Dark Matter throughthe Axion PortalJesse Thaler (UC Berkeley)

arXiv:0810.5397with Yasunori Nomura

Recent progress with Jeremy Mardon and Daniel Stolarski

New source of galactic electrons/positrons!

[Allahverdi, Arkani-Hamed, Baek, Bai, Barger, Bergstrom, Bertone, Bi, Bringmann, Brun, Chen, Cholis, Chun, Cirelli, Delahaye, Delaunay, Dobler, Donato, Dutta, Edsjo, Fairbairn, Feldman, Finkbeiner, Fox, Goodenough,

Grajek, Hamaguchi, Han, Harnik, Hisano, Hooper, Huh, Ibe, Ishiwata, Kadastik, Kamionkowski, Kane, Kawasaki, Keung, Kim, Ko, Kohri, Kribs, Kyae, Lattanzi, Lineros, Liu, March-Russell, Marfatia, Matsumoto, Maurin, Moroi, Murayama,

Nakayama, Nath, Nelson, Nojiri, Nomura, Park, Perez, Phalen, Pierce, Poppitz, Pospelov, Profumo, Raidal, Richardson-McDaniel, Ritz, Salati, Santoso,

Shaughnessy, Silk, Simet, Slatyer, Spitzer, Stebbins, Strumia, Takahashi, Taoso, JT, Torii, Watson, Weiner, West, Yanagida, Yin, Yuan, Zhang, Zhu, Zupan, Zurek, ...]

Paradigm shift in astrophysics?in dark matter physics?

Astrophysical source?

Dark matter decay?

Dark matter annihilation?

SNR/Pulsars are e+e– machines

τ ~ 1026 sec ~ (MGUT)4/TeV5

<σv> ~ 103 x WIMP thermal freezeout

[Arvanitaki, Bi, Chen, Dimopoulos, Dubovsky, Graham, Hamaguchi, Harnik, Hisano, Ibarra, Ishiwata, Kawasaki, Kohri, Liu, Matsumoto,

Moroi, Nakayama, Nardi, Nojiri, Pospelov, Rajendran, Sannino, Shirai, Strumia, Takahashi, Torii, Tran, Trott, Yanagida, Yin, Yuan, Zhang, Zhu, ...]

[Blasi, Hall, Hooper, Kistler, Pohl, Profumo, Serpico, Stanev, Yuksel, ...]

Confirms PPB-BETS anomaly

ATIC

Confirms HEAT/AMS anomalyEnergy (GeV)

0.1 1 10 100

))

-(e!

)+

+(e!

) / (

+(e!

Po

sit

ron

fra

cti

on

0.01

0.02

0.1

0.2

0.3

0.4

Muller & Tang 1987

MASS 1989

TS93

HEAT94+95

CAPRICE94

AMS98

HEAT00

Clem & Evenson 2007

PAMELA

FIG. 3: PAMELA positron fraction with other experimental data. The positron fraction

measured by the PAMELA experiment compared with other recent experimental data[24, 29, 30,

31, 32, 33, 34, 35]. One standard deviation error bars are shown. If not visible, they lie inside the

data points.

a shower tail catcher scintillator (S4) and a neutron detector. The ToF system provides

a fast signal for triggering the data acquisition and measures the time-of-flight and ioniza-

tion energy losses (dE/dx) of traversing particles. It also allows down-going particles to

be reliably identified. Multiple tracks, produced in interactions above the spectrometer,

were rejected by requiring that only one strip of the top ToF scintillator (S1 and S2) layers

registered an energy deposition (’hit’). Similarly no hits were permitted in either top scintil-

lators of the AC system (CARD and CAT). The central part of the PAMELA apparatus is

12

PAMELA

Physics of EWSB

Physics of Dark MatterWhat is

connection?

Annihilation rate is 1000x larger than thermal freezeout!

DM Annihilation Interpretation?{

Energy (GeV)

0.1 1 10 100

))

-(e!

)+

+(e!

) / (

+(e!

Po

sit

ron

fra

cti

on

0.01

0.02

0.1

0.2

0.3

0.4

Muller & Tang 1987

MASS 1989

TS93

HEAT94+95

CAPRICE94

AMS98

HEAT00

Clem & Evenson 2007

PAMELA

FIG. 3: PAMELA positron fraction with other experimental data. The positron fraction

measured by the PAMELA experiment compared with other recent experimental data[24, 29, 30,

31, 32, 33, 34, 35]. One standard deviation error bars are shown. If not visible, they lie inside the

data points.

a shower tail catcher scintillator (S4) and a neutron detector. The ToF system provides

a fast signal for triggering the data acquisition and measures the time-of-flight and ioniza-

tion energy losses (dE/dx) of traversing particles. It also allows down-going particles to

be reliably identified. Multiple tracks, produced in interactions above the spectrometer,

were rejected by requiring that only one strip of the top ToF scintillator (S1 and S2) layers

registered an energy deposition (’hit’). Similarly no hits were permitted in either top scintil-

lators of the AC system (CARD and CAT). The central part of the PAMELA apparatus is

12

Mass is 10x larger than standard

SUSY neutralino!

There are certainly DM models that can explain PAMELA/ATIC

Lepton-rich annihilation!

Are there models as compelling as the standard SUSY neutralino?

W = WYukawa + λSHuHd + κS3

Novel connection between EWSB and DM!

Independent motivation: PQ limit of NMSSM (has light “axion”)

The Axion Portal

Novel collider signatures!Rare Υ decays to γ μ+ μ– at BaBar/BelleModified Higgs physics at Tevatron/LHC

Muon-rich SUSY cascade decays (no, not CDF anomaly)

As well as interesting constraints from LEP,direct detection, gamma ray and neutrino telescopes, ...

Simple construction to explain PAMELA/ATIC as DM annihilationCommon origin for Higgsino and DM mass!

+ ξSΨΨc

A Revised TeV-Scale Paradigm?

Introducing the Axion Portal

Connecting DM and EWSB

Galactic Signals and Constraints

The Axion Portal Outline

A Revised TeV-Scale Paradigm?

Introducing the Axion PortalDM and Spontaneous Symmetry Breaking

Connecting DM and EWSB

Galactic Signals and Constraints

Basic Setup

Model: Fermion mass from spontaneous symmetry breaking

Goal: Heavy dark matter with enhanced halo annihilationand large annihilation rate to leptons

scalar s: enhanced halo annihilation(non-perturbative effects for ms << fa)

[Nomura, JT]

S =(

fa +s√2

)exp

[i√2

a

fa

]L = −ξSψψc

“axion” a: annihilation to leptons(S hu hd coupling make a like a heavy DFSZ axion)

mDM = ξfa

(hierarchy problem?)

mDM, fa ∼ TeV

ms ∼ 1–10 GeV

ma >∼ 2m!

Thermal Relic Abundance

〈σv〉 ∼ O(v2)

〈σv〉 ∼ O(v2)

〈σv〉 ∼ O(v0)〈σv〉 =

m2DM

128πf4a

+O(v2)

! 3× 10−26cm3/sec(standard WIMP thermal relic)

0 500 1000 1500 2000 2500 3000mDM!GeV"0

500

1000

1500

2000fa !GeV"s

ψ

ψ̄

s

a

ψ

ψ̄

a

ψ̄

ψ

s

a

S =(

fa +s√2

)exp

[i√2

a

fa

]L = −ξSψψc

(micrOMEGAs result)

Scalar s mediates attractive force between DMNon-perturbative annihilation enhancements at vhalo ~ 10–3

(Need to explain why s is so light)

Halo Annihilation

Dominant s Decay

s

a

a

L =1√2fa

s(∂µa)2

Axion Portal to SM

a

!+

!−

Γa→!! = c2!

ma

16π

m2!

f2a

ψ

ψ̄

s s s · · ·s

a

a

a

!+

!−

!+

!−

!+

!−

[Hisano, Matsumoto, Nojiri, Saito; Cirelli, Kadastik, Raidal, Strumia; Arkani-Hamed, Finkbeiner, Slatyer, Weiner;

March-Russell, Hooper, West; Pospelov, Ritz; ...]

vhalo < αξ < vfreezeout

αξ ≡ξ2

4π

(For enhancement today and not at freezeout)

L = −ξSψψc

B ! αξmDM

msto

αξ

v2halo

ms

mDM

Sommerfeld effect or WIMPonium formation

(All these constraints can be avoided for leptophilic axion)

Low Energy Axion ConstraintsAxion a is not the QCD axion, since we take axion mass asfree parameter. For PQ charges, like a heavy DFSZ axion.

(S hu hd coupling gives standard model fields U(1)PQ charges)

2me

ma

2mµ 2mτ 2mb

K → π a Decays

mK −mπ

Too many galactic

antiprotons

2mp

CERN Beam Dump excludes fa < 10 TeV

Too many galacticγ from τ decays

Too many galactic γ in π+π–π0

mρ + mπ

360 MeV < ma < 800 MeV

}

Υ(nS)

γ

a

µ+

µ−

Br(Υ→ aγ) ∼ 3× 10−6 sin4 β

(TeVfa

)2

CLEO: < few x 10–6 from 20M Υ(1S)

Belle: ~50M Υ(3S) on tape! BaBar: ~110M Υ(3S) & ~50M Υ(2S) on tape!

n = 1, 2, 3

The Axion Portal

ψ

ψ̄

s s s · · ·s

a

a

a

!+

!−

!+

!−

!+

!−

mDM, fa ∼ TeV

ms ∼ 1–10 GeV

ma >∼ 2m!

S =(

fa +s√2

)exp

[i√2

a

fa

]L = −ξSψψc

DM mass from SSB s: enhanced halo annihilation

a: annihilation to leptons(U(1)PQ: 360 MeV < ma < 800 MeV, Rare Υ Decays)

Υ(nS)

γ

a

µ+

µ−

0 500 1000 1500 2000 2500 3000mDM!GeV"0

500

1000

1500

2000fa !GeV"

Annihilation in halo...

...and at freezeout

A Revised TeV-Scale Paradigm?

Introducing the Axion Portal

Connecting DM and EWSBA Supersymmetric Axion Portal

Galactic Signals and Constraints

PQ-symmetric NMSSM(Solves μ problem with spontaneous U(1)PQ violation)

SUSY Axion Portal:Just add DM

Higgsino and DM masses have common origin!

For light scalar s, need small λ and small SUSY breaking for Ψ/Ψc. Axion a mass from explicit U(1)PQ violation (κ term, say).

Adding SupersymmetryFocus on a heavy Peccei-Quinn axion

W = λSHuHd + ξSΨΨc+ κS3SUSY extension:

[Ciafaloni, Pomarol; Hall, Watari] [Nomura, JT]

(Assuming DM is a thermal relic, no free parameters beyond PQ-SUSY!)

L = −AλShuhd − ξSψψc2 –1 –1 2 –1 –1

4 free parameters! Assuming DM thermal relic, same as PQ-SUSY

PQ Limit of NMSSM (with DM)

{mDM, µH , tanβ, ma}

W = λSHuHd + ξSΨΨc

Lsoft = −λAλShuhd + m21|hu|2 + m2

2|hd|2

Spectrum controlled by two O(10-1) parameters

ε ≡ vEW

faλ ≡ µH

fa

All else derived from thermal relic or EWSB

Aλ =2µH

sin 2βvEW = vEW(m2

1, m22, Aλ)

mDM = ξfaµH = λfa tanβ = tanβ(m21, m

22, Aλ)

µH

ms̃

ms

ma

mDM, fa

vEW

λfa

εfa

λεfa

λε2fa

TeV

100 GeV

10 GeV

1 GeV

Constraints and Subtleties

Three states below Z: s, a, s̃. Mixing angles with Higgs fields O(ε), and LEP bounds safe on direct production for fa at TeV or higher. Chargino bound also satisfied.

Must ensure that s̃ does not overclose the universe. Assume s̃ decays to 1-10 eV gravitino, and it is cosmologically ok. Actual DM stabilized by additional Z2.

To have light scalar s, scalar/fermion DM must be nearly degenerate. Coannihilation shifts preferred values of mDM/fa.

Scalar s can give a large DM-nucleon force. Mild fine-tuning necessary to get Sommerfeld enhancement without contradicting CDMS/XENON bounds.

mZ –––– 91 GeV

mgravitino –––– 1-10 eV

µH

ms̃

ms

ma

mDM, fa

vEW

λfa

εfa

λεfa

λε2fa

TeV

100 GeV

10 GeV

1 GeV

––––

––––

Higgs decays to muons via axion portal

Lots of muons from a decays.

Collider Phenomenology

h0

a

a

µ+

µ−

µ+

µ−

(Also, h0 → 2s → 4a→8μ)

Since we are in small λ limit, not expected to be dominant mode.

Br(h0 → aa)Br(h0 → bb̄)

∼ λ4

λ2b

Extended SUSY Cascades with s/a Fields

“χ0”

“χ0”

+ standard SUSY final states

a

a

s̃

s

a

s̃

s̃ is typically stable on collider time scales,   and gives “massless” missing energy.

Would-be lightest neutralino decays to s̃.

Because of mixing, χ0 can decay to Higgs or Z, too.

Lots of muons from s → aa decays.

µ+

µ−

µ+

µ−

µ+

µ−

!ET

!ET

A SUSY Axion Portal

Extend PQ-SUSY with DM

µH

ms̃

ms

ma

mDM, fa

vEW

λfa

εfa

λεfa

λε2fa

TeV

100 GeV

10 GeV

1 GeV

{mDM, µH , tanβ, ma}

W = λSHuHd + ξSΨΨc

“χ0”

“χ0”

+ standard SUSY final states

a

a

s̃

s

a

s̃µ+

µ−

µ+

µ−

µ+

µ−!ET

h0

a

a

µ+

µ−

µ+

µ−

Same number of free parameters

Muon-rich ColliderSignals

A Revised TeV-Scale Paradigm?

Introducing the Axion Portal

Connecting DM and EWSB

Galactic Signals and ConstraintsFrom Positrons to Gamma Rays

Axion portal is in broader class of cascade annihilation models

Generic Axion Portal is like a One-and-a-Half

Step Cascade(ΨΨ→sa, s→aa, a→ℓℓ)

For muon decays, electron spectrum looks

as if two extra steps

U(1)PQ Axion Portal is effectively a Three-and-a-Half

Step Cascade(ΨΨ→sa, s→aa, a→μμ, μ→eνν)

[Mardon, Nomura, Stolarski, JT]

Cascade Annihilations

[see also Cholis, Dobler, Finkbeiner, Goodenough,

Weiner; Bergstrom, Bertone, Bringmann, Edsjo, Taoso; ...]

Direct

One-Step

Two-Step

(Muon Decay)

Folded with Galactic Propagation

Electrons diffuse in (turbulent) galactic magnetic fields (~μG)...

...and lose energy from inverse Compton scattering, synchrotron.

From Injection to Earthμ→e injection

0.0 0.2 0.4 0.6 0.8 1.0x

0.01

0.1

1

10

100dN!dx

DirectOne-StepTwo-Step

e injection

0.0 0.2 0.4 0.6 0.8 1.0x

0.01

0.1

1

10

100dN!dx

Direct

One-Step

Two-Step

x! ≡E!

mDM

dN!

dxn+1∼

∫ 1

xn+1

dxn

xn

dN!

dxn

[Moskalenko, Strong; Baltz, Edsjo; Delahaye, Lineros, Donato, Fornengo, Salati; ...]

dE

dt∼ E2

TeV Myr

Hard electrons/positrons come from “local” region (< kpc, compare galactic center at 8 kpc)

K ∼ (100 pc)2

Myr

(for hierarchical scalar decays)

e+e– Cascades μ+μ– Cascades

Any of these cascades give reasonable fit to PAMELA/ATIC

Best Fits for Cascade Models

0.01

0.1

1 10 100 1000 10000

posit

ron

fract

ion

E [GeV]

0.01

0.1

1 10 100 1000 10000

posit

ron

fract

ion

E [GeV]

0.01

0.1

1 10 100 1000 10000

posit

ron

fract

ion

E [GeV]

0.01

0.1

1 10 100 1000 10000

posit

ron

fract

ion

E [GeV]

0.01

0.1

1 10 100 1000 10000

E3(e

! +e+)

[GeV

2 cm!2s!1 sr!1 ]

E [GeV]

0.01

0.1

1 10 100 1000 10000

E3(e

! +e+)

[GeV

2 cm!2s!1 sr!1 ]

E [GeV]

0.01

0.1

1 10 100 1000 10000

E3(e

! +e+)

[GeV

2 cm!2s!1 sr!1 ]

E [GeV]

0.01

0.1

1 10 100 1000 10000

E3(e

! +e+)

[GeV

2 cm!2s!1 sr!1 ]

E [GeV]

0.01

0.1

1 10 100 1000 10000

E3(e

! +e+)

[GeV

2 cm!2s!1 sr!1 ]

E [GeV]

0.01

0.1

1 10 100 1000 10000

E3(e

! +e+)

[GeV

2 cm!2s!1 sr!1 ]

E [GeV]

0.01

0.1

1 10 100 1000 10000

E3(e

! +e+)

[GeV

2 cm!2s!1 sr!1 ]

E [GeV]

0.01

0.1

1 10 100 1000 10000

E3(e

! +e+)

[GeV

2 cm!2s!1 sr!1 ]

E [GeV]

0.01

0.1

1 10 100 1000 10000

posit

ron

fract

ion

E [GeV]

0.01

0.1

1 10 100 1000 10000

posit

ron

fract

ion

E [GeV]

0.01

0.1

1 10 100 1000 10000

posit

ron

fract

ion

E [GeV]

0.01

0.1

1 10 100 1000 10000

posit

ron

fract

ion

E [GeV]

PAM

ELA

e+ F

ract

ion

ATIC

e+ +

e–

Spec

trum

(Approximate HESS electron spectrum also shown)

PRELIMINARY

PRELIMINARY

PRELIMINARY

PRELIMINARY

Cascade annihilation give softer photons & fewer photons

Gamma Rays from FSR

dNγ

dx∼ αEM

π

1x

logQ

mµ

Photon Spectrum in Collinear Limit:

Direct: Q = mDM

Cascades: Q = mportal & Softer

!!

102 103 104102

103

104

mDM

2 step to Μ!Μ# !Einasto"G.C. mΦ%0.6GeVG.R.

G.C. mΦ%1GeVG.R.

Cascade annihilation weaken FSR gamma ray bounds!

!!

102 103 104102

103

104Direct to Μ!Μ# !Einasto"

G.C.G.R.

!!

102 103 104102

103

1041 step to Μ!Μ# !Einasto"

G.C. mΦ%0.6GeVG.R.

G.C. mΦ%1GeVG.R.

PRELIMINARYPRELIMINARYPRELIMINARY

(Inverse Compton scattering affects these bounds, but dependent on galactic starlight maps.)

Direct to μ 1-Step to μ 2-Step to μ

HESS Galactic Center (solid): ~10 pc HESS Galactic Ridge (dashed): ~100 pcEγ > 250 GeV. Einasto halo profile. Ovals are best fit regions to PAMELA/ATIC.

mDMmDMmDM

<σv

>/<σv

>th

erm

al

<σv

>/<σv

>th

erm

al

<σv

>/<σv

>th

erm

al

Neutrinos from Galactic Center in Muon Cascades

Direct Detection ConstraintsScalar s: Couples to strange quark through mixing with

down-type Higgs. Mediates spin-independent DM-nucleon force. CDMS/XENON bounds very sensitive to mDM, ms, and mixing angle.

Axion a: Only contributes spin-dependent DM-nucleon force,but not at zero velocity. What are the bounds? How does one properly calculate this? (violates micrOMEGAs assumptions)

Under Investigation...

[see also Liu, Yin, Zhu; Hisano, Kawasaki, Kohri, Nakayama; ...]

For TeV neutrinos, standard assumptions about neutrino-nucleon scattering cross section and muon energy loss start to break down.

Muon-type neutrinos hit rock, create upward-going muon flux. Important constraints from Super-K

A question for the experts

WMAP Haze vs. 408 MHz Radio?

But 408 MHz sky map used to extract Haze!

Q: Is WMAP Haze from DM annihilationconsistent with 408 MHz observations?

WMAP Haze: apparent excess of synchrotron emissions from galactic center (23-61 GHz).

[Finkbeiner; Hooper, Dobler, Finkbeiner]

In light of PAMELA/ATIC, DM annihilation uniquely positioned to explain haze[Zhang, Bi, Liu, Liu, Yin, Qiang Yuan, Zhu; ...]

Recent claims that DM annihilation givestoo much synchrotron at 408 MHz

[Bertone, Cirelli, Strumia, Taoso; Bergstrom, Bertone, Bringmann, Edsjo, Taoso; see also Borriello, Cuoco, Miele]

Foregrounds meeting, July 16, 2008

The Axion Portal Enhanced halo annihilation...

ψ

ψ̄

s s s · · ·s

a

a

a

!+

!−

!+

!−

!+

!−

...with copious lepton production

...that (re)connects DM and EWSB

W = λSHuHd + ξSΨΨc

Straightforward idea...L = −ξSψψc 〈S〉 = fa

Muon-Rich Collider Signals

Υ(nS)

γ

a

µ+

µ−

“χ0”

“χ0”

+ standard SUSY final states

a

a

s̃

s

a

s̃µ+

µ−

µ+

µ−

µ+

µ−!ET

h0

a

a

µ+

µ−

µ+

µ−

Is this the right explanationfor PAMELA/ATIC?

0.01

0.1

1 10 100 1000 10000

E3(e

! +e+)

[GeV

2 cm!2s!1 sr!1 ]

E [GeV]

0.01

0.1

1 10 100 1000 10000

E3(e

! +e+)

[GeV

2 cm!2s!1 sr!1 ]

E [GeV]

0.01

0.1

1 10 100 1000 10000

E3(e

! +e+)

[GeV

2 cm!2s!1 sr!1 ]

E [GeV]

0.01

0.1

1 10 100 1000 10000

E3(e

! +e+)

[GeV

2 cm!2s!1 sr!1 ]

E [GeV]

PRELIMINARY