Sub-GeV Dark Matter
Kenji Kadota
IBS Center for Theoretical Physics of the Universe (CTPU)
Institute for Basic Science, Korea

A Korean-government-funded research institute establ

Mass: Light massunder the Special Act on Establishment of and SupporØ Concrete example for light DM:

Science and Business Belts

ü Sterile neutrino DM
ü Axion-like Particle
ü AxionInteractions: beyond ΛCDM
DM-baryon interactions with a light mediatorØ Concrete example for light mediator:
ü Dark photon

Kenji Kadota (IBS)

http://www.ibs.re.kr/

Osaka Axion workshop, Dec 2017searches can’t
prove it’s
Direct detection experiments
SUSY

Motivation for sub-GeV

solar neutrino

atmospheric neutrino

Kenji Kadota (IBS)Osaka Axion workshop, Dec 2017

Snowmass 2013

10

Cosmologicalmotivation
for sub-GeV: Small scale suppressions
M. Vogelsberger
et al.
How c

4

How c

M. Vogelsberger et al.

(Vogelsberger et al (2016))

Figure 6.Kenji
DM Kadota
density (IBS)
projections of the zoom MW-like halo
simulations
four different
DM models. The suppression of substructure, relative to the CDM
OsakaAxion forworkshop,Dec 2017
model, is evident for the ETHOS models ETHOS-1 to ETHOS-3, which have a primordial power spectrum suppressed at small scales. The projection has aside length and depth of 500 kpc.

Sub-GeV Dark Matter
Kenji Kadota
IBS Center for Theoretical Physics of the Universe (CTPU)
Institute for Basic Science, Korea

A Korean-government-funded research institute establ

Mass: Light massunder the Special Act on Establishment of and SupporØ Concrete example for light DM:

Science and Business Belts

ü Sterile neutrino DM
ü Axion-like Particle
ü AxionInteractions: beyond ΛCDM
DM-baryon interactions with a light mediatorØ Concrete example for light mediator:
ü Dark photon

Kenji Kadota (IBS)

http://www.ibs.re.kr/

Osaka Axion workshop, Dec 2017

scales: 0.5/h-50/h com. Mpc

1.00
MIKE&HIRESAge of the Universe: 1-3 Gyr

62F(k)

z=5.4

0.10

z=5
z=4.6
z=4.2

A concrete example for the warm dark matter: Sterile Neutrinos
z=4.0
z=3.8
z=3.6
z=3.4
z=3.2

best fit

z=3

SDSS

z=2.8

Dodelson-Widrow
mechanism: Thermal active neutrinos conversion to sterile neutrinos
0.01
WDM thermal relic 2keV

z=2.6
z=2.4
z=2.2

0.001

0.100
1
MNN
2

0.010

L = − yNLHk (s/km)
−

y H
M

θ =

10-7
10-8
10-9

10

-10

10-11

Tremaine-Gunn / Lyman-αInteraction strength Sin2(2θ)

Figure 17. Best fit model for the data sets used in the analysis (SDSS+HIRES+MIKE) shown as
green curves. We also show a WDM model that has the best fit values of the green model except for
the WDM (thermal relic) mass of 2 keV (red dashed curves). These data span about two orders ofmagnitude in scale and the period 1.1-3.1 Gyrs after the Big Bang. From this plot is is apparent how
the WDM model does not fit the data at small scales and high redshift.

DM overproduction
Excluded by X-ray observations

e⌥
N

Ue

⌫e
W±

Figure 18. Decay channels of the sterile neutrino
N with the mass below twiceP the electron mass.
P
Left panel: dominant decay channel to three (anti)neutrinos. Right panel shows radiative decay
channel that allows to look for the signal of sterile neutrino DM in the spectra of DM dominatedobjects.

10-12panel). The decay width of this process is about 128 times smaller that the main into active
neutrinos ⌫a and photon with energy E = ms /2, with the width [485, 766]10-13= 256 · 4⇡ sin 2✓ m = 5.5 ⇥ 10 ✓ 1 keV s .
N ! ⌫a10-14

9 ↵ G2F

2

5
s

4

22 2

h m

s

i5

1

(4.13)

X

X

Figure 16. Evolution of the phase space density in time: initially occupying the compact region (leftpanel) particles spread over the phase space (right panel). The volume remains intact, but the coarse
grained– 70phase– space density decreases in the dense regions.

1

2
5
10
Drewes et al (2016)50
Dark matter mass MDM [keV]

which are provided by observations of the stellar dynamics in the smallest structures, dwarf
spheroidal galaxies, [378]M /pc3Q = (0.005 0.02).
(4.4)(km/s)The galaxies are compact and dim with mass strongly dominated even in the central part by
the DM component. Hence, one has ⇢0 = MX nX with nX standing for the number densityof the DM particles in the galaxy center. For the spheroidal dwarfs one can substitutehvk2 i = hv2 i/3, where hv2 i is the average squared velocity. For the DM particles with average
2 hv2 i.
squared momentum hp2 i = MX
Collecting all terms together we arrive atn
2 (p, X, t ) ,Q = 3 Mangle' 3sin
M f˜(2✓)
Figure 19. Limits on the mixing
as a function of sterile neutrino DM mass. The
hp i
in the last equality we used
the phase space
distributionof DM particles in thegalaxy2017
Kenji Kadota (IBS)
Osaka
Axion
workshop,Decbounds are based onwhere
theworks [270,
449,
466,
469, 480,
499, 500, 500, 501, 503, 504, 776, 780–
center, x ' 0 at present, t = t . Then from eq. (4.3) we obtain the lower limit on the DM
particle mass known as the Tremaine–Gunn-type bound [74],784, 787–789, 791, 792, 794, 795, 854]. ✓All bounds
are smoothed and additionally divided by a factor
◆
3/2

4
X

3/2

4
X

2 3/2

0

MX &

1/4

Q

3/2

˜

0

Production from (active-sterile) neutrino oscillation

ΩN> ΩDM

X-ray

ΩN< ΩDM

Cherry,Horiuch(2017)

Kenji Kadota (IBS)Osaka Axion workshop, Dec 2017

esaw mechanism. We also demonstrate that, in our scenario,
the decay of a heavier RHN is subdominant compared with
the X-ray and small scale structure constraints.

re mass [1, 2],
mixinghoweverus (andnaturence forAn inld be toeutrinoan wellng theirmmetryDMtight
constraints
heavily depend
the production
mechanism!
X-ray
andon DM
lifetimeboundson the DM masscan be evaded because our scenario does not necessarily requireDM
mixingwith SM neutrinos and the desir1) Active-Sterile
neutrino
oscillation(e.g. Dodelson-Widrow)able sterile RHN DM abundance can be realized for both2) Active-Sterile
neutrino
oscillation
the resonance(e.g. Shi-Fuller)
warm and
cold
DMwithmass
ranges.
3) Decay of a heavier particle, Thermal freeze-out, variable mixing angle, ...
( e.g. Kusenko, Petraki, Asaka, Shaposhnikov, Merle, Schneider ,Berlin, Hooper,.. )

II.

SETUP

4) Sterile-sterile
oscillation! (KK and we
Kanetastudy(2017)) is the SM with three MajoThe Lagrangian

rana
RHNs,
given
by
Also
the left-handed
neutrino
massesvia the seesaw mechanism!
L = LSM + LN ,
cT/ R
LN = ⌫ R i@⌫
⌫R
y⌫ LH

Ω N1h 2 ∝ sin 2 2θ N M1 (yν yν+ )22

(1)
1 cT
c
⌫R MN ⌫R
+ h.c. ,
2
(2)

e RHN
where LSM is the SM Lagrangian, and H, L, ⌫R are,in parrespectively, Higgs doublet, lepton doublet and RHN.
Osaka Axion workshop, Dec 2017
f sterile Kenji Kadota (IBS)
While we have omitted flavor indexes, the neutrino
ur pro-Sub-GeV Dark Matter
Kenji Kadota
IBS Center for Theoretical Physics of the Universe (CTPU)
Institute for Basic Science, Korea

A Korean-government-funded research institute establ

Mass: Light massunder the Special Act on Establishment of and SupporØ Concrete example for light DM:

Science and Business Belts

ü Sterile neutrino DM
ü Axion-like Particle
ü AxionInteractions: beyond ΛCDM
DM-baryon interactions with a light mediatorØ Concrete example for light mediator:
ü Dark photon

Kenji Kadota (IBS)

http://www.ibs.re.kr/

Osaka Axion workshop, Dec 2017

Model: ALP (Axion-like particles) i.e. Ultra-light scalars
10000• Ultra-light mass :density contrast: δ

mu ~ H 0 ~ 10

−33

1000

eV

mu ~ 10 −22 eV

CDM (k=0.1 h/Mpc)
ULPs (k=0.1 h/Mpc))
CDM (k=0.001 h/Mpc))
ULPs (k=0.001 h/Mpc)

100

DE (Barbieri et al (2005),…)
Fuzzy DM (Hu (2000),…)String axiverse (Arvanitaki et al (2009),...)
10
1

0.1

0.01

0.001

0.0001mu ~ 10−22eV −10

−10

eV

1e-07

1e-06

1e-05

0.00010.001

scale factor:

Figure1:uTheperturbation
evolutions for ULPs (mu , f= Ω/ Ω~ O(0.01)ummu ≤ H (t ) : ρ u = const
mu > H (t ) : ρ u ∝ 1 / a 3

KK, Mao, Ichiki, Silk (2014)
1.1
1
0.9

P(k) ratio

P(k)[(Mpc/h)3]

10000

1000

0.8
0.7
0.6

100
0.001

Linear: fu=0
fu=0.05
Nonlinear: fu=0
fu=0.05
0.01

0.5

0.1

1

0.4
0.0

k [h/Mpc]

Figure2: Left:Kenji Kadota
(IBS)
5

The
(linearand nonlinear) power spectr
Osaka Axion
workshop, Dec 2017
mu = 10 H0 , fu = 0.05. Right: The transfer function T
the ratio of the power spectrum including the ULPs (f−33

21 cm signals
1420 MHz

Kenji Kadota (IBS)Osaka Axion workshop, Dec 2017

Years since
the Big Bang
~300000(z~1000)

Brief History of Universe
ß Big Bang:the Universe is filled with ionized gas
ß Recombination:The gas cools and becomes neutral

Dark Ages~100 million(z~20-40)

ß The first structures begin to form.
Reionization starts (z ~12)

Reionization~1 billion(z~6)~13 billion(z=0)
Kenji Kadota (IBS)ß Reionization is completeß Today’s structures
Osaka Axion workshop, Dec 2017

Square Kilometer ArraySouth Africa- Karoo
Australia- Western Outback

dio Technology The Square Kilometre Array
Construction 2019-2025, Early Science 2022-, Full Science 2025-2030
Cost: ~650 M Euros, Operation ~ 50 M Euros per year.

Project Description for Astro2010
Response to Program Prioritization Panels
1 April 2009

Contact Author:
James Cordes
Chair, US SKA Consortium
607 255‐0608
Cornell University
cordes@astro.cornell.edu

CERN-SKA Big data co-operation agreement

Kenji Kadota (IBS)Osaka Axion workshop, Dec 2017

Authors and Participants:

What can we do with 21cm?
High precision on small-scale power spectrum

ΔP / P ~ 1 /N

4Kleban+(2007)

0.024

mu=1e3

0.022. 1: The scales probed by cosmic microwave background anisotropies(solid line ) and cosmic 21-cmmfluctuations(dashedu=1e5=1e7) ≃ 13.6 Gpc is). The two power spectra have been aligned using the small-scale relation k ≃ l/dA (zCMB ), where dA m
(zuCMB
0.02
comoving angular diameter distance at the surface of recombination in
the standard cosmological model.

∂ Vr
∂r

=

H (z )∂ (v · r̂)
+
.
1 + z
∂r

(8)

mbining Eqs. (7) and (8) and expanding to linear orwe findδTb = −T b

∂ Tb
1 + z ∂ vr+
δ,
H (z ) ∂ r∂δKenji Kadota (IBS)

(9)

0.018
is the peculiar velocity in the radial direction, and δ =0.016(nH − n
H )/nH is the overdensity of the gas.
Moving to Fourier space, we find
0.014
1 + z
∂ Tb
2
!
(10)
0.012 δ Tb = −T b H (z ) µ (ik ṽ) + ∂ δ δ̃,
" 2
#
!
(11)
0.01 δ Tb = T b µ + ξ δ̃,fν

asured in a radial direction r̂ at redshift z (corrending to 21-cm radiation observed at frequency ν =λ21 (1 + z )]). Here, A is the Einstein spontaneous emisn coeﬃcient for the 21-cm transition, Vr is the physvelocity in the radial direction (including both thebble flow and the peculiar velocity of the gas v), and/∂ r is the velocity gradient in the radial direction.
plicitly, we havewhere 0.008µ = k̂ · r̂ = cos θk is the cosine of the angle
between the radial direction and the direction of the
0.006 k, and ξ is defined by ξ ≡ (1/T b )(∂ Tb /∂ δ).
wavevector
The second line, Eq. (11), uses the additional relation
0.004δ̃ = −(ikṽ)(1 + z )/H , which is, strictly speaking, valid
00.02than0.04 the0.06 Jean’s
0.08
0.1 length
0.12 0.14
0.16 0.18
on scales larger
duringthe matfu
ter dominated epoch. The total
brightness-temperature
power spectrum is thus [32, 51]

Osaka Axion workshop, Dec 2017

Oyama+(2013)

ontoursof 90%
forecasts
in Σmν -Nere
T b is themean C.L.
brightness
temperature,vr ν= plane,v · r̂

KK, Mao, Ichiki, Silk (2014)3′!b (k)δ
!b (k′ )⟩ =by adopting
Planck+ (2π)
Polarbear
21 cm
expe
⟨δ T
T
δ (3) (k + k+
)Peach(12)
T (k),), or CMBPol + each 21 cm experiment (right two panels). Fiducial values of neutrino parameters, Nν anb

Figure 3: 1σ error contour for the ULP and neutrino fractions with respect to t

Kelley, Quinn [ApJ Letter (2017)]

Figure 3.

The sensitivity of SKA-mid shows considerable
improvement on the pre-cursor telescopes, the Australian
SKA Pathfinder (ASKAP) and the Karoo Array Telescope
Kenji Kadota (IBS)Osaka
Axion workshop,
Dec 2017(MEERKAT).
In thisFigureweshow the coupling strengththat could be probed by observing the Interstellar Medium

Sub-GeV Dark Matter
Kenji Kadota
IBS Center for Theoretical Physics of the Universe (CTPU)
Institute for Basic Science, Korea

A Korean-government-funded research institute establ

Mass: Light massunder the Special Act on Establishment of and SupporØ Concrete example for light DM:

Science and Business Belts

ü Sterile neutrino DM
ü Axion-like Particle
ü AxionInteractions: beyond ΛCDM
DM-baryon interactions with a light mediatorØ Concrete example for light mediator:
ü Dark photon

Kenji Kadota (IBS)

http://www.ibs.re.kr/

Osaka Axion workshop, Dec 2017

−

ε
2

DM
DM

γD

Z µν F µνε×γ

Field re-definition to themass eigenstates (ie physical states)(B. Holdom (1986))

εe

DM
DM

Kenji Kadota (IBS)γDOsaka Axion workshop, Dec 2017

COBE

Launched on Nov.
rocket.

DIRBE: Measured
brightness in the
wavelength range
Infrared Backgrou

FIRAS: Measured t
CMB, finding it to
blackbody with T0

DMR: Found “anisCMB for the first t
part in 105

CMB spectral distortion: FIRAS: |μ|<9×10-5

2
N
pr
ph

Credit: NASA

Observational Cosmology

Kenji Kadota (IBS)Osaka Axion workshop, Dec
2017

Lectures 4+5 (K. Basu): CMBThermal equilibrium:
Chemical equilibrium: Creation and destruction of photons
Radiative (double) Compton scattering: e + γ ↔ e + γ + γ
Bremsstrahlung:e + N ↔ e + N +γ
Kinetic equilibrium: Energy distribution changes by scattering
Compton scattering:e +γ ↔ e +γ
μ-type distortion: The number stays same but modifies the phase space distribution
Thomson scattering:e +γ ↔ e +γ
y-type distortions: Kinematically decouple too, so it just adds energy shifte+/e−annihilation
9

CMB

8

Bang

Blackbody
Photosphere

z=2x10

y

µ

6

z=10

Khatri&Sunyaev’12

5
3

z=10

Kenji Kadota (IBS)y ~ σ T nekTe

Reionization...

f = [e(E−µ )/T −1]−1Last scattering surface

Big

Blackbody surface

10 > z > 10
BBN 8
z ~ 3x10

z=30

z=6

z=0

a

Osaka Axion workshop, Dec 2017

Figure 1. Important events in the history of the CMB spectrum and anisotropy formation in big bang cos-‘Early’ Energy Release (z ≥ 50000)

 y-type spectral distortion

 µ-type spectral distortion

Processµ
electron-positron annihilation
10−178up-scatteringof photons
BBN tritium decay
2× 10−15
BBN 7Be decay
10−16
WIMP dark matter annihilation 3 × 10−9 fγ 10GeV
mWIMP−8Silk damping
10 − 10−9
Adiabatic cooling of matter and
Bose-Einstein condensation −2.7 × 10−9
Zeldovich, Sunyaev (1969)

Table 1. Census ofZeldovich,energy release Sunyaev
and µ distortions
in standard cosmological model. The neg(1970)
from adiabatic cooling of matter is shown in red.

Sunyaev & Zeldovich, 1970, Ap&SS, 7, pp.20-30
Zeldovich & Sunyaev, 1969, Ap&SS, 4, pp. 301
Illarionov & Sunyaev, 1975, Sov.Astr., 18, pp. 413−5Sunyaev −5
Zeldovich, 1980, ARAA, 18, 537
Danese & de Zotti, 1982, A&A, 107,
39-42
µ < 9 ×10 (95%CL), y < 1.2
×10 & (95%CL)

Current Limits:

PIXIE: |μ|~10-8

Kenji Kadota (IBS)

ProcessµProcessyelectron-positron annihilation
10−178−10 f 10GeV
−15
WIMP
dark
matterannihilation
6×10
γ mWIMPBBN tritium decay
2 × 10
Silk damping
10−8 − 10−9
BBN 7Be decay
10−16
Adiabatic cooling of matter and
WIMP dark matter annihilation 3 × 10−9 fγ 10GeV
mWIMP
Silk damping
10−8 − 10−9
Bose-Einstein condensation−6 × 10−10
Adiabatic cooling of matter andReionization
10−7
Bose-Einstein condensation−2.7workshop,× 10−9 Dec 2017 Mixing of blackbodies: CMB ℓ ≥ 2 multipoles 8 × 10−10
Osaka Axion• $200M Cost Cap + launchvehicle• 22 full missions
PIXIE not selected; urged to re-propose• Category I science rating• Broad recognition of science appeal• Absolute spectra “guaranteedscience”
Re-propose to next full Explorer AO• 2015 proposal for 2021 launch?

Primordial Inflation Explorer
Name

Role

Institution

A. KogutPI

GSFC

D. Fixsen

IS

UMD

D. Chuss

Co-I

GSFC

J. Dotson

Co-I

ARC

E. Dwek

Co-I

GSFC

M. Halpern

Co-I

UBC

G. Hinshaw

Co-I

UBC

S. Meyer

Co-I

U. Chicago

H. Moseley

Co-I

GSFC

M. Seiffert

Co-I

JPL

D. Spergel

Co-I

Princeton

E. Wollack

Co-I

GSFC

PIXIE: |μ|~10-8
Choi, KK and Park (2017)

Dark Photon Model−ε2

Z µν F µν

Spectral Distortions Provide New Window to Early Universe

targetRESULTS AND PERSPECTIVES IN DARK PHOTON PHYSICS

Figure 1: Elastic scattering between baryone−( ) and DM ( )shieldthrough a dark photon (Zd ) exchange.

b

b

b

detector

γ
e−
E
e+
E
0 γ3
0
where m , N = N a are the baryon mass and number density

cn is a constant of the order of unity depending on the powern of the DM-baryon elastic scatteringcross section tr (v) =L totnn v with v being the DM-baryon relative velocity. We use theconventional
sectionfor themomentum-transfer
L shscattering
LDM
Figure 3: The expected bounds from the CMB spectral
Figure 4:
The bounds duecrossto the elastic
betweendec
distortion by PIXIE (colored regions are excluded) whenand electrons, to be compared with theZbounds from the DMd
Fig.
9.proton–workshop,
Sketch
ofDec
the
setup
electronbeam dump
KadotaOsaka
mZd Kenji
keV
for a(IBS)
few representative DM masses (m= Axionscatteringin2017
Fig. 3. of an tr⌘d⌦(1
cos experiment.
✓)
.
(13)
d⌦
1 MeV, 300 MeV, 1 GeV), due to the elastic scattering between
DM and protons. ↵ = 0.1 is used for concreteness and the pa-

Sub-GeV Dark Matter
Kenji Kadota
IBS Center for Theoretical Physics of the Universe (CTPU)
Institute for Basic Science, Korea

A Korean-government-funded research institute establ

Mass: Light massunder the Special Act on Establishment of and SupporØ Concrete example for light DM:
ü Sterile neutrino DM
ü Axion-like Particle
ü Axion

Science and Business Belts

Conclusion:
Let us be open minded.
Complimentarity between particle physics and cosmology.

Interactions: beyond ΛCDM
DM-baryon interactions with a light mediatorØ Concrete example for light mediator:
ü Dark photon

Kenji Kadota (IBS)

http://www.ibs.re.kr/

Osaka Axion workshop, Dec 2017