Composite Dark Matter - kmi.nagoya-u.ac.jp

Composite Dark MatterGeorge T. Fleming

Yale University

Sakata-Hirata Hall, Nagoya University March 4, 2015

E. Rinaldi LLNL

Lattice Strong Dynamics Collaboration

Xiao-Yong Jin

Outline• Motivations for searches of composite dark matter

• Features of strongly-coupled composite dark matter

• Searches for a class of models interesting for phenomenology

• Importance of lattice field theory simulations

• Lower bounds on composite dark matter models

[LSD collab., Phys. Rev. D88 (2013) 014502][LSD collab., Phys. Rev. D89 (2014) 094508]

+ LSD collab., in preparation (x2)

BSM Is Out There• Discovery of SM-like Higgs boson doesn’t mean BSM

physics is dead:

➡ What is the meaning of the hierarchy problem and naturalness?

➡ What solves the strong CP problem?

➡ What explains the matter-antimatter asymmetry?

BSM Is Out There• Discovery of SM-like Higgs boson doesn’t mean BSM

physics is dead:

➡ What is the meaning of the hierarchy problem and naturalness?

➡ What solves the strong CP problem?

➡ What explains the matter-antimatter asymmetry?

➡ What is dark matter? Can it couple to the standard model? Is the mass scale related to the EW Higgs mechanism? Is it self-interacting?

The gravity of Dark MatterWe Are

Here(QCD, EM,

SM, etc.)

??????

How do we know Dark Matter is there?

New Physics!!

Cosmological Backgrounds

Gravitational Lensing

Rotational velocity Curves of Galaxies

[Planck and ESA]


Here(QCD, EM,

SM, etc.)

??????


New Physics!!




[Planck and ESA]


Here(QCD, EM,

SM, etc.)

??????


New Physics!!




Gravitational Interactions

Problems?

Problems?• Number of observed dwarf galaxies is inconsistent

with predictions from dark matter simulations “Missing Satellites”



• Predicted dwarf galaxies are too dense “Too Big To Fail”




• Density profiles of dwarf galaxies is more cored than in simulations “Cusp vs. Core”




• Density profiles of dwarf galaxies is more cored than in simulations “Cusp vs. Core”

ameliorated by Self-Interacting Dark Matter

Self-Interacting Dark Matter• In ΛCDM, galactic sub-halos have very

dense, cuspy cores.

• Any dwarf galaxies residing in a cuspy sub-halo will be smaller and dimmer than in a sub-halo with more uniform density.

• Larger Milky Way and Andromeda dwarf galaxies are too bright for their expected sub-halos, if those sub-halos are made of non-interacting dark matter (ΛCDM).

Self-interacting dark matter (SIDM) will make sub-halo cores less dense, enabling larger dwarf galaxies.

O. D. Elbert et al., arXiv:1412.1477 [astro-ph.GA]

�(vrms)/M ⇠ 0.5 – 50 cm2 g�1, vrms ' 10 – 100 km s�1

Self-Interacting Dark Matter

Strongly-Coupled Composite Dark Matter

interactions with SM particles that can evade current

experimental constraints

View from Snowmass (I)mSUGRA

R-parityConserving

Supersymmetry

pMSSM

R-parityviolating

Gravitino DM

MSSM NMSSM

DiracDM

Extra Dimensions

UED DM

Warped Extra Dimensions

Little Higgs

T-odd DM

5d

6d

Axion-like Particles

QCD Axions

Axion DM

Sterile Neutrinos

LightForce Carriers

Dark Photon

Asymmetric DM

RS DM

Warm DM

?

HiddenSector DM

WIMPless DM

Littlest Higgs

Self-InteractingDM

Q-balls

T Tait

Solitonic DM

QuarkNuggets

Techni-baryons

Dynamical DM

Where is composite dark matter?

Snowmass 2013: The Cosmic Frontier [arXiv:1401.6085]

View from Snowmass (I)mSUGRA

R-parityConserving

Supersymmetry

pMSSM

R-parityviolating

Gravitino DM

MSSM NMSSM

DiracDM

Extra Dimensions

UED DM

Warped Extra Dimensions

Little Higgs

T-odd DM

5d

6d

Axion-like Particles

QCD Axions

Axion DM

Sterile Neutrinos

LightForce Carriers

Dark Photon

Asymmetric DM

RS DM

Warm DM

?

HiddenSector DM

WIMPless DM

Littlest Higgs

Self-InteractingDM

Q-balls

T Tait

Solitonic DM

QuarkNuggets

Techni-baryons

Dynamical DM



View from Snowmass (II)


1 10 100 1000 10410!5010!4910!4810!4710!4610!4510!4410!4310!4210!4110!4010!39

10!1410!1310!1210!1110!1010!910!810!710!610!510!410!3

WIMP Mass !GeV"c2#

WIMP!nucleoncrosssection!cm2 #

WIMP!nucleoncrosssection!pb#

7BeNeutrinos

NEUTRINO C OHER ENT SCATTERING

NEUTRINO COHERENT SCATTERING(Green&ovals)&Asymmetric&DM&&(Violet&oval)&Magne7c&DM&(Blue&oval)&Extra&dimensions&&(Red&circle)&SUSY&MSSM&&&&&&MSSM:&Pure&Higgsino&&&&&&&MSSM:&A&funnel&&&&&&MSSM:&BinoEstop&coannihila7on&&&&&&MSSM:&BinoEsquark&coannihila7on&&

8BNeutrinos

Atmospheric and DSNB Neutrinos

CDMS II Ge (2009)

Xenon100 (2012)

CRESST

CoGeNT(2012)

CDMS Si(2013)

EDELWEISS (2011)

DAMA SIMPLE (2012)

ZEPLIN-III (2012)COUPP (2012)

SuperCDMS Soudan Low ThresholdSuperCDMS Soudan CDMS-lite

XENON 10 S2 (2013)CDMS-II Ge Low Threshold (2011)

SuperCDMS Soudan

Xenon1T

LZ

LUX

DarkSide G2

DarkSide 50

DEAP3600

PICO250-CF3I

PICO250-C3F8

SNOLAB

SuperCDMS

Parti

al w

ave

unita

rity?


View from Snowmass (II)


1 10 100 1000 10410!5010!4910!4810!4710!4610!4510!4410!4310!4210!4110!4010!39

10!1410!1310!1210!1110!1010!910!810!710!610!510!410!3

WIMP Mass !GeV"c2#



7BeNeutrinos



8BNeutrinos


CDMS II Ge (2009)

Xenon100 (2012)

CRESST

CoGeNT(2012)

CDMS Si(2013)

EDELWEISS (2011)

DAMA SIMPLE (2012)




SuperCDMS Soudan

Xenon1T

LZ

LUX

DarkSide G2

DarkSide 50

DEAP3600

PICO250-CF3I

PICO250-C3F8

SNOLAB

SuperCDMS

Parti

al w

ave

unita

rity?


Dark SU(3) Baryon

Strongly-coupled composite dark matter

• Dark matter is a composite object

• Composite object is electroweak neutral

• Constituents can have electroweak charges

• Dark matter is stable thanks to a global symmetry (like baryon number)






Akin to a technibaryon







Suppressed interactions with SM








Mechanisms to provide observed relic abundance








Mechanisms to provide observed relic abundance

Guaranteed in many models

What do we have in mind?• In general we think about a new strongly-coupled gauge

sector like QCD with a plethora of composite states in the spectrum

• Dark fermions have dark color and also have electroweak charges

• Depending on the model, dark fermions have electroweak breaking masses (chiral), electroweak preserving masses (vector) or a mixture

• A global symmetry of the theory naturally stabilizes the dark baryonic composite states (e.g. neutron)

What do we have in mind?• In general we think about a new strongly-coupled gauge

sector like QCD with a plethora of composite states in the spectrum

• Dark fermions have dark color and also have electroweak charges

• Depending on the model, dark fermions have electroweak breaking masses (chiral), electroweak preserving masses (vector) or a mixture

• A global symmetry of the theory naturally stabilizes the dark baryonic composite states (e.g. neutron)

we construct a minimal model with these features

• dimension 4 ➥ Higgs exchange

• dimension 5 ➥ magnetic dipole

• dimension 6 ➥ charge radius

• dimension 7 ➥ polarizability

“How dark is Dark Matter?”Interactions of neutral object with photons + Higgs

(��µ⌫�)Fµ⌫

⇤dark

(��)vµ@⌫Fµ⌫

⇤2dark

(��)Fµ⌫Fµ⌫

⇤3dark






(��µ⌫�)Fµ⌫

⇤dark

(��)vµ@⌫Fµ⌫

⇤2dark


⇤3dark






(��µ⌫�)Fµ⌫

⇤dark

(��)vµ@⌫Fµ⌫

⇤2dark


⇤3dark






(��µ⌫�)Fµ⌫

⇤dark

(��)vµ@⌫Fµ⌫

⇤2dark


⇤3dark

Coupling Dark Baryons to SMψ σMag. Moment#

dim. 5

(ψψ) Charge Radius#

dim. 6

(ψψ) FPolarizability#

dim. 7

Odd NNo Flavor Sym. ✔ ✔ ✔

Odd NFlavor Sym ✔

Even NNo Flavor Sym. ✔ ✔

Even NFlavor Sym. ✔

Magnetic moment and charge radius of DM

• Need non-perturbative calculation of form-factors for DM composite object

• Negligible dependence on constituent mass and number of flavors

• Magnetic moment dominates for masses > 25GeV

Magnetic moment dominates for MB & 25 GeV

—Dashed lines show charge radius⌦r2↵ contribution to full rate

—Suppressed by 1/M2B relative to magnetic moment contribution

10�2 10�1 100 101 102

M� = MB [TeV]

10�16

10�14

10�12

10�10

10�8

10�6

10�4

10�2

100

102

104

Rat

e,ev

ent/

(kg·d

ay)

Nf = 2

Nf = 6

XENON100 [1207.5988], 95% CL exclusion

XENON100 resultsonly sensitive to

⌦r2↵

for MB . 0.5 TeV

Estimate MB . O(0.01) TeVsensitive to polarizability

= 0 automatically for SU(N) gauge theories with even N. . .

Composite dark matter on the lattice Theory Seminar, 24 March 2014 13 / 20

[LSD collab., Phys. Rev. D88 (2013) 014502]

SU(3) model: DM is neutral baryon with spin 1/2








10�2 10�1 100 101 102

M� = MB [TeV]

10�16

10�14

10�12

10�10

10�8

10�6

10�4

10�2

100

102

104

Rat

e,ev

ent/

(kg·d

ay)

Nf = 2

Nf = 6



⌦r2↵

for MB . 0.5 TeV





without magnetic moment contribution









10�2 10�1 100 101 102

M� = MB [TeV]

10�16

10�14

10�12

10�10

10�8

10�6

10�4

10�2

100

102

104

Rat

e,ev

ent/

(kg·d

ay)

Nf = 2

Nf = 6



⌦r2↵

for MB . 0.5 TeV





without magnetic moment contribution Excludes dark matter

mass below 10 TeV!


“Stealth Dark Matter” model

• Let’s focus on a SU(N) dark gauge sector with N=4

• Let dark fermions interact with the SM Higgs and obtain current/chiral masses

• Let’s introduce vector-like masses for dark fermions that do not break EW symmetry

3

Field SU(N)D

(SU(2)L

, Y ) Q

F1

=

Fu

1

F d

1

!N (2, 0)

+1/2

�1/2

!

F2

=

Fu

2

F d

2

!N (2, 0)

+1/2

�1/2

!

Fu

3

N (1,+1/2) +1/2

F d

3

N (1,�1/2) �1/2

Fu

4

N (1,+1/2) +1/2

F d

4

N (1,�1/2) �1/2

TABLE I. Fermion particle content of the composite dark mattermodel. All fields are two-component (Weyl) spinors. SU(2)

L

refers to the standard model electroweak gauge group, and Y isthe hypercharge. The electric charge Q = T

3

+Y for the fermioncomponents is shown for completeness.

yet have the ability to simulate on the lattice. Naive di-mensional analysis applied to the annihilation rate suggeststhe dark matter mass scale should be >⇠ 10-100 TeV, but amore precise estimate is not possible at this time. In anycase, for dark matter with mass below this value, there isan underproduction of dark matter through the symmet-ric thermal relic mechanism, and so this does not restrictconsideration of dark matter mass scales between the elec-troweak scale up to this thermal abundance bound.

CONSTRUCTING A VIABLE MODEL

[placeholder for a description of how a viable modelwith interactions with the Higgs can be constructed whilesatisfying the various (gross) experimental constraints]

We consider a new, strongly-coupled SU(N)

D

gaugegroup with fermionic matter in the vector-like representa-tions shown in Table I.

This is not the only possible choice for the charges, butthe requirement for the presence of Higgs Yukawa cou-plings, along with extremely strong bounds on the ex-istence of stable fractionally-charged particles based onsearches for rare isotopes [? ], greatly constrains the num-ber of possible models.

DARK FERMION INTERACTIONS AND MASSES

The fermions F u,d

i

transform under a global U(4) ⇥U(4) flavor symmetry that is broken to [SU(2) ⇥ U(1)]4by the weak gauging of the electroweak symmetry. Fromthis large global symmetry, one SU(2) (diagonal) sub-group will be identified with SU(2)

L

, one U(1) subgroup

will be identified with U(1)

Y

, and one U(1) will be iden-tified with dark baryon number. The total fermionic con-tent of the model is therefore 8 Weyl fermions that pairup to become 4 Dirac fermions in the fundamental oranti-fundamental representation of SU(N)

D

with electriccharges of Q ⌘ T

3,L

+ Y = ±1/2. We use the notationwhere the superscript u and d (as in F u, F d and later u, d, u, d) to denote a fermion with electric charge ofQ = 1/2 and Q = �1/2 respectively.

The fermion kinetic terms in the Lagrangian are givenby

L =

X

i=1,2

iF †i

�µDi,µ

Fi

+

X

i=3,4;j=u,d

iF j

i

†�µDj

i,µ

F j

i

,

(1)where the covariant derivatives are

D1,µ

⌘ @µ

� igW a

µ

�a/2 � igD

Gb

µ

tb (2)

D2,µ

⌘ @µ

� igW a

µ

�a/2 + igD

Gb

µ

tb

⇤(3)

Dj

3,µ

⌘ @µ

� ig0Y jBµ

� igD

Gb

µ

tb (4)

Dj

4,µ

⌘ @µ

� ig0Y jBµ

+ igD

Gb

µ

tb

⇤(5)

with the interactions among the electroweak group and thenew SU(N)

D

. Here Y u

= 1/2, Y d

= �1/2 and tb

are the representation matrices for the fundamental N ofSU(N)

D

.The vector-like mass terms allowed by the gauge sym-

metries are

L � M12

✏ij

F i

1

F j

2

�Mu

34

F u

3

F d

4

+Md

34

F d

3

F u

4

+h.c., (6)

where ✏12

⌘ ✏ud

= �1 = �✏12 and the relative minussigns between the mass terms have been chosen for laterconvenience. The mass term M

12

explicitly breaks the[SU(2) ⇥ U(1)]2 global symmetry down to the diagonalSU(2)

diag

⇥ U(1) where the SU(2)

diag

is identified withSU(2)

L

. The mass terms Mu,d

34

explicitly break the re-maining [SU(2)⇥U(1)]2 down to U(1)⇥U(1) where oneof the U(1)’s is identified with U(1)

Y

. (In the special casewhen Mu

34

= Md

34

, the global symmetry is accidentally en-hanced to SU(2)⇥U(1), where the global SU(2) acts as acustodial symmetry.) Thus, after weakly gauging the elec-troweak symmetry and writing arbitrary vector-like massterms, the unbroken flavor symmetry is thus U(1)⇥U(1).

Electroweak symmetry breaking mass terms arise fromcoupling to the Higgs field H that we take to be in the(2, +1/2) representation. They are given by

L � yu

14

✏ij

F i

1

HjF d

4

+ yd

14

F1

· H†F u

4

� yd

23

✏ij

F i

2

HjF d

3

� yu

23

F2

· H†F u

3

+ h.c., (7)

where again the relative minus signs are chosen for laterconvenience. After electroweak symmetry breaking, H =

(0 v/p

2)

T , with v ' 246 GeV. Inserting the vev

[LSD collab., in preparation]





3

Field SU(N)D

(SU(2)L

, Y ) Q

F1

=

Fu

1

F d

1

!N (2, 0)

+1/2

�1/2

!

F2

=

Fu

2

F d

2

!N (2, 0)

+1/2

�1/2

!

Fu

3

N (1,+1/2) +1/2

F d

3

N (1,�1/2) �1/2

Fu

4

N (1,+1/2) +1/2

F d

4

N (1,�1/2) �1/2


L


3






D




The fermions F u,d

i


L

, one U(1) subgroup


Y


D


3,L



L =

X

i=1,2

iF †i

�µDi,µ

Fi

+

X

i=3,4;j=u,d

iF j

i

†�µDj

i,µ

F j

i

,


D1,µ

⌘ @µ

� igW a

µ

�a/2 � igD

Gb

µ

tb (2)

D2,µ

⌘ @µ

� igW a

µ

�a/2 + igD

Gb

µ

tb

⇤(3)

Dj

3,µ

⌘ @µ

� ig0Y jBµ

� igD

Gb

µ

tb (4)

Dj

4,µ

⌘ @µ

� ig0Y jBµ

+ igD

Gb

µ

tb

⇤(5)


D

. Here Y u

= 1/2, Y d

= �1/2 and tb


D


metries are

L � M12

✏ij

F i

1

F j

2

�Mu

34

F u

3

F d

4

+Md

34

F d

3

F u

4

+h.c., (6)

where ✏12

⌘ ✏ud


12


diag


diag


L


34


Y


34

= Md

34



L � yu

14

✏ij

F i

1

HjF d

4

+ yd

14

F1

· H†F u

4

� yd

23

✏ij

F i

2

HjF d

3

� yu

23

F2

· H†F u

3

+ h.c., (7)


(0 v/p

2)


L �+ yu14✏ijFi1H

jF d4 + yd14F1 ·H†Fu

4

� yd23✏ijFi2H

jF d3 � yu23F2 ·H†Fu

3 + h.c.






3

Field SU(N)D

(SU(2)L

, Y ) Q

F1

=

Fu

1

F d

1

!N (2, 0)

+1/2

�1/2

!

F2

=

Fu

2

F d

2

!N (2, 0)

+1/2

�1/2

!

Fu

3

N (1,+1/2) +1/2

F d

3

N (1,�1/2) �1/2

Fu

4

N (1,+1/2) +1/2

F d

4

N (1,�1/2) �1/2


L


3






D




The fermions F u,d

i


L

, one U(1) subgroup


Y


D


3,L



L =

X

i=1,2

iF †i

�µDi,µ

Fi

+

X

i=3,4;j=u,d

iF j

i

†�µDj

i,µ

F j

i

,


D1,µ

⌘ @µ

� igW a

µ

�a/2 � igD

Gb

µ

tb (2)

D2,µ

⌘ @µ

� igW a

µ

�a/2 + igD

Gb

µ

tb

⇤(3)

Dj

3,µ

⌘ @µ

� ig0Y jBµ

� igD

Gb

µ

tb (4)

Dj

4,µ

⌘ @µ

� ig0Y jBµ

+ igD

Gb

µ

tb

⇤(5)


D

. Here Y u

= 1/2, Y d

= �1/2 and tb


D


metries are

L � M12

✏ij

F i

1

F j

2

�Mu

34

F u

3

F d

4

+Md

34

F d

3

F u

4

+h.c., (6)

where ✏12

⌘ ✏ud


12


diag


diag


L


34


Y


34

= Md

34



L � yu

14

✏ij

F i

1

HjF d

4

+ yd

14

F1

· H†F u

4

� yd

23

✏ij

F i

2

HjF d

3

� yu

23

F2

· H†F u

3

+ h.c., (7)


(0 v/p

2)


L �+ yu14✏ijFi1H

jF d4 + yd14F1 ·H†Fu

4

� yd23✏ijFi2H

jF d3 � yu23F2 ·H†Fu

3 + h.c.

L � M12✏ijFi1F

j2 �Mu

34Fu3 F

d4 +Md

34Fd3 F

u4 + h.c.


MPSêMV=0.77

10 50 100 500 1000

1¥10-46

5¥10-461¥10-45

5¥10-451¥10-44

5¥10-441¥10-43

5¥10-43

mB HGeVL

DM-nucleoncrosssectionHcm

2 L !=0.64

!=0.16

!=0.04

!=0.01

Higgs exchange cross section in Stealth DM

• Need to non-perturbatively evaluate the σ-term of the dark baryon (scalar nuclear form factor)

• Effective Higgs coupling non-trivial with mixed chiral and vector-like masses

• Model-dependent answer for the cross-section in this channels

• A non-negligible vector mass is needed to evade direct detection bounds

mf (h) = m+yhp2

↵ ⌘ v

mf

@mf (h)

@ h

��h=v

=yvp

2m+ yv 1


MPSêMV=0.77

10 50 100 500 1000

1¥10-46

5¥10-461¥10-45

5¥10-451¥10-44

5¥10-441¥10-43

5¥10-43

mB HGeVL

DM-nucleoncrosssectionHcm

2 L !=0.64

!=0.16

!=0.04

!=0.01

Higgs exchange cross section in Stealth DM

• Need to non-perturbatively evaluate the σ-term of the dark baryon (scalar nuclear form factor)

• Effective Higgs coupling non-trivial with mixed chiral and vector-like masses

• Model-dependent answer for the cross-section in this channels

• A non-negligible vector mass is needed to evade direct detection bounds

mf (h) = m+yhp2

↵ ⌘ v

mf

@mf (h)

@ h

��h=v

=yvp

2m+ yv 1

LEP bound on charged pseudoscalar mesons LHC could be do better here. LUX bound

[Phys. Rev. Lett. 112 (2014)]


• remove magnetic dipole moment:

• lightest stable baryon is a boson with S=0

• remove charge radius:

• 2 flavors with degenerate masses mu=md

• polarizability can not be removed

Electromagnetic polarizability

O�F = C�

F ��Fµ⌫Fµ⌫

� �

Nucleus Nucleus

p p0

k k0

` `� q

k + `

q = k0 � k = p� p0







O�F = C�


� �

Nucleus Nucleus

p p0

k k0

` `� q

k + `

q = k0 � k = p� p0







O�F = C�


� �

Nucleus Nucleus

p p0

k k0

` `� q

k + `

q = k0 � k = p� p0Lattice







O�F = C�


� �

Nucleus Nucleus

p p0

k k0

` `� q

k + `

q = k0 � k = p� p0

Nuclear Physics

Importance of lattice field theory techniques

• lattice simulations are naturally suited for models where dark fermion masses are comparable to the confinement scale



• controllable systematic errors and room for improvement




• Naive dimensional analysis and EFT approaches can miss important non-perturbative contributions





• NDA is not precise enough when confronting experimental results and might not work for certain situations





• NDA is not precise enough when confronting experimental results and might not work for certain situations

22

u

dd3-color

4-color

E

u

dd

u

Uncorrelated Pauli-paired

ud

d

ud

ud

↵3 ⇠ ↵4 ↵3 � ↵4

FIG. 1. Fix notation in plot from � to CF Visualizations ofsimplified models comparing SU(3) and SU(4) baryon polariz-abilities. In the case where charged constituents are uncorrelatedwithin the baryon, the size of the polarizabilities are expected tobe comparable. For the case in which opposite flavors are Pauli-paired (a-la dipoles), the SU(4) baryon polarizability would besuppressed compared to the SU(3) polarizability.

Nc even. The dominant modes of interaction with the stan-dard model are the polarizability operator, and direct Higgsboson exchange. The latter was studied in some detail in[19], placing bounds on the allowed dark Higgs couplings.In this work we study the polarizability, which unlike theHiggs interaction has no adjustable parameters, but ratheris completely determined by the strong dynamics once thegauge group and matter content are specified.

SU(4) baryons and polarizabilities – A full construc-tion of the stealth dark matter model is given in [? ]; herewe briefly summarize the relevant details. The dark sectorconsists of an unbroken SU(4) gauge theory, which con-tains baryonic bound states made up of four constituentfermions. The dark matter candidate itself is made up oftwo pairs of fermions which are degenerate in mass andcarry equal but opposite electric charges of ±1/2; the sym-metry properties of this candidate leave the electromag-netic polarizability as the dominant interaction with pho-tons.

The primary quantity in question is the strength of thebaryon polarizability in units of the dark matter (baryon)mass, from which we can derive an exclusion curve.Estimates from QCD have been made previously to be10

�48 cm2 [15], around the cross-sections when back-ground neutrinos are expected to contaminate the dark mat-ter recoil signal. However, these estimates have alwaysused naıve dimensional analysis (NDA) with uncontrollederrors of the interaction strength. This is one clear area thata lattice calculation can alleviate.

One plausible reason that NDA might not be sufficientfor these bosonic baryons is depicted in Fig 1. Froma simplified model stand-point, one could expect signifi-cantly different behaviors between 3-fermion baryons and4-fermion baryons depending on how the internal electriccharges are correlated. In one limit where the internal con-

stituents are uncorrelated, the polarizabilities are expectedto be comparable. However, if alternate flavors tend toform pairs based on their Pauli statistics, the 4-fermionbaryon polarizability would be derivative suppressed com-pared to the 3-fermion baryon (i.e. two dipoles vs. onedipole and one charge). Thus, the QCD, 3-fermion NDAestimate could be significantly different than the 4-fermionresult. To this end, we do lattice calculations of both SU(3)and SU(4) baryon polarizabilities to quantify this effect inaddition to calculating the relevant cross-section curves.

Polarizability and Direct Detection– The polarizabilityoperator can be written as an effective operator of the form

OF = CF �

†�F

µ⌫Fµ⌫ , (1)

where � is the scalar composite dark matter field. Thisis a two-photon vertex, so that the scattering off of nucleiwill involve a virtual photon loop. Because this operatoris induced at a high scale (roughly the dark confinementscale ⇤D ⇠ M�), it is expected to generate other interac-tions with SM particles when the appropriate effective fieldtheory matching and running down to the nuclear scale iscarried out [20–23]; in fact, an explicit treatment for the po-larizability operator is given in [24]. Although the effectsof these induced operators are not negligible in general, wefind that they are small compared to the uncertainties (par-ticularly from nuclear physics) in the leading interactionthrough Eq. 1, and we will therefore omit them here.

From the interaction shown above, the coherent darkmatter-nucleus scattering cross section (per nucleon) isgiven by

� ' µ

2n�

⇡A

2

D��CF f

AF

��2E

, (2)

where µn� = mnm�/(mn + m�), the angular bracketsrepresent the momentum-averaged form factors for heavydark matter candidates in a given experiment,

hf2i =

� Emax

Emin

dER Acc(ER)g(vmin[ER])f

2(ER), (3)

Acc(ER) is the acceptance of a given experiment andg(vmin) is the integrated dark matter velocity distributionas a function of the minimum velocity for a given recoilenergy, ER.

The primary source of systematic uncertainty in deter-mining the cross-section will be the method used for eval-uating the non-perturbative nuclear matrix element f

AF =

hA|F µ⌫Fµ⌫ |Ai. Due to its long-range nature, this matrix

element must be determined by a non-perturbative nuclearstructure calculation. Various attempts to estimate thesematrix elements have been performed with varying levelsof complexity in a perturbative set-up [24–26], but this ma-trix element has nontrivial excited state structures that re-quire a fully non-perturbative treatment not dissimilar fromdouble-beta decay matrix elements, which are not agreedupon within a factor of 5 [27, 28]. Until an accurate extrac-tion of this matrix element is performed, we will use naıve

E E

C

3F ⇠ C

4F C

3F � C

4F

FIG. 1. Visualizations of simplified models comparing SU(3) andSU(4) baryon polarizabilities. In the case where charged con-stituents are uncorrelated within the baryon, the size of the polar-izabilities are expected to be comparable. For the case in whichopposite flavors are Pauli-paired (a la dipoles), the SU(4) baryonpolarizability would be suppressed compared to the SU(3) polar-izability.

Higgs interaction has no adjustable parameters, but ratheris completely determined by the strong dynamics once thegauge group and matter content are specified.

SU(4) baryons and polarizabilities – A full construc-tion of the stealth DM model is given in [20]; here webriefly summarize the relevant details. The dark sectorconsists of an unbroken SU(4) gauge theory, which con-tains baryonic bound states made up of four constituentfermions. The DM candidate itself is made up of two pairsof fermions which are degenerate in mass and carry equalbut opposite electric charges of ±1/2; the symmetry prop-erties of this candidate leave the electromagnetic polariz-ability as the dominant interaction with photons.

The primary quantity in question is the strength of thebaryon polarizability in units of the DM (baryon) mass,from which we can derive an exclusion curve. Previous es-timates have led to direct-detection cross sections on the or-der of 10

�48 cm2 [16], approaching the interaction strengthat which background neutrinos are expected to contami-nate the DM recoil signal. However, these estimates relyon naıve dimensional analysis (NDA), which has uncon-trolled uncertainties.

One plausible reason that NDA might give misleadingresults for these bosonic baryons is depicted in Fig 1. Froma simplified model standpoint, one could expect signifi-cantly different behaviors between 3-fermion baryons and4-fermion baryons depending on how the internal electriccharges are correlated. In one limit where the internal con-stituents are uncorrelated, the polarizabilities are expectedto be comparable. However, if alternate flavors tend toform pairs based on their Pauli statistics, the 4-fermionbaryon polarizability would be derivative-suppressed com-pared to the 3-fermion baryon (i.e. two dipoles vs. onedipole and one charge). Thus, the QCD, 3-fermion NDAestimate could be significantly different than the 4-fermion

result. To this end, we perform lattice calculations for boththe SU(3) and SU(4) baryon polarizabilities to quantify thiseffect.

Polarizability and Direct Detection – The polarizabil-ity operator can be written as an effective operator of theform

OF = CF �

†�F

µ⌫Fµ⌫ , (1)

where � is the scalar composite DM field and Fµ⌫ is thestandard electromagnetic field strength tensor. This is atwo-photon vertex, so that the scattering off of nuclei willinvolve a virtual photon loop. Because this operator is in-duced at a high scale (roughly the dark confinement scale⇤D ⇠ M�), it is expected to generate other interactionswith SM particles when the appropriate effective field the-ory matching and running down to the nuclear scale arecarried out [22–25]; in fact, an explicit treatment for thepolarizability operator is given in [26]. Although the ef-fects of the additional induced operators are not negligiblein general, we find that they are small compared to the un-certainties (particularly from nuclear physics) in the lead-ing interaction through Eq. 1, and we will therefore omitthem here.

From the interaction shown above, the coherent DM-nucleus scattering cross section (per nucleon) is given by

� ' µ

2n�

⇡A

2

D��CF f

AF

��2E

, (2)

where µn� = mnm�/(mn + m�), A is the mass numberof the target nucleus, and the angular brackets representthe momentum-averaged form factors for heavy DM can-didates in a given experiment [26].

The primary source of systematic uncertainty in deter-mining the cross section will be the method used for eval-uating the non-perturbative nuclear matrix element, f

AF =

hA|F µ⌫Fµ⌫ |Ai. Due to its long-range nature, this matrix

element must be determined by a non-perturbative nuclearstructure calculation. Various attempts to estimate thesematrix elements have been performed with varying lev-els of complexity in a perturbative setup [26–28], but thismatrix element has nontrivial excited-state structures thatlikely require a fully non-perturbative treatment. This ma-trix element is similar to those needed for double-beta de-cay experiments, estimates for which have substantial vari-ation [29, 30]. Until a more accurate extraction of this ma-trix element is performed, we will use the naıve dimen-sional analysis arising from non-relativistic loop momentacounting,

f

AF ⇠ 3Z

2↵

M

AF

R

, (3)

where R = 1.2A

1/3 fm, as used in the double beta de-cay context, Z is the atomic number, ↵ is the fine-structureconstant, and M

AF is a dimensionless parameter which,

with the factor of 3 in front, approximately matches on tothe results of [26, 27] for heavy nuclei when M

AF = 1. In

• Background field method: response of neutral baryon to external electric field

• Measure the shift of the baryon mass as a function of

!

!

• Precise lattice results

Lattice: Polarizability of DM[LSD collab., in preparation]

[Detmold, Tiburzi & Walker-Loud, Phys. Rev. D79 (2009) 094505 and Phys. Rev. D81 (2010) 054502]

preliminary

preliminary

SU(3)

SU(4)ESU(4) = M� +

1

2

(C�F )E

2+ h.o.

ESU(3) = M� +

1

2

(C�F +

µ2

4M3�

)E2+ h.o.

E

E

• several attempts to estimate this in the past, with increasing level of complexity in a perturbative setup

• multiple scales are probed by the momentum transfer in the virtual photons loop

• mixing operators and threshold corrections appear at leading order and interference is possible

• nuclear matrix element has non-trivial excited state structure that requires non-perturbative treatment

Nuclear: Polarizability (Rayleigh scattering)

[Weiner & Yavin, Phys. Rev. D86 (2012) 075021][Frandsen et al., JCAP 1210 (2012) 033]

[Pospelov & Veldhuis, Phys. Lett. B480 (2000) 181]

[Ovanesyan & Vecchi, arxiv:1410.0601]

q

q

q

��

Q Q

Q

g g

A A

A

MM

OMMM

OMMM

OM

Figure 1. One-loop Feynman graphs showing the contributions to the DM-nucleus cross sectionin the case of OM . Mixing diagram generating OM

q (left), matching contribution giving rise to OMG

(middle), and matrix element describing the low-energy two-photon scattering of DM on the nucleus(right). See text for further details.

where eq is the electric charge of the quark q and mt < µ < M⇤. Notice that we have assumedthat the Wilson coe�cient of OM

q vanishes at M⇤.

We now evolve the Wilson coe�cient CMq from M⇤ down to mt, where we integrate out

the top quark. Removing the heavy quark as an active degree of freedom gives rise to a finitethreshold correction to the Wilson coe�cient of the operator

OMG = CM

G MMG

a,µ⌫G

aµ⌫ , (4.3)

where G

a,µ⌫ denotes the field strength tensor of QCD. The relevant leading-order (LO) di-agram is shown in the middle of Figure 1. The corresponding matching is captured by thesimple replacement [30]

mtMMtt CMt (mt) ! MMG

a,µ⌫G

aµ⌫ CM

G (mt) , (4.4)

with CMG given at next-to-leading order (NLO) by

CMG (mt) = �↵s(mt)

12⇡

�1 + �t

� CMt (mt) , (4.5)

where �t = 11↵s(mt)/(4⇡) [31]. Although �t is formally of higher order, we will include suchfinite two-loop contributions in our analysis, because they are numerically non-negligible.Notice that once the top quark has been removed, the Wilson coe�cient CM

t and the corre-sponding logarithm is frozen at the threshold mt in the EFT.

After the top quark has been integrated out, we then have to consider the mixing ofthe set of three operators OM , OM

q and OMG . Like OM the operator OM

G mixes into OMq .

The relevant diagram is the QCD counterpart of the one displayed on the left in Figure 1with the photons replaced by gluons. As shown in Appendix B, the associated correctionsare subleading and we will neglect them in what follows. The operator OM

G itself evolves likethe QCD coupling constant, so that for scales mb < µ < mt its Wilson coe�cient takes theform

CMG (µ) ' ↵

⇡

↵s(µ)

⇡

e

2t

4

�1 + �t

�ln

✓M

2⇤

m

2t

◆CM (M⇤) . (4.6)

At the scales mb and mc, the bottom and charm quarks are integrated out, which infull analogy to (4.5) results in finite matching corrections to CM

G . Including all heavy-quark

– 6 –

similar structure arising in double beta decay matrix elements

hA|��Fµ⌫Fµ⌫ |Ai

NDA for• it is hard to extract the momentum

dependence of this nuclear form factor

• similarities with the double-beta decay nuclear matrix element could suggest large uncertainties ~

• to asses the impact of uncertainties on the total cross section we start from naive dimensional analysis

• we allow a “magnitude” factor to change from 0.3 to 3

q

q

q

��

Q Q

Q

g g

A A

A

MM

OMMM

OMMM

OM

Figure 1. One-loop Feynman graphs showing the contributions to the DM-nucleus cross sectionin the case of OM . Mixing diagram generating OM

q (left), matching contribution giving rise to OMG

(middle), and matrix element describing the low-energy two-photon scattering of DM on the nucleus(right). See text for further details.

where eq is the electric charge of the quark q and mt < µ < M⇤. Notice that we have assumedthat the Wilson coe�cient of OM

q vanishes at M⇤.

We now evolve the Wilson coe�cient CMq from M⇤ down to mt, where we integrate out

the top quark. Removing the heavy quark as an active degree of freedom gives rise to a finitethreshold correction to the Wilson coe�cient of the operator

OMG = CM

G MMG

a,µ⌫G

aµ⌫ , (4.3)

where G

a,µ⌫ denotes the field strength tensor of QCD. The relevant leading-order (LO) di-agram is shown in the middle of Figure 1. The corresponding matching is captured by thesimple replacement [30]

mtMMtt CMt (mt) ! MMG

a,µ⌫G

aµ⌫ CM

G (mt) , (4.4)

with CMG given at next-to-leading order (NLO) by

CMG (mt) = �↵s(mt)

12⇡

�1 + �t

� CMt (mt) , (4.5)

where �t = 11↵s(mt)/(4⇡) [31]. Although �t is formally of higher order, we will include suchfinite two-loop contributions in our analysis, because they are numerically non-negligible.Notice that once the top quark has been removed, the Wilson coe�cient CM

t and the corre-sponding logarithm is frozen at the threshold mt in the EFT.

After the top quark has been integrated out, we then have to consider the mixing ofthe set of three operators OM , OM

q and OMG . Like OM the operator OM

G mixes into OMq .

The relevant diagram is the QCD counterpart of the one displayed on the left in Figure 1with the photons replaced by gluons. As shown in Appendix B, the associated correctionsare subleading and we will neglect them in what follows. The operator OM

G itself evolves likethe QCD coupling constant, so that for scales mb < µ < mt its Wilson coe�cient takes theform

CMG (µ) ' ↵

⇡

↵s(µ)

⇡

e

2t

4

�1 + �t

�ln

✓M

2⇤

m

2t

◆CM (M⇤) . (4.6)

At the scales mb and mc, the bottom and charm quarks are integrated out, which infull analogy to (4.5) results in finite matching corrections to CM

G . Including all heavy-quark

– 6 –

MAF

hA|��Fµ⌫Fµ⌫ |Ai

O(5)

� 'µ2n�

⇡A2

D|CF f

AF |2

EfAF ⇠ 3Z2 ↵

MAF

R

fAF = hA|Fµ⌫Fµ⌫ |Ai

Stealth DM Polarizability

preliminary


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1 10 100 1000 10410!5010!4910!4810!4710!4610!4510!4410!4310!4210!4110!4010!39

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WIMP Mass !GeV"c2#



7BeNeutrinos



8BNeutrinos


CDMS II Ge (2009)

Xenon100 (2012)

CRESST

CoGeNT(2012)

CDMS Si(2013)

EDELWEISS (2011)

DAMA SIMPLE (2012)




SuperCDMS Soudan

Xenon1T

LZ

LUX

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DEAP3600

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PICO250-C3F8

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1 10 100 1000 10410!5010!4910!4810!4710!4610!4510!4410!4310!4210!4110!4010!39

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WIMP Mass !GeV"c2#



7BeNeutrinos



8BNeutrinos


CDMS II Ge (2009)

Xenon100 (2012)

CRESST

CoGeNT(2012)

CDMS Si(2013)

EDELWEISS (2011)

DAMA SIMPLE (2012)




SuperCDMS Soudan

Xenon1T

LZ

LUX

DarkSide G2

DarkSide 50

DEAP3600

PICO250-CF3I

PICO250-C3F8

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LSD paper to appear next week.

1 10 100 1000 10410!5010!4910!4810!4710!4610!4510!4410!4310!4210!4110!4010!39

10!1410!1310!1210!1110!1010!910!810!710!610!510!410!3

WIMP Mass !GeV"c2#



7BeNeutrinos



8BNeutrinos


CDMS II Ge (2009)

Xenon100 (2012)

CRESST

CoGeNT(2012)

CDMS Si(2013)

EDELWEISS (2011)

DAMA SIMPLE (2012)




SuperCDMS Soudan

Xenon1T

LZ

LUX

DarkSide G2

DarkSide 50

DEAP3600

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LSD paper to appear next week.

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10!1410!1310!1210!1110!1010!910!810!710!610!510!410!3

WIMP Mass !GeV"c2#



7BeNeutrinos



8BNeutrinos


CDMS II Ge (2009)

Xenon100 (2012)

CRESST

CoGeNT(2012)

CDMS Si(2013)

EDELWEISS (2011)

DAMA SIMPLE (2012)




SuperCDMS Soudan

Xenon1T

LZ

LUX

DarkSide G2

DarkSide 50

DEAP3600

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Direct detection signal is below the neutrino coherent scattering background for MB>1TeV

LSD paper to appear next week.Reason for “STEALTH” name

Concluding remarks• BSM physics has many opportunities for

composite particles, e.g. dark matter.

• Dark matter constituents can carry electroweak charges and still the stable composites are currently undetectable. Stealth!

• No new forces required beyond SU(N) confining dark color force.

• Abundance can arise either by symmetric thermal freeze-out or by asymmetric baryogenesis.

• Future experiments could eventually rule out dark baryons with mag moments.

• Composite dark matter around 1 GeV is still a challenge due to LEP bounds.

• We need to work harder to inform the broader DM community about our exciting results!

- Max Planck

"A new scientific truth does not triumph by convincing its opponents and making them see

the light, but rather because its opponents eventually die, and a new generation grows up

that is familiar with it.”

Backup slides

A Composite “Miracle”(I)

• For Mdm ~ 100 GeV and α ~ 0.01 can be a thermal relic, but such WIMPs are being ruled out by XENON100/LUX.

• Current bounds on composite fermion dark matter are Mdm>20 TeV [LSD Collab., Phys. Rev. D 88, 014502 (2013)].

• Analogous to NN annihilation,α ~ 16 which would mean Mdm ~ 320 TeV. Not ruled out but not likely to be observed soon.

• But, by dialing up the quark masses, we can bring down α to make a thermal relic Mdm ~ 20 TeV.

• Challenge: quark mass dependence of NN annihilation, incl. heavy quarks.

• Strongly-interacting DM also helps with “Too Big To Fail” problem.

Asymmetric dark matterS. Barr, R. S. Chivukula, and E. Farhi, Phys. Lett. B241 (1990) 387D. B. Kaplan, Phys. Rev. Lett. 68 (1992) 741

S. Nussinov, Phys. Lett. B165 (1985) 55

Asymmetric dark matter

• It is an observational fact that the number density for dark matter and baryonic matter are of the same order of magnitude

⌦DM ⇡ 5 ⌦B

[Planck and ESA]

S. Barr, R. S. Chivukula, and E. Farhi, Phys. Lett. B241 (1990) 387D. B. Kaplan, Phys. Rev. Lett. 68 (1992) 741




• This can be explained in Technicolor theories where dark matter is a baryon of a new strongly-coupled sector which shares an asymmetry with standard baryonic matter

⌦DM ⇡ 5 ⌦B

nDM � nDM ⇡ nB � nB

[Planck and ESA]





• This can be explained in Technicolor theories where dark matter is a baryon of a new strongly-coupled sector which shares an asymmetry with standard baryonic matter

⌦DM ⇡ 5 ⌦B

nDM � nDM ⇡ nB � nB

[Planck and ESA]

2

20

0

10

15

5

100 8642m

/T

X

Dρ /ρDM B

T = 10 GeV

T = 20 GeV

T = 1000 GeV

T = 100 GeV

T = 200 GeV

D

D

DD

D

FIG. 1: The ratio of dark matter energy density ⇢DM

to baryon energy density ⇢B as a function of dark matter mass mX inunits of the temperature at which the B �X transfer decouples TD, for labeled values of TD. As light solution (correspondingto mX/TD ⇠ 0 is not shown. See Section II and Eq. (6) for detailed explanation. The observed ratio of ⇢

DM

/⇢B is 5.86 [21].

These mechanisms have been successfully applied to generate the relevant energy densities in the context of anexisting baryon asymmetry being transferred to light dark matter, though mechanisms named darkogenesis [17] andhylogenesis [18] have also been suggested which transfer the asymmetry in the opposite direction. If, on the otherhand, dark matter is not relativistic at the temperature TD at which the X-transfer operators decouple, then thenumber density of dark matter is suppressed. In general, we find when the ratio mX/TD is about 10, we get therequired density of dark matter compared to baryons in the Universe. This thermal suppression is a generic feature,allowing heavy dark matter in many scenarios of Xogenesis.

We also discuss two other reasons that dark matter number density might be suppressed relative to baryon numberso that dark matter can naturally be weak scale in mass.. In the first, the SU(2)L sphaleron transfer is only active fora bounded temperature range between the masses of two doublets whose net number density would cancel if they weredegenerate [22]. In the second, excess X-number is bled o↵ into leptons. That is, even after the baryon asymmetryis established (possibly at the sphaleron temperature where a lepton asymmetry gets transferred into an asymmetryin the baryon sector), X- and lepton-number violating operators are still in thermal equilibrium allowing X numberdensity to be reduced while lepton number density is increased. Both these mechanisms cause the transfer to baryonsto not be active for the entire temperature range down to TD when the X-number violating operators decouple.

Xogenesis models must also remove the symmetric thermally produced dark matter component, so that the asym-metric component dominates. When the transfer mechanism is due to higher order operators, the operators necessaryto transfer the asymmetry may also lead to the annihilation of this component. In other examples, new interactionsare assumed, which in some cases also lead to detectable signatures. A new non-abelian W 0 with masses much belowmW allows the dark matter to annihilate into dark gauge bosons, but with few – if any – direct detection constraintsand probably no visible signatures in the near future. Annihilation via a light Z 0 that mixes with the photon allowsthe chance for direct detection, depending on the size of the mixing parameter. While not strictly necessary, thephoton-Z 0 mixing is a generic property, and may be accessible in beam experiments [23].

We also note one additional constraint that applies to supersymmetric models in which higher dimension operatorslink X to L or B via the lepton or baryon superpartners. In these cases, the neutralinos that come from thesuperpartner decay must also be eliminated via self-annihilation. This generally implies that the neutralino shouldbe primarily wino so that the annihilation cross section is su�ciently large to make the neutralino component of darkmatter a small percentage of the total.

[Buckley & Randall, JHEP1109 (2011)]


higher dimensional operators

nDM ⇡ nB ! MDM ⇡ 5 MB

sphaleron processes

MDM � MB ! nB � nB ⇡ e�MDM/T?


A Composite “Miracle”(II)

10�2 10�1 100 101 102

M� = MB [TeV]

10�16

10�14

10�12

10�10

10�8

10�6

10�4

10�2

100

102

104

Rat

e,ev

ent/

(kg·

day)

Nf = 2

Nf = 6


• [LSD Collab., Phys. Rev. D 88, 014502 (2013)]

• Composite fermion dark matter from new vector-like SU(3) gauge theory with Dirac mass terms. Can be a thermal relic.

• Solid lines: magnetic moment. Dashed lines: charge radius.

SU(3) SU(2) U(1) SU(3)

Q 1 1 2/3 3

Q 1 1 -1/3 3

Q 1 1 0 3

Stealth Dark Matter (I)• Composite dark matter can be lighter than 20 TeV if the leading

low-energy interaction is dim. 7 polarizability.

• Requires even Nc so that baryons are scalars to eliminate magnetic moment interaction.

• Requires a global SU(2) custodial symmetry to eliminate charge radius interaction.

• Minimal coupling to weak SU(2) to enable dark pion decay. Now some coupling to Higgs boson.

• Also need vector-like masses so that dark sector doesn’t impact Higgs vacuum alignment.

• Minimal model: Dark SU(4) color with Nf = 4 Dirac flavors.

Stealth Dark Matter (II)• Stable dark baryon is (ψ1u ψ1u ψ1d ψ1d).

• Splitting between ψ1 and ψ2 Dirac doublets due either to vector mass splitting Δ or Yukawa couplings y.

• Coupling to Higgs can be made as small as needed (not a fine tuning) so that polarizability is dominant DM interaction, yet large enough to ensure no relic density of dark pions.

• Higgs VEV still dominates electroweak vacuum alignment and contributions to S and T parameters are small.

SU(4) Polarizability

• Coherent DM-nucleus cross section:

• Nuclear matrix element [O(3) uncertainty]:

• Direct detection signal below neutrino background for MB > 1 TeV. Stealth!

1 10 100 1000 10410!5010!4910!4810!4710!4610!4510!4410!4310!4210!4110!4010!39

10!1410!1310!1210!1110!1010!910!810!710!610!510!410!3

WIMP Mass !GeV"c2#



7BeNeutrinos



8BNeutrinos


CDMS II Ge (2009)

Xenon100 (2012)

CRESST

CoGeNT(2012)

CDMS Si(2013)

EDELWEISS (2011)

DAMA SIMPLE (2012)




SuperCDMS Soudan

Xenon1T

LZ

LUX

DarkSide G2

DarkSide 50

DEAP3600

PICO250-CF3I

PICO250-C3F8

SNOLAB

SuperCDMS

� 'µ2n�

⇡A

D��CF fAF

��2E

fAF = hA |Fµ⌫Fµ⌫ |Ai

E0(E) = MB + 2CF |E|2|E|2

Documents

Composite Dark Matter - kmi.nagoya-u.ac.jp