Minimal Dark Matter,research.ipmu.jp/seminar/sysimg/seminar/1628.pdfKolb,Turner, The Early Universe, 1995 Ω X ≈ 6 10−27cm3s−1 σ ann v Boltzmann eq. in the Early Universe: Weak

!"#$%

Marco Cirelli(CNRS LPTHE Jussieu Paris)

NewDark

5 February 2016IPMU, Kashiwa, Japan

Minimal Dark Matter,reloaded

Based on: Cirelli, Fornengo, Strumia ‘Minimal Dark Matter’, NPB 2006 +…Cirelli, Sala, Taoso, JHEP 2014Cirelli, Hambye, Panci, Sala, Taoso, JCAP 2015

IntroductionIntroduction

IntroductionIntroductionDM exists

IntroductionDM exists

galactic rotation curvesweak lensing (e.g. in clusters)

‘precision cosmology’ (CMB, LSS)

IntroductionDM exists

galactic rotation curvesweak lensing (e.g. in clusters)

‘precision cosmology’ (CMB, LSS)

But: what is it?

weakly int., massive, neutral, stableMost likely a

relic particle.

weakly int., massive, neutral, stableMost likely a

has the correct relic abundance today!

Kolb

,Tur

ner,

The

Early

Univer

se, 1

995

ΩX ≈6 10−27cm3s−1

⟨σannv⟩

Boltzmann eq. in the Early Universe:

Weak cross section:

⟨σannv⟩ ≈α2

w

M2≈

α2w

21TeV

ΩX ∼ O(few 0.1)⇒

Most likely a


Kolb

,Tur

ner,

The

Early

Univer

se, 1

995

ΩX ≈6 10−27cm3s−1

⟨σannv⟩


Weak cross section:

⟨σannv⟩ ≈α2

w

M2≈

α2w

21TeV

ΩX ∼ O(few 0.1)⇒

weakly int., massive, neutral, stable(or we would

have seen it...)

Most likely a


Kolb

,Tur

ner,

The

Early

Univer

se, 1

995

ΩX ≈6 10−27cm3s−1

⟨σannv⟩


Weak cross section:

⟨σannv⟩ ≈α2

w

M2≈

α2w

21TeV

(or we would have seen it...)

at least on cosmological time scales, i.e.

ΩX ∼ O(few 0.1)⇒

weakly int., massive, neutral, stable

τ > tuniverse

Most likely a


Popular candidates:

Theories beyond the SM have ambitious goals (hierarchy prob, EWSB, unification).As a byproduct, they can provide DM candidates at the EW scale.

...BUT:

SuperSymmetric LSP, Extra dimensional LKP...

Most likely a


Popular candidates:


...BUT: (i) these theories are by now very uncomfortably fine tuned (the LHC did not find New Physics, at least yet)


Most likely a


Popular candidates:

...BUT:

(ii) these theories have many parameters, DM phenomenology is unclear (scatter plots)


(i) these theories are by now very uncomfortably fine tuned (the LHC did not find New Physics, at least yet)


Most likely a


Popular candidates:

...BUT:

(ii) these theories have many parameters, DM phenomenology is unclear (scatter plots)

(iii) DM stability is imposed by hand (R-parity, T-parity, KK parity)


(i) these theories are by now very uncomfortably fine tuned (the LHC did not find New Physics, at least yet)


Minimalistic approach

Minimalistic approachOn top of the SM, add only one extra multiplet X

and systematically search for the ideal DM candidate...

=

⎛

⎜

⎝

X1

X2...

⎞

⎟

⎠

L = LSM + X̄ (iD/ + M)X if is a fermionX

if is a scalarXL = LSM + |DµX|2 − M2|X |2

Minimalistic approachOn top of the SM, add only one extra multiplet X

and systematically search for the ideal DM candidate...

=

⎛

⎜

⎝

X1

X2...

⎞

⎟

⎠

L = LSM + X̄ (iD/ + M)X if is a fermion

if is a scalar

X

X

gauge interactions the only parameter, and will be fixed by .ΩDM

(other terms in the scalar potential)

(one loop mass splitting)

L = LSM + |DµX|2 − M2|X |2

X

X

W±

, Z, γ

[g2, g1, Y ]

weakly int., massive, neutral, stableThe ideal DM candidate is

weakly int., massive, neutral, stableSU(2)L U(1)Y

2

4

5

7

spin

3

The ideal DM candidate is

6( is similar to )4

α−1

2 (E′) = α−12 (M) −

b2(n)

2πln

E′

M

n ≤ 5

n ≤ 7

these are all possible choices:for fermionsfor scalars

to avoid explosion in the running coupling

X =

⎛

⎜

⎜

⎜

⎝

X1

X2...

Xn

⎞

⎟

⎟

⎟

⎠

(actually, including 2-loops, for real (complex) scalars) n 6 (n 4)

Di Luzio, Nardecchia et al., 1504.00359


2

4

5

7

spin

3


1/2

3/2

0

1

1/2

0

1

2

0

Q = T3 + Y

e.g. for : T3 =⎛

⎝

+ 12

−

1

2

⎞

⎠n = 2 ⇒ |Y | =1

2

≡ 0

Each multiplet contains a neutral component with a proper assignment of the hypercharge, according to

e.g. for :n = 3 T3 =

⎛

⎝

+10−1

⎞

⎠⇒ |Y | = 0 or 1

etc.


2

4

5

7

spin

3


1/2

3/2

0

1

1/2

0

1

2

0

Q = T3 + Y

e.g. for : T3 =⎛

⎝

+ 12

−

1

2

⎞

⎠n = 2 ⇒ |Y | =1

2

≡ 0

Each multiplet contains a neutral component with a proper assignment of the hypercharge, according to

e.g. for :n = 3 T3 =

⎛

⎝

+10−1

⎞

⎠⇒ |Y | = 0 or 1

etc.

F

S

F

S

F

S

F

F

F

S

S

S

F

S

F

S

S


2

4

5

7

1/2

3/2

0

1

spin

3


1/2

0

1

2

0

0.43

1.2

2.0

2.6

1.4

1.8

2.4

2.4

2.5

2.5

5.0

8.5

The mass is determined by the relic abundance:

M (TeV)

for scalarX

for fermionX

M

(- include co-annihilations) (- computed for ) M ≫ MZ,W

X

X

X

Vµ

Vµ

X

X

Vµ

Vµ

µVµV

µ

X

X

Vµ

Vµ

(- include co-annihilations) (- computed for ) (- computed for ) Z,W(- computed for )

X

X h

hX

X f̄

f

F

S

F

S

F

S

F

F

F

S

S

S

F

S

F

S

S

3.5

3.5

ΩDM =6 10−27cm3s−1

⟨σannv⟩∼= 0.24

3.2

3.2

⟨σAv⟩ ≃g42 (3 − 4n

2 + n4) + 16 Y 4g4Y

+ 8g22g2Y

Y 2(n2 − 1)

64π M2 gX

⟨σAv⟩ ≃g42 (2n

4 + 17n2 − 19) + 4Y 2g4Y

(41 + 8Y 2) + 16g22g2Y

Y 2(n2 − 1)

128π M2 gX

4.2


2

4

5

7

1/2

3/2

0

1

spin

3


1/2

0

1

2

0

M (TeV)

h

h

F

S

F

S

F

S

F

F

F

S

S

S

F

S

F

S

S

2.7

2.5

25

1.0

Non-perturbative corrections (and other smaller corrections) induce modifications:

(more later)

⟨σannv⟩ ! R · ⟨σannv⟩ + ⟨σannv⟩p−wave

with R ∼ O(few) → O(102)

full

� �� !��

��!��

��!��

��!��

��!��

��!��

��!��

� !��"�

��

〈σ��〉

!�� "�

#

�"� ��! �

��

�� ! ��

�!� ��! �

��

�� ! � ��

� � � � � ��

��

��

��

��

��

Ω ��

�!� ��

�!��

�� ! �σ

��

��

9.4


2

4

5

7

1/2

3/2

0

1

spin

3


1/2

0

1

2

0

M (TeV)

348

342

166

540

526

353

347

729

712

166

166

166

166

∆M(MeV) EW loops induce a mass splittinginside the n-uplet:

∆M

MQ − MQ′ =α2M4π

{

(Q2 − Q′2)s2W

f(MZM

)

+ (Q − Q′)(Q + Q′ − 2Y )

[

f(MWM

) − f(MZM

)

]}

with f(r) r→0−→ −2πr

The neutral component is the lightest

DM0

DM+

∆M

F

S

F

S

F

S

F

F

F

S

S

S

F

S

F

S

S

537

906

534

900

X X

W, Z, γ

tree level

2.7

2.5

25

1.0

9.4


2

4

5

7

1/2

3/2

0

1

spin

3


1/2

0

1

2

0

M (TeV)

348

342

166

540

526

353

347

729

712

166

166

166

166

∆M(MeV) decay ch. List all allowed SM couplings:EL

EH

HH∗

LH

HH, LH

LH

HHH∗

(LHH∗)

HHH

(LHH)(HHH∗H∗)

e.g.

e.g.1/2 1/2−1

2 21

XEH

X

e

h

XLHH∗

1/2 −1/2 1/2 −1/2

2 2 2

dim=5 operator, induces

Λ ∼ MPlforτ ∼ Λ2TeV−3 ≪ tuniverse

F

S

F

S

F

S

F

F

F

S

S

S

F

S

F

S

S

(HH∗H∗H∗)

(H∗H∗H∗H∗)

537

906

534

900

4

2.7

2.5

25

1.0

(��H⇤H) dim=5, loop decayDi Luzio,

Nardecchia et al.,

1504.00359

9.4


2

4

5

7

1/2

3/2

0

1

spin

3


1/2

0

1

2

0

M (TeV)

348

342

166

540

526

353

347

729

712

166

166

166

166

∆M(MeV) decay ch. List all allowed SM couplings:EL

EH

HH∗

LH

HH, LH

LH

HHH∗

(LHH∗)

HHH

(LHH)(HHH∗H∗)

e.g.

e.g.1/2 1/2−1

2 21

XEH

X

e

h

XLHH∗

1/2 −1/2 1/2 −1/2

2 2 2

dim=5 operator, induces

Λ ∼ MPlforτ ∼ Λ2TeV−3 ≪ tuniverse

F

S

F

S

F

S

F

F

F

S

S

S

F

S

F

S

S

(HH∗H∗H∗)

(H∗H∗H∗H∗)

No allowed decay! Automatically stable!

537

906

534

900

4

2.7

2.5

25

1.0

(��H⇤H)

9.4


2

4

5

7

1/2

3/2

0

1

spin

3


1/2

0

1

2

0

M (TeV)

348

342

166

540

526

353

347

729

712

166

166

166

166

∆M(MeV) decay ch.EL

EH

HH∗

LH

HH, LH

LH

HHH∗

(LHH∗)

HHH

(LHH)(HHH∗H∗)

F

S

F

S

F

S

F

F

F

S

S

S

F

S

F

S

S

(HH∗H∗H∗)

(H∗H∗H∗H∗)

537

906

not excluded by direct searches!

and

534

900

2.7

2.5

25

1.0

(��H⇤H)

9.4


2

4

5

7

1/2

3/2

0

1

spin

3


1/2

0

1

2

0

M (TeV)

348

342

166

540

526

353

347

729

712

166

166

166

166


EH

HH∗

LH

HH, LH

LH

HHH∗

(LHH∗)

HHH

(LHH)(HHH∗H∗)

F

S

F

S

F

S

F

F

F

S

S

S

F

S

F

S

S

(HH∗H∗H∗)

(H∗H∗H∗H∗)

537

906


and

X

N

σ ≃ G2F M2NY

2

≫ present bounds

Candidates with interact as

Y ̸= 0

need Y = 0

e.g. LUX

X

N

Y

Z0

X

534

900

2.7

2.5

25

1.0

Goodman Goodman Witten Witten 19851985

(��H⇤H)

9.4


2

4

5

7

1/2

3/2

0

1

spin

3


1/2

0

1

2

0

M (TeV)

348

342

166

540

526

353

347

729

712

166

166

166

166


EH

HH∗

LH

HH, LH

LH

HHH∗

(LHH∗)

HHH

(LHH)(HHH∗H∗)

F

S

F

S

F

S

F

F

F

S

S

S

F

S

F

S

S

(HH∗H∗H∗)

(H∗H∗H∗H∗)

537

906


and

534

900

2.7

2.5

25

1.0

(��H⇤H)

9.4


2

4

5

7

1/2

3/2

0

1

spin

3


1/2

0

1

2

0

M (TeV)

348

342

166

540

526

353

347

729

712

166

166

166

166


EH

HH∗

LH

HH, LH

LH

(LHH∗)

HHH

(LHH)(HHH∗H∗)

F

S

F

S

F

S

F

F

F

S

S

S

F

S

F

S

S

(HH∗H∗H∗)

(H∗H∗H∗H∗)

537

906


and

HHH∗

4

1/2353

347 (LHH∗)S

F

HHH∗

4

3/2729

712

HHH

(LHH)FS

534

900

2.7

2.5

25

1.02 1/2

348

342

EL

EHF

S 1.0

1540

526

HH, LH

LH

S

F

1S

F

(HH∗H∗H∗)537

534

2S

F

(H∗H∗H∗H∗)906

900

(��H⇤H)

9.4


2

4

5

7

1/2

3/2

0

1

spin

3


1/2

0

1

2

0

M (TeV)

348

342

166

540

526

353

347

729

712

166

166

166

166


EH

HH∗

LH

HH, LH

LH

(LHH∗)

HHH

(LHH)(HHH∗H∗)

F

S

F

S

F

S

F

F

F

S

S

S

F

S

F

S

S

(HH∗H∗H∗)

(H∗H∗H∗H∗)

537

906


and

HHH∗

3

534

900

2.7

2.5

25

1.02 1/2

348

342

EL

EHF

S 1.0

0166

166

HH∗

LHF

S

2.7

2.5

166 (HHH∗H∗)S

1S

F

(HH∗H∗H∗)537

534

2S

F

(H∗H∗H∗H∗)906

900

1540

526

HH, LH

LH

S

F

4

1/2353

347 (LHH∗)S

F

HHH∗

4

3/2729

712

HHH

(LHH)FS

(��H⇤H)7 0 166S 25 (��H⇤H)

9.4


2

4

5

7

1/2

3/2

0

1

spin

3


1/2

0

1

2

0

M (TeV)

348

342

166

540

526

353

347

729

712

166

166

166

166


EH

HH∗

LH

HH, LH

LH

(LHH∗)

HHH

(LHH)(HHH∗H∗)

F

S

F

S

F

S

F

F

F

S

S

S

F

S

F

S

S

(HH∗H∗H∗)

(H∗H∗H∗H∗)

537

906


and

HHH∗

3

We have a winner!

534

900 (oth

er te

rms

in th

e

scal

ar p

oten

tial

)

2.7

2.5

25

1.02 1/2

348

342

EL

EHF

S 1.0

0166

166

HH∗

LHF

S

2.7

2.5

1540

526

HH, LH

LH

S

F

4

1/2353

347 (LHH∗)S

F

HHH∗

4

3/2729

712

HHH

(LHH)FS

166 (HHH∗H∗)S

1S

F

(HH∗H∗H∗)537

534

2S

F

(H∗H∗H∗H∗)906

900

7 0 166S 25

9.4

e.g. mixing with an extra state splits the 2 components of ; if splitting is large enough, NC scattering is kinematically forbidden...

If you want to cure ill candidates...: introduce some mechanism to forbid coupling with anyway

Y ̸= 0

impose some symmetry to forbid decays (e.g. R-parity)...stability:

X

Z0

Y

Z0

impose some symmetry to forbid decays (e.g. R-parity)...

Y

Z0

X

NN

X′

...the case of SuSy higgsino...the case of SuSy higgsinomixing is with bino;

even for pure higgsino, some mixing is ‘inevitable’

due to higher dim operators

A fermionic quintuplet with ,provides a DM candidate with ,

which is fully successful: - neutral

- automatically stable and

not yet discovered by DM searches.

Recap:SU(2)L Y = 0

(Other candidates can be cured via non-minimalities.)

like proton stability in SM!

M = 9.4 TeV

Detection and Phenomenology

1. Collider searchesAt 9.4 TeV, no hope at the LHC.

relax the mass constraint consider next-to-minimal cases (e.g. the triplet = pure wino) explore reach of 100 TeV future collider

q'

q

W±

c±

c0

c0

g p±

qq

q'g

W± c±

c0

c0

p±' tra

cker'

Mono-X VBF Disappearing tracksq

q

q'

q'

W±

W±

c±

c±

c0

c0

c0

p±

p±

di-jets + MET

1. Collider searchesAt 9.4 TeV, no hope at the LHC.

relax the mass constraint consider next-to-minimal cases (e.g. the triplet = pure wino) explore reach of 100 TeV future collider

For triplet MDM (a.k.a. wino DM)

Cire

lli, S

ala,

Taos

o 14

07.7

058

For 5plet MDM

Ostd

iek, 1

506.

0344

5

2. Direct DetectionNo tree level scattering. 1-loop and 2-loops:

Cirelli, Fornengo, Strumia hep-ph/0512090

Essig 0710.1668

Hisano, Ishiwata, Nagata1007.2601

Hisano, Ishiwata, Nagata, Takesano 1104.0228

Hill, Solon 1111.0016

Hisano, Ishiwata, Nagata1010.5985

Farina, Pappadopulo, Strumia 1303.7244



Hisano, Ishiwata, Nagata 1504.00915

�nSI = 2 · 10�46 cm2

2. Direct DetectionSensitivity Projections: Spin-Independent Interactions

�� μ��

�� !��!��!��!��!��!��!��!��!��!��!��!��!��!��

��!��!��!��!��!��!��!��!��!��!��!��!��!��!�

�� !��"��#

��!��"�� #

��!��"��#

CDMS II Ge (2009) Xen

on100 (2012

)

CRESST

CoGeNT!(2012)

CDMS Si!(2013)

EDELWEISS (2011)

DAMA SIMPLE (20

12)

ZEPLIN-III (201

2)COUPP (201

2)

LUX (2013)

DAMIC (2012)

CDMSlite (2013)

DarkSide-50

(2014)

CRESST (2015)

Xenon1T

LZ

LUX 300day

SuperCDMS S

NOLAB

DEAP3600

XMASS

DarkSide-G2

SuperCDMS

EDELWEISS

CRESST

Cush

man

et a

l., 13

10.8

327

PS: SD cross section equally challenging Hisano, Ishiwata, Nagata 1010.5985

3. Indirect Detection

8 kpc

i.e. , , , , from MDM annihilations in MW halo.p̄ � D̄e+�

3. Indirect Detectioni.e. , , , , from MDM annihilations in MW halo.�

c

c

c±Z

Z

c

c

c±W+

W-

(channels for MDM with Y=0)

W±, Z � p̄, e+, � . . .+

�

, �

, �

Enhanced cross section due to ‘Sommerfeld corrections’


Hisano et al., 2004, 2005Cirelli, Strumia, Tamburini 2007

c

c

c±Z

Z

c

c

c±W+

W-

(channels for MDM with Y=0)

W±, Z � p̄, e+, � . . .+

Cirelli, Hambye, Panci, Sala, Taoso 1507.05519

i.e. , , , , from MDM annihilations in MW halo.�

, �

, �


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Consistent conclusions in: Garcia-Cely et al. 1507.05536

Bonus trackSome interesting recent extensions:

- millicharged MDMDel Nobile, Nardecchia, Panci 1512.05353

assume Y = ! " 0, -> implies stability -> for suitable !, no DD

relic abundance constraints

- decaying MDM, if " < MPlanckDel Nobile, Nardecchia, Panci 1512.05353

-‘natural’ MDMFabbrichesi, Urbano 1510.03861

-> observable consequences in gamma rays

MDM induces (at 2-loops) mh corrections => small hierarchy prob -> supersymmetrize it!:

- fermion/boson cancellations restore naturalness - stability preserved by SuSy

Bonus trackSome interesting recent extensions:

-MDM and vacuum stabilityCai,Ramsey-Musolf et al., 1108.0969 Cai et al., 1508.04034

-asymmetric MDMBoucenna, Krauss, Nardi 1503.01119

-non-thermally produced MDMAoki, Toma, Vicente 1507.01591

ConclusionsThe DM problem requires physics beyond the SM.

Introducing the minimal amount of it, we find one fully successful DM candidate:

massive, neutral, automatically stable.

fermionic quintuplet with , mass = 9.4 TeV

- too heavy to be produced at LHC, - challenging in next gen direct detection exp’s, - tested by indirect detection (ữ ray) exp’s:

Its phenomenology is precisely computable:

SU(2)L Y = 0

(Other candidates have different properties.)

- excluded if cuspy - not probed if cored

ConclusionsThe DM problem requires physics beyond the SM.

Introducing the minimal amount of it, we find one fully successful DM candidate:

massive, neutral, automatically stable.

fermionic quintuplet with , mass = 9.4 TeV

SU(2)L Y = 0

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The cosmic inventoryMost of the Universe is Dark

Ωlum ∼ 0.01

Ωb ≃ 0.040 ± 0.005

-mass to light ratio in typical systems

-BBN -CMB

Ωde ∼ 0.7 - CMB + SNIa - CMB - DM - acoustic peak in baryons

(

Ωx =ρx

ρc; CMB first peak ⇒ Ωtot = 1 (flat);

HST h = 0.71 ± 0.07)

ΩDM ∼ 0.24

- CMB + SNIa

particle physics cosmology

⋂

1) galaxy rotation curves

Beg

eman

et a

l., M

NR

AS

249

(199

1)

ΩM ! 0.1

vc(r) ∼ const ⇒ ρM (r) ∼1

r2

vc(r) =

√2GNM(r)

r

The Evidence for DM

[bac

k to

mai

n sl

ide]


2) clusters of galaxies- “rotation curves” - gravitation lensing - X-ray gas temperature

“bullet cluster” - NASA astro-ph/0608247

ΩM ! 0.1

ΩM ∼ 0.2 ÷ 0.4

[further developments]

The Evidence for DM

[bac

k to

mai

n sl

ide]

3) CMB+LSS(+SNIa:)

ΩM ≈ 0.26 ± 0.05

TT TE

EE LSS

M.Cirelli and A.Strumia, astro-ph/0607086

WMAP-3yr ACbarCBI

Text

BoomerangDASIVSA

SDSS, 2dFRGSLyA Forest Croft LyA Forest SDSS

ΩM ! 0.1

ΩM ∼ 0.2 ÷ 0.4


2) clusters of galaxies

The Evidence for DM

[bac

k to

mai

n sl

ide]

Comparison with SplitSuSy-like modelsA-H, Dimopoulos and/or Giudice, Romanino 2004

Pierce 2004; Arkani-Hamed, Dimopoulos, Kachru 2005 Mahbubani, Senatore 2005

MDMSplitSuSy-like- Higgsino (a fermion doublet)

- + something else (a singlet)

- stabilization by R-parity

- want unification also

- unification scale is low, need to embed in 5D to avoid proton decay

- arbitrary multiplet, scalar or fermion

- nothing else (with Y=0)

- automatically stable

- forget unification, it’s SM

- nothing

Common feature: the focus is on DM, not on SM hierarchy problem.

Mahbubani, Senatore 2005

Non-Minimal terms in the scalar caseλH(X

∗T

a

XX ) (H∗T

a

HH) + λ′

H |X |2|H|2 +

λX

2(X ∗T aXX )

2 +λ′X

2|X |4

Quadratic and quartic terms in and :X H

- do not induce decays (even number of , and )⟨X ⟩ = 0X- [3] and [4] do not give mass terms

[1] [2] [3] [4]

- after EWSB, [2] gives a common mass to all components; negligible for

√

λ′H

v ≈ O(! 100 GeV)

Xi

M = O(TeV)

- after EWSB, [1] gives mass splitting between components; assume so that

Xi

∆Mtree =λHv

2|∆T 3X|

4M= λH · 7.6 GeV

TeV

M

λH ! 0.01 ∆Mtree ≪ ∆M

(Anyway, scalar MDM is less interesting.) [back to Lagrangian]

- [1] (and [2]) gives annihilations assume so that these are subdominant |λ′H | ≪ g2Y , g22

X̄X → H̄H

[back to table]

( basis)

Neutralino “properties’’

Mχ =

⎛

⎜

⎜

⎝

M1 0 −mZcβsW mZsβsW0 M2 mZcβcW −mZsβcW

−mZcβsW mZcβcW 0 −µmZsβsW −mZsβcW −µ 0

⎞

⎟

⎟

⎠

neutralino mass matrix in MSSM B̃ − W̃ 3 − H̃01 − H̃02

superpotentialW = −µH1H2 + H1h

ij

eLLiERj + H1h

ij

dQLiDRj −H2h

ij

uQLiURj

soft SUSYB terms

Lsoft = −1

2

(

M1¯̃BB̃ + M2

¯̃W

a

W̃a + M3

¯̃G

a

G̃a

)

+ . . .

tanβ =⟨v1⟩

⟨v2⟩

3. Indirect DetectionPropagation for positrons:

[back]

�f

�t�K(E) ·⇤2f � �

�E(b(E)f) = Q

K(E) = K0(E/GeV)� b(E) = (E/GeV)2/�E�E = 1016 s

Model � K0 in kpc2/Myr L in kpcmin (M2) 0.55 0.00595 1med 0.70 0.0112 4max (M1) 0.46 0.0765 15

diffusion energy loss

Q =12

��

MDM

⇥2finj, finj =

⇤

k

�⇥v⇥kdNke+dE

�e+(E,�r�) = Bve+

4⇥⇤EE2

� MDM

EdE⇥ Q(E⇥) · I (�D(E,E⇥))

Solution:

⇥2D = 4K0⇤E�(E/GeV)��1 � (E⇥/GeV)��1

� � 1

⇥

3. Indirect DetectionPropagation for antiprotons:

diffusion convective wind

Solution:

⇥f

⇥t�K(T ) ·⇤2f + ⇥

⇥z(sign(z) f Vconv) = Q� 2h �(z) �annf

K(T ) = K0� (p/GeV)�spallations

Model � K0 in kpc2/Myr L in kpc Vconv in km/smin 0.85 0.0016 1 13.5med 0.70 0.0112 4 12max 0.46 0.0765 15 5

�p̄(T,�r�) = Bvp̄4�

�⇥�

MDM

⇥2R(T )

⇤

k

12�⇤v⇥k

dNkp̄dT

T kinetic energy

[back]

Indirect Detection

AMS-01 Caprice

BESSBESSCaprice

Solar wind Modulation of cosmic rays:

spectrum at Earth

d�p̄�dT�

=p2�p2

d�p̄dT

, T = T� + |Ze|�Fspectrum

far from Earth

Fisk potential �F � 500 MV

Indirect DetectionBoost Factor: local clumps in the DM halo enhance the density, boost the flux from annihilations. Typically:

Lava

lle e

t al.

2006

Lava

lle e

t al.

2007

positrons antiprotons

In principle, B is different for e+, anti-p and gammas, energy dependent, dependent on many astro assumptions, with an energy dependent variance, at high energy for e+, at low energy for anti-p.

B ⇥ 1� 20 (104)

[back]

Indirect DetectionBoost Factor: local clumps in the DM halo enhance the density, boost the flux from annihilations. Typically: B ⇥ 1� 20 (104)

Ber

tone

, Bra

nchi

ni, P

ieri

200

7

Kuh

len,

Die

man

d, M

adau

200

7

Milky Way

Milky Way

For illustration:

Results for anti-protons:3. Indirect Detection

Astro uncertainties:- propagation model - DM halo profile - boost factor B

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10-1

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flux

in1êHG

eVm

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csrL

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5

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Background?MEDMAX

MIN

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1 10 102 103 10410-10

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10-4

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10-1

T HGeVL

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i-pr

oton

flux

in1êHG

eVm

2se

csrL

MED propagation

5

Boost = 15

Background?NFWMoore

IsoT

Results for anti-protons:3. Indirect Detection

Astro uncertainties:- propagation model - DM halo profile - boost factor B

Documents

Minimal Dark Matter,research.ipmu.jp/seminar/sysimg/seminar/1628.pdfKolb,Turner, The Early Universe, 1995 Ω X ≈ 6 10−27cm3s−1 σ ann v Boltzmann eq. in the Early Universe: Weak