contains factors. of MPl, s0, ···

  −1 ( )( )− 1 2  ⟨ ⟩  2 xf g∗  σv 0  ΩDMh ≈ 0.1.   20 80 3 × 10−26. cm3/s

⟨ . ⟩ 2 ∼ α v (100 GeV)2

Logarithmic miracle: Within orders of magnitude! . 2/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 2/4848 . . Abundance vs direct detection

∼. . −9 σann. 0.1 pb σSI ∼ 7.0 × 10 pb 50 GeV WIMP

Typical strategy: pick parameters such that σSI is suppressed, then use tricks to enhance σann..

• Tune the neutralino composition (Be vs. Wf , He ) • Coannihilations (accidental slepton degeneracy) • Resonant annihilation

3/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 3/4848 . . Abundance vs direct detection CMSSM 1042 Ruled out

43 10 Well tempered neutralino

44 0 2 10 h resonance cm in

SI slepton co-annihilations σ 1045

A0 resonance 1046 stop co-annihilations

1047 0 200 400 600 800

. MDM in GeV Farina, Kadastik, Raidal, Pappadopulo, Pata, Strumia [1104.3572] 4/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 4/4848 . . The timid amoeba

1104.2549 5/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 5/4848 . . MSSM Dark Matter and EWSB Tuning

100-1000 GeV 1-10 TeV 10-100 GeV

. Perelstein and Shakya [1107.5048] 6/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 6/4848 . . Abundance vs direct detection

∼. . −9 σann. 0.1 pb σSI ∼ 7.0 × 10 pb 50 GeV WIMP

Assumed that these come from the same effective operator:

χ SM χ χ

. .

χ SM SM SM

Can we separate into two different sectors? One way to do this is with a Goldstone supermultiplet.

7/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 7/4848 . . Abundance vs direct detection

∼. . −9 σann. 0.1 pb σSI ∼ 7.0 × 10 pb 50 GeV WIMP

Assumed that these come from the same effective operator:

χ a χ χ . s . h χ a N N

Can we separate into two different sectors? (Higgs portal) One way to do this is with a Goldstone supermultiplet.

7/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 7/4848 . . Motivation: natural WIMP . Typical MSSM WIMP: σ too large . SI 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

. .Goldstone Fermion Dark Matter Parameterized class of models with a hidden sector and a .spontaneously broken U(1) 8/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 8/4848 . . Motivation: a natural WIMP

Annihilation: p-wave. decay to Goldstones

( ) ( ) 1 m2 T . µ 5 ⇒ ⟨ ⟩ ≈ χ f. ≈ 1 pb χγ γ χ∂µa σv 4 f f mχ

Direct detection: CP-even Goldstone mixing. with Higgs

( ) 2 . mχv mχv MSSM −45 2 ∼ 0.01 ⇒ σSI = . σ ≈ O(10 cm ) f 2 f 2 SI .

9/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 9/4848 . . ‘Historical’ Motivation: Buried Higgs

Idea: Light Higgs buried in QCD background (((( ((( ∼ 1 2 2 (Global( symmetry at f 500 GeV with coupling f 2 h (∂a)

a jet . h a jet

Bellazzini, Csáki, Falkowski, Hubisz, Shao, Weiler: 0906.3026, 1012.1316; Luty, Phalen, Pierce: 1012.1347 Can we bury the Higgs through a decays, but dig up dark matter in χ?

10/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 10/4848 . . Goldstone Boson Review

¨ Global ¨U(1)¨ ⇒ massless pseudoscalar Shift symmetry ⇒ derivative coupling

11/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 11/4848 . . Nonlinear Σ Model (NLΣM) e.g. chiral perturbation theory

{ ≫ QCD is a theory of quarks, gluons (E ΛQCD) pseudoscalar mesons (πs) (E ≪ ΛQCD)

⟨qq⟩ : SU(3)L × SU(3)R → SU(3)V

. .Nonlinear realization f 2 U(x) = exp (2iπa(x)T a/f ) L = Tr |∂U|2 . 4 ̸ mqi s explicitly break ﬂavor symmetry, mπ = 0

12/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 12/4848 . . Couple NLΣM to the [low energy] SM

± NLΣM (π(x) theory) Gauge bosons, e , ··· SU(2) x U(1) .

13/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 13/4848 . . Our construction

Goldstone Supermultiplet q, g, γ, h MSSM .

13/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 13/4848 . . The Goldstone Supermultiplet . . . sGoldstone Goldstone boson Goldstone fermion

1 ( ) √ A = √ s. + i a. + 2θ χ. + θ2F 2

Carries the low-energy degrees of freedom of the UV ﬁelds, ∑ qi A/f 2 2 2 Φi = fi e f = qi fi i SUSY ⇒ explicit s mass, mχ ≈ qi ⟨Fi ⟩/f , a massless ¨ a mass through small supersymmetric explicit ¨U(1)¨ terms .

14/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 14/4848 . . ¨¨ A simple example of a ¨U¨(1) sector

. UV theory . ( ) † K = N N + N†N + S†SW = S NN − µ2 .

N ∼ fe+A/f N ∼ fe−A/f

. Effective theory . † . K = cosh(A + A ) W = 0

15/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 15/4848 . . SUSY Breaking and the χ mass Tamvakis-Wyler Thm. Phys. Lett B 112 (1982) 451; Phys. Rev. D 33 (1986) 1762

iαqi Global symmetry: W [Φi ] = W [e Φi ] so that

iαqi ∑ ∂W [e Φi ] 0 = = Wj qj Φj , ∂α j

Taking a derivative ∂/∂Φi gives:  

∑ ∑ ∂   0 = Wj qj Φj = Wij qj fj + Wi qi ∂Φi j ⟨Φ⟩ j

. ∑ χ = i qi fi ψi /f mass depends on the vevs of U(1)-charged .F -terms in the presence of soft SUSY terms Assuming no D-term mixing with gauginos 16/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 16/4848 . . SUSY Breaking and the χ mass

If R symmetry unbroken: R[χ] = −1 & no Majorana mass • Soft scalar masses preserve R • A-terms are holomorphic and generally break R symmetry

Assuming Ai , mi < fi , generic size is |Fi | ≈ Ai fi

mχ ∼ Ai qi

. Often the A-terms are suppressed relative to other soft terms, so .it’s reasonable to expect χ to be the LSP.

17/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 17/4848 . . SUSY Breaking and the χ mass Contribution from Planck ‘sloperators’

But one might worry (1104.0692) about Planck-scale operators giving an irreducible contribution to mχ,

∫ † 2 † 4 (A + A ) (X + X ) d θ ∼ m3/2χχ MPl

. .However... The A-term contribution to mχ is equivalent to F -term mixing .between U(1) charged ﬁelds and the SUSY spurion, X.

18/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 18/4848 . . SUSY Breaking and the χ mass Contribution from Planck ‘sloperators’

For concreteness, consider gravity mediation with msoft ∼ F /MPl. ∑ † † K = Z(X, X )Φi Φi i

Analytically continue into superspace hep-ph/9706540 ( ) ∂ ln Z Φ → Φ′ ≡ Z 1/2 1 + F θ2 Φ ∂X

Canonical normalization generates A-terms: ( )

∂W ∂ ln Z F L −1/2 − ∆ soft = Z ∂Φ Φ=ϕ ∂ ln X M

19/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 19/4848 . . SUSY Breaking and χ mass

( )

∂W ∂ ln Z F L −1/2 − ∆ soft = Z ∂Φ Φ=ϕ ∂ ln X M

† Completely incorporates F -term mixing of the form FFi Φi . Assuming Ai , mi < fi , generic size is |Fi | ≈ Ai fi so that mχ ∼ Ai qi .

. ¨¨ Not a problem when ¨U(1) sector sequestered from SUSY So ≲ ≪ indeed. reasonable to consider ma mχ ms .

20/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 20/4848 . . Parameterize couplings to the MSSM

Goldstone Supermultiplet q, g, γ, h MSSM .

21/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 21/4848 . . Interactions: Overview . . . coupling to a coupling to H coupling to g, γ

Kähler potential . scalar NLΣM Mixing Kähler

. . . kinetic

Goldstone coupling to a Fermion. MSSM

interactions . .

Explicit Anomaly breaking Superpotential 22/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 22/4848 . . Interactions: Overview . . . coupling to a coupling to H coupling to g, γ

Kähler potential . scalar NLΣM Mixing Kähler

. . . kinetic

Goldstone coupling to a Fermion. MSSM

interactions . .

Explicit Anomaly breaking Superpotential 22/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 22/4848 . . Interactions: NLΣM Kähler potential Non-linearly realized global U(1) leads to interactions of the Goldstone ﬁelds in through the Kähler terms:

∂2K q 1 ∑ † ··· 3 2 † = 1 + b1 (A + A ) + b1 = 2 qi fi ∂A∂A f qf i Note the manifest shift-invariance. This leads to: ( √ ) 2 L = (usual kinetic terms) 1 + b s + ··· 1 f √ ( ) . 1 1 2 µ 5 + √ b1 + b2 s + ··· (χγ γ χ) ∂ a + ··· 2 2 f f 2 µ . b1 controls the annihilation cross section. Zumino, Phys. Lett. B 87 (1979) 203 . 23/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 23/4848 . . Interactions: Overview . . . coupling to a coupling to H coupling to g, γ

Kähler potential . scalar NLΣM Mixing Kähler

. . . kinetic

Goldstone coupling to a Fermion. MSSM

interactions . .

Explicit Anomaly breaking Superpotential 23/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 23/4848 . . 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: ( ) ( ) 1 1 2 K = A + A† (c H H + ··· ) + A + A† (c H H + ··· ) f 1 u d 2f 2 2 u d The new scalar interactions take the form   [ . ] . 1 1 v L ⊃ (∂a)2 + χ∂χ/ 1 + c h + ···  2 2 h f

c depends on c and the Higgs mixing angles. h i . ch controls direct detection

2 ch → (mh/ms ) in the large ms limit. We neglect mixing with the heavy higgses. .

24/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 24/4848 . . Interactions: other mixing The higher order terms in K also induce kinetic He –χ mixing. . . µ e 0 µ e 0 L ⊃ iϵu χγ ∂µHu + iϵd χγ ∂µHd + h.c.

e where ϵ ∼ v/f . For large µ: χ has a small H component of O(vmχ/f µ).

Mixing with other MSSM ﬁelds is suppressed. Assuming MFV, ( ) ( ) 1 † Yu K = A + A QHuU + ··· f Mu

where the scales Mu,d,ℓ are unrelated to f or v and can be large and dependent on the UV completion

25/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 25/4848 . . Interactions: Overview . . . coupling to a coupling to H coupling to g, γ

Kähler potential . scalar NLΣM Mixing Kähler

. . . kinetic

Goldstone coupling to a Fermion. MSSM

interactions . .

Explicit Anomaly breaking Superpotential

25/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 25/4848 . . Interactions: anomaly Fermions Ψ charged under global U(1) and Standard Model . ( . ) g L ⊃ can a e a a µν 5 a an √ aGµνGµν + 2χGµνσ γ λ f 2 a . . α c = q N g an 8π Ψ Ψ 2 U(1) SU(3)c 2 U(1) U(1)QED Integrating out λa generates χ couplings to gluons, photons ( ) . ( ) . c2 c2 L ⊃ − an χχ GG − an χγ5χ GGe 2 i 2 2Mλf 2Mλf . These contribute to collider and astro operators. . 26/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 26/4848 . . Interactions: Overview . . . coupling to a coupling to H coupling to g, γ

Kähler potential . scalar NLΣM Mixing Kähler

. . . kinetic

Goldstone coupling to a Fermion. MSSM

interactions . .

Explicit Anomaly breaking Superpotential

26/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 26/4848 . . Interactions: explicit breaking ¨¨ Include explicit ¨U(1) spurion Rα = λαf with λα ≪ 1 ∑ ¨ 2 aA/f W¨U(1) = f R−αe α Perserve SUSY ⇒ at least two spurions with opposite charge.

This generates ma = mχ = ms and couplings . m m L ⊃ − √a aχγ5χ a 2 2 2 (α + β) i + 2 (α + αβ + β ) a χχ |2 2f {z } |8f {z } δ ρ

By integration by parts this is equivalent to a shift in the b1 coefﬁcient from the Kähler potential

27/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 27/4848 . . Main parameters. . . coupling to a coupling to H coupling to g, γ

Kähler potential .

. scalar ch . NLΣM Mixing b1 Kähler

. σSI σann . . kinetic

Goldstone coupling to a . Fermion. mχ; MSSM SSB at f

. . collider, astro . . Explicit δ Anomaly . can breaking Superpotential

28/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 28/4848 . . Parameter space scan 4 m2 ⟨ ⟩ ≈ b1 Tf χ ≈ Abundance: σv 4 1 pb 8π mχ f p-wave: b1 ≳ 1, all other parameters take natural values

Parameter Description Scan Range f Global symmetry breaking scale 500 GeV − 1.2 TeV mχ Goldstone fermion mass 50 − 150 GeV ma Goldstone boson mass 8 GeV – f /10 b1 χχa coupling [0, 2] can Anomaly coefﬁcient 0.06 ch Higgs coupling [−1, 1] δ Explicit breaking iaχγ5χ coupling 3/2

[ ] ( ) 1 2 1 v b1 µ 5 can e 5 L ⊃ (∂a) + χ∂χ/ ch h + √ χγ γ χ ∂µa + √ aGG + iδaχγ χ 2 2 f 2 2f f 2

29/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 29/4848 . . Main Interactions summary   χ a, s b1   × . a, s . s, a f χ a, s   χ a v ×  . . .  f 2 h h s h χ a   ( )   g 2 a g αS N   αS N 1   × a . × . 8πf 8πf Mλ g a g

ma < mχ ≪ ms

30/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 30/4848 . . Annihilation: Contours of ﬁxed Ω

2 Dominant contribution Ωh = 0.11 ¨ Kähler, anomaly, ¨U(1)¨ 3.5 χ g ma χ a . 3.0 mχ . 1 b χ a χ g 2.5 Subleading Coupling 2.0 10 % Mixing with Higgs χ h χ a

1.5 . . 40 % χ χ 70 % h h 1.0 60 80 100 120 140 Negligible t,u χχ → s → aa, χχ → hh . mχ [GeV] 31/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 31/4848 . . Direct Detection Relevant couplings from EWSB and anomaly: c v c 2 ic 2 L ⊃ h / − an − an 5 e χ∂χh 2 χχGG 2 χγ χGG 2f 2Mλf 2Mλf g χ N χ s a . h .

χ N χ g

Effective coupling to nucleons: L = GnucNNχχ, ( )   2 ∑ λ√N mχmN 4πcan mN  − (N) Gnuc = ch 2 2 + 1 fi 2 2 mhf 9αs Mλf i=u,d,s 32/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 32/4848 . . Direct Detection

Higgs exchange typically dominates by a factor of O(103). ( ) ( ) . 125 700 4 m µ λ 2 H ≈ · −45 2 2 GeV · GeV χ · χ · N σSI 2 10 cm ch mh f 100 GeV GeV 0.5 L 1 Compare this to the MSSM Higgs with = 2 cgχχh: c2g 2 λ2 µ2m2 MSSM ∼ N N ≈ 2 × −42 2 σSI 2 2 c 10 cm 2π mhv

2 2 Natural suppression: (mχv/f )

Is it enough to avoid current direct detection bounds?

33/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 33/4848 . . Parameter space scan & direct detection

-43 1 x 10 -44 5 x 10 Ruled out

-44 XENON ’11 ] x 2 1 10 -45 5 x 10 [cm XENON ’12 σ

-45 1 x 10 700 GeV 800 GeV 900 GeV -46 f < f < f < 5 x 10 < < < 500 700 800 900 < f < 1000 GeV

-46 1 x 10 100 150 . mχ [GeV]

34/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 34/4848 . . Indirect detection: p ﬂux vs. PAMELA 3 f = 700 GeV, QΨ = 2, δ = 2 , NΨ = 5 Dashed: Dotted: Solid: m 1

m χ m − a 0.01 m

= 0.5 50 = χ mχ χ 150 = 100 = s sr] 2

0.001 GeV, Einasto Max GeV, GeV,

-4 b 1 [GeV m 10 3 = b b 1 1 dK 1 = -5 1.5 =

ϕ/ 10

d Einasto Min

10-6 .1 .5 1 5 10 50 100 . Kinetic energy [GeV]

Using Einasto DM Halo proﬁle in 1012.4515, 1009.0224 35/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 35/4848 . . Indirect detection: Fermi-LAT Annihilation is p-wave, but this is suppressed at late times. Indirect detection from anomaly diagrams: χ γ χ g . .

χ γ χ g

γ-ray line search: 30 – 200 GeV • χχ → a → γγ via anomaly • O(10) smaller than bound even for extreme parameters Diffuse γ-ray spectrum: 20 – 100 GeV • χχ → a → gg → π0s • O(10) smaller than bound http://fermi.gsfc.nasa.gov/science/symposium/2011/program 36/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 36/4848 . . Goldstone fermions at the LHC

Collider production through gluons. N ∼ −46 2 −1 ISR monojets: sensitive to σSI 10 cm with 100 fb . The dim-7 anomaly operators are too small:

c 2 ic 2 L ⊃ − an − an 5 e 2 χχGG 2 χγ χGG 2Mλf 2Mλf

gg → a∗ → χχ may be within 5σ reach with 100 fb−1 1005.1286, 1005.3797, 1008.1783, 1103.0240, 1108.1196, 1109.4398

37/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 37/4848 . . Goldstone fermions at the LHC

700 1109.4398 Tsai: Kopp, Harnik, Fox, ATLAS 7 TeV, 1/fb 90 C.L. 600

αs χχGG

GeV 500

expected scale 400

Cutoff 300

200 veryHighPt

0.1 1 10 100 1000 WIMP mass mΧ GeV . 38/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 38/4848 . . The γγ games

Experimental progress, model-building directions:

1. mh = 125 GeV, possible enhancement in h → γγ? 2. FERMI line at 130 GeV, possibly χχ → γγ?

Can we realize this in Goldstone Fermion DM? Maybe. Work in progress with B. Bellazzini, M. Cliche

1. Goldstone boson decays modify Higgs branching ratios 2. Anomaly coupling, SUSY framework to control spectrum for narrow box-shaped γ-ray spectrum.

39/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 39/4848 . . Non-standard Higgs decays

Hard to completely bury the Higgs. LEP: Br(SM)≳ 20% ⇒ mh ≳ 110 GeV

f = 500 GeV, ma = 45 GeV, mχ = 100 GeV, ch = 2 1.0

0.8 WW ∗ aa 0.6

0.4 bb ∗ 0.2 ZZ Higgs branching ratio

0.0 100 110 120 130 140 150 160

. Higgs mass mh [GeV]

40/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 40/4848 . . Non-standard Higgs decays For larger f , can suppress h → aa

f = 700 GeV, ma = 45 GeV, mχ = 100 GeV, ch = 2 1.0

0.8 WW ∗

0.6 bb

0.4 ZZ ∗ 0.2 Higgs branching ratio aa

0.0 100 110 120 130 140 150 160

. Higgs mass mh [GeV]

41/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 41/4848 . . Non-standard Higgs decays

Partially buried & invisible: Suppressed SM channels, MET, Γtot < 1

f = 400 GeV, ma = mχ = 60 GeV, ch = 2 1.0

0.8 WW ∗

0.6 bb

0.4 aa χχ

0.2 ∗ Higgs branching ratio ZZ

0.0 100 110 120 130 140 150 160

. Higgs mass mh [GeV]

42/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 42/4848 . . The 130 GeV Weniger Line 1204.2797

43/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 43/4848 . .

Figure 4. Upper sub-panels: the measured events with statistical errors are plotted in black.The horizontal bars show the best-fit models with (red ) and without DM (green), the blue dotted line indicates the corresponding line flux component alone. In the lower sub-panel we show residuals after subtracting the model with line contribution. Note that we rebinned the data to fewer bins after performing the fits in order to produce the plots and calculatethep-value and the reduced χ2 χ2/dof. The counts are listed in Tabs. 1, 2 and 3. r ≡

–10– 4 2 29 3 typically) a factor of e /(8π ) lower, i.e. σv (γγ) 10− cm /s. So we expect robust tension between continuum gamma-ray〈 bounds〉 ∼ and annihilation through loops of SM matter.

3. Subdominant wino DM? To illustrate the previous point: computing for winos in the MSSM with Micromegas [?], we ﬁnd at 128 GeV:

˜ 0 ˜ 0 + 24 3 σv (W W W W −) 3 10− cm /s (10) 〈 〉 ˜ 0→˜ 0 ≈ × 27 3 σv (W W γZ) 9 10− cm /s (11) 〈 〉 ˜ 0 ˜ 0 → ≈ × 27 3 σv (W W γγ) 2 10− cm /s (12) 〈 〉 → ≈ × If we believe Hooper’s results, then even if winos are only about 1/10 of all the dark matter there is some tension with the galactic center, and the corresponding photon lines 28 3 would be at the 10− cm /s level, too small to explain the observation. The suggestion of Acharya et al. [?] is then ruled out, in an especially decisive way if Hooper’s bound is correct.

4. Direct detection: Any dark matter that annihilates to γγ or γZ can in principle show up in direct-detection experiments through either a loop process (exchanging two photons or a photon and a Z with the nucleus) or the 2 3 process χN χNγ. However, these will typically be small enough that there is→ no limit (in fact,→ they may be small enough that the neutrino background swamps any possible detection, possibly with the exception of directional direct detection). Estimates for a particular model appear in [?], and are several orders of magnitude below the current limits. I expect that any model consistent with Hooper’s tree-level continuum gamma-ray con- straints will also be safe, or at worst borderline, from direct detection through Higgs exchange. Can we make this statement more precise? This is interesting even inde- pendent of the gamma-ray line, since it suggests that Fermi-LAT is doing roughly as well as Xenon at constraining models. .

5.ModelNeutrinos: buildingAnnihilation for to Z bosonsthe Weniger in the sun lead Line to a ﬂux of neutrinos that may be detectableProblem: onphoton Earth. What continuum are theCohen, numbers? Lisanti,Edit: Slatyer, I think Wacker it’s hopeless—but(1207.0800) still should maybe write down some numbers.

⇒

TunedFigure 3:pseudoscalarIllustrating the processes role of chargeFan particles & Reece in arguments (1209.1097) about the γ-ray line.

χ γ DM πh . 5 0 h π0 DM χ γ

Figure 4: Topology leading to a box-shaped gamma ray44 feature/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 44/4848 . γ, Z

mp mq 1/fa ∝ − 1/fa π0 × η0 × a γ, Z

Figure 5: Decay of π0

References

[1] R. Essig, “Direct Detection of Non-Chiral Dark Matter,” Phys. Rev. D 78, 015004 (2008) arXiv:0710.1668 [hep-ph].

[2] M. Farina, M. Kadastik, D. Pappadopulo, J. Pata, M. Raidal and A. Strumia, “Implica- tions of XENON100 and LHC results for Dark Matter models,” Nucl. Phys. B 853, 607 (2011) arXiv:1104.3572 [hep-ph].

[3] C. P.Burgess, M. Pospelov and T. ter Veldhuis, “The Minimal model of nonbaryonic dark matter: A Singlet scalar,” Nucl. Phys. B 619, 709 (2001) hep-ph/0011335.

[4] J. Giedt, A. W. Thomas and R. D. Young, “Dark matter, the CMSSM and lattice QCD,” Phys. Rev. Lett. 103, 201802 (2009) arXiv:0907.4177 [hep-ph].

[5] M. Ackermann et al. [Fermi-LAT Collaboration], “Constraining Dark Matter Models from a Combined Analysis of Milky Way Satellites with the Fermi Large Area Tele- scope,” Phys. Rev. Lett. 107, 241302 (2011) arXiv:1108.3546 [astro-ph.HE].

[6] E. Aprile et al. [XENON100 Collaboration], “Dark Matter Results from 100 Live Days of XENON100 Data,” Phys. Rev. Lett. 107, 131302 (2011) arXiv:1104.2549 [astro- ph.CO].

[7] E. Aprile on behalf of the XENON100 Collaboration, “The XENON1T Dark Matter Search Experiment,” arXiv:1206.6288 [astro-ph.IM].

6 . Sommerfeld enhancement for singular potentials

O(few) sufﬁcient to open up parameter space. Larger enhancement may be used for γγ signal

Pseudoscalar exchange ⇒ 1/r 3 potential, need to regulate and renormalize effective non-relativistic theory.

Need to clarify UV sensitivity, viability of matching. 0810.0713, 0902.0688, 0907.0235

45/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 45/4848 . . Pseudoscalar Yukawa enhancement

Preliminary Sommerfeld Enhancement

. Singular potential cutoff scale [GeV−1]

46/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 46/4848 . . Other applications: Stealth SUSY limit

5 8 10 GeV ≲ f < 10 GeV mχ → 0

Fan, Reece, Ruderman: 1201.4875

47/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 47/4848 . . Conclusions . Executive summary: Goldstone Fermion dark matter . • SSB: global U(1) ⇒ Goldstone boson a and fermion χ • χ is LSP and DM, a can modify Higgs branching ratios .

Simple extension of MSSM with natural WIMP dark matter • Kähler χχa interaction controls abundance • Higgs mixing, anomaly controls direct detection

Further directions: • p-wave Sommerfeld enhancement • Non-abelian generalization • h, χχ → γγ hints

48/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 48/4848 . .

Extra Slides

48/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 48/4848 . . Examples of Linear Models Simplest example: ( ) W = yS NN − µ2 + Nϕϕ + SH H + W | {z } | {zu d} | explicit{z } ¨ anomaly mixing explicit¨U(1)

Example with |b1| ≥ 1: λe W = λXYZ − µ2Z + Y 2N − µeNN 2 − − qZ = 0, qN = qN = 2qY = 2qX . Goldstone multiplet: ∑ ( ) qi fi ψi qY − A = = YfY XfX + 2NFN i f f −f 2 + f 2 + 8f 2 b = X Y N 1 f 2 + f 2 + 4f 2 X Y N 48/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 48/4848 . . Direct Detection Relevant couplings from EWSB and anomaly: c v c 2 ic 2 L ⊃ h / − an − an 5 e χ∂χh 2 χχGG 2 χγ χGG 2f 2Mλf 2Mλf g χ N χ a . h .

χ N χ g

Effective coupling to nucleons: L = GnucNNχχ, ( )   2 ∑ λ√N mχmN 4πcan mN  − (N) Gnuc = ch 2 2 + 1 fi 2 2 mhf 9αs Mλf i=u,d,s 48/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 48/4848 . . Direct Detection Some details: ( )   2 ∑ λ√N mχmN 4πcan mN  − (N) GχN = ch 2 2 + 1 fi 2 2 mhf 9αs Mλf i=u,d,s

−1 −1 −1 For reduced mass µχ = (mχ + mN ) ,

4µ2 σHiggs = χ [G Z + G (A − Z)] SI A2π χp χn

( ) ( ) ( ) ( ) ( ) 115 4 700 4 m 2 µ 2 λ 2 H ≈ · −45 2 2 GeV GeV χ χ N σSI 3 10 cm ch mh f 100 GeV 1 GeV 0.5 ( ) ( ) ( ) 2 4 4 ( )4 ( )2 glue ≈ · −48 2 700 GeV 700 GeV NΨ qΨ µ σSI 2 10 cm Mλ f 5 2 1 GeV

using can = αs qΨNΨ/8π 48/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 48/4848 . . 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 → GGe is s-wave while χχ → aa is p-wave.

48/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 48/4848 . . Nuclear matrix element and matching

The nucleon matrix element at vanishing momentum transfer:

∑ β(α) ⟨ µ⟩ ⟨ | a a | ⟩ MN = Θµ = N mi qi qi + GαβGαβ N i=u,d,s 4α

from: Shifman, Vainshtein, Zakharov. Phys. Lett 78B (1978)

β = −9α2/2π + ··· contains only the light quark contribution, MN is the nucleon mass. The GG matches onto the nucleon operator NN. ∑ (N) ⟨ | | ⟩ (N) − (N) MN fi=u,d,s = N mi qi qi N fg = 1 fi i=u,d,s

48/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 48/4848 . . Nuclear matrix element and matching

  β(α) ∑ a a −→  − (N) GαβGαβ MN 1 fi NN 4α i=u,d,s

(N) ≪ (N) ≈ Where fu,d fs 0.25. For a detailed discussion, see 0801.3656 and 0803.2360.

48/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 48/4848 . . 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

48/ Flip Tanedo [email protected] Goldstone Fermion Dark Matter 48/4848 .