Particle Dark Matter~Current status of theory & search~
Motoko Fujiwara (Technische Universität München)

53rd Summer school on Astronomy & Astrophysics @Hongo, Tokyo August 3rd, 2023

Contents••••

What is Dark Matter (DM)?
DM candidates

Part 1DM search directions
New direction of DM search(Neutron star as DM target)

Part 2

What is Dark Matter?

: Thermal History of Dark Matter, Weakly Interacting Massive Particle, Coan-

Dark Matter

cf. M(r) = dr4πr 2ρ(r)∫[Oort WIMP
(1932)]
Missingmassandrk Matterevidence
hypothesis

2-1. ダークマターの存在•

Verticalof solarneighborhood
ce is discovered
in stellar
variousmotion
independent
astrophysicalobservables of various cos→ the
Ourtotal
universe(=visible
component)
lacks the→ Missingcales. First,
mass ofthe cluster
can be estimatedfrommassthe visible
source mass problem
Dynamical
massmassof Comaclusteris(Fritz
Zwicky,1933)
ophysical
observation
where
the
missinginouruniverse
discovered[1].
“Dark Matter” [Zwicky (1933)]
Fritz Zwicky
istence in our universe was first claimed by Zwicky [1] through the analysis of the
Dynamical
mass
of Coma cluster is analyzed
mass of the
Coma galaxy
cluster.
the rotation
curvesof spiralgalaxies also imply a missing gravitational source [2,Virialtheorem
is appliediral velocities
are measured
throughthe Doppler
shift of@stable
Hydrogen
21 cm line
system2(Kinetic
energy)= (Potential
energy)s. Applying the Newton’s gravitationallaw for the spiral galaxy, the circular
2-1. ダークマターの存在
estimatedto be[Rubin, et al. (1970)]
Rotational
curveofgalaxyRotationcurve of Milky Way (Sofue et al. 2009)!
et al.
2KSofue+W=(2009)0
GM< (Newtonian gravity)
Expectation:
vc =
,
(2.1)
r
rhv 2 i••••<latexit sha1_base64="6Bm1rbvqmN0+h3hyEqLi4Ak+Yl8=">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</latexit>

Observed:(constant)
the gravitational
constant vandc ∼M< is the mass in the range of radius r. The© NASA, JPL-Caltech, SDSS, Leigh Jenkins,locity is flat in large r thatis outsideof thedisc.
Ann Hornschemeier(Goddard
Spacevisible
Flight Center)
et al. This fact implies an
3
2

mv(r)
GmM(r)=72rr→ M(r) ∼ r→ ρ(r) ∝ 1/r 2→ Invisible mass?

M⇠

G

太陽系の位置Solar position

8.0kpc=26100光年

R0 = 8.0 kpc, Θ0 = 200 km/s を仮定。
<latexit sha1_base64="hbFjR7a5XWugEX4EAt4vXXYpgGE=">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</latexit>

DM: Necessary condition
DM evidences (summary)•••Rotational curves of galaxy

Rubin et al. (1980)

Bullet clusters

Markevich et al. (2002), Clowe et al. (2006)

Gravitational lensing

Oguri et al. (2018)

Implication?

Invisible(=“Dark”) unknown massive source

10 kpcX-ray photo by Chandra※ Evidences are discovered independently in various scales※ Required as necessary component in our universe (discussed later)

Qualitative feature of DM•••

Electrically neutral
Behave as matter @structure formation (~Massive)
Stable /long-lived

Vast possibilities for DM candidates
But no suitable candidate in the Standard Model (SM)0.5 Mpc

(review) Standard Model Particles
SM particle contents [Picture from Wikipedia]: unstable: charged

Quarks→ Exist as baryon/meson: masslessProton : charged
Neutron : neutral but unstablePion: charged &/or unstable: strong int.

Leptons
Electron : stable but charged
Neutrino?: neutral but relativistic@ structure formation

W boson: charged & unstable
Z boson : neutral but unstable
H boson : neutral but unstable

If DM is an elementary particle, we need to update the SM table
What is the particle nature of DM?
(eg. DM mass, DM spin, DM interaction w/ SM particle, DM self-interaction, …)

rs

duction of Dark Matter: Exercise

rs

where

DM
density
profileMotoko Fujiwara, Martin Wolf∗

rs = 24.42 kpc,
ρs = 0.184 GeV cm−3 .

†ysik-Department, Technische Universität, München,
Hint: In the center part of the galaxy, there is a black ho-bodysimulation
N
James-Franck-Straße, 85748 Garching, Germany
density that can contribute to the experimental/observation

May 12, 2023
•
∼
100
kpc
•
or the course of “Applied Multi-Messenger Astronomy 2.”

get rid of themodel
region thatis characterized
the Schwarzsc
Realizing DM halo in computer fixing cosmological(suchas ΛCDMbymodel)
hole (BH) [1].



 0
) profile of DM halo can be predicted → vs observations(r ≤ 2Rsch )Global (ρχ (r) = 

ρNFW (r) (2Rsch < r ≤ Rvir

Navarro-Frenk-White profile
This classification is crucial to avoid the singularity in ρ
[Navarro, Frenk, White (1996)]

NF
1/r behavior around center is discussed in [Dubinski, Carlberg (1991)]

N-body simulationof Coldprofile
DM profiletter• (DM)density

the following numerical values for the plot.

∝ 1/r

•
ter) by using python. The NFW profile
is defined below as function∼rfrom •
the galactic center, r.

−1
c = 299792458 m/s,
Centerpart:
shallowerthan∼ro-Frenk-White (NFW) profile density as function of r (distance from

Near viral radius: steeper thanρNFW (r) ≡ ρs

!

r
rs

"−1 !

r
1+
rs

−2

"−2

,

: Speed of lig

G = 6.67430(15) × 10−11 m3 kg−1 s−2 , : Gravitation
MBH = 4.154(14) × 106 M" ,: Mass of BH
r" $ 8.4 kpc,
: Distance fr
2GMBH
2
−10
Rsch =
=
3.975
×
10
kpc,
:
Schwarzsch
∝
1/r
c2
(1)
Solar position ↑ : Halo’s viria
Rvir = 200 kpc.

Answer: See the blue curve in Fig. 2.

rs = 24.42 kpc,
ρs = 0.184 GeV cm−3 .

∗E-mail address: motoko.fujiwara@tum.de†E-mail address: martin.wolf@tum.de

(2)
(3)

1

uded region by using the experimental bound shown in Fig. 6 of Ref. [30]. In

the final state particles are assumed to be massless, and thus we can directly

Variation of DM density profiles

18iline bystraints with h vrel iline,Z . We can also derive the constraint on h vrel
Z0

orizontal axis of Fig. 6 in Ref. [30] corresponds to E . These constraints are3

presence can account for the missing mass that is apparTable II: The cuspy DM density profiles used in Ref. [30].
[Abramowski, et al. [H.E.S.S] (2015)]
ent in astrophysicalenvironments[1]. The annihilation
ng the three cuspy DM density
profiles as defined
below.
Cored Einasto
ProfilesEinastoof[31]
NFW[33] particles
Einasto2 is[32]darkmatterexpected to produce photons
210with energies up to the mass of the dark matter particles
3
⇢
[GeV
cm
]
0.079
0.307
0.033
Cored NFWsfile [31]/Einasto2
profile [32][2]. The detection of γ-rays from a given direction canrs Cusped[kpc]
20.0thus indirectly
profileprobe28.4
the presence
Cusped Einasto
21.0 ✓✓◆
◆ of dark matter parti↵s
10
cles along–theline of sight.
2 corresponding
r0.17
↵⇢s
0.17
(r)
⌘
⇢
exp
1 Way
. is of particular in- (4.5)
Cusped NFW
s central region of the Milky
EinastoThe↵srs
terest for indirect searches for annihilating dark matter1
because the squared dark matter density integrated overdefined as shown
below.
Coredprofile
profilenk-White (NFW)[33]
the line of sight towards the target region (i.e. the as8
trophysical or J-factor) is expected to be18large [17].
18 The< ⇢Einasto
!
10-1
(r)
for
r
>
r
,
1
c
✓
◆
J-factor for observations2 (ofGalactic
de: coreradius)center region
rc the⇢(r) =(4.7)
r
r: ⇢(r) pendsondark matter
density distribution (4.6)
⇢NFW
⌘ (r
⇢sc ) strongly.
for 1r +< rthec,
Einastorprofiles
rsin Ref.Simulations
s inwithin
the
Milky
Way.
of the dynamics ofTable II: The
Table
cuspy
II: TheDM cuspydensityDM
profilesdensity
used
Ref.
used
[30].
[30].
10-1
1
10
the dark matter content of galaxies predict to universal
4s defined
in Eq.Profiles(4.5). [31]For
the[31]
coredprofile,⇢Einasto:chosento etrealizethe values is[32]
Einasto2
EinastoProfilesEinastoEinasto
NFW
[33]
NFW
Einasto2[33][32]
Einasto2[Bertone,al. (2009)]
Distanceto
Galactic
Center(kpc)
dark matter density distributions. Towards the center
Einasto2:[Cirelli,
et al. (2011)]
3 parameters3
ummarize
the
for
the
cuspy
density
profilesused
in Ref. [30].
⇢s [GeVWe
cm⇢sshow
[GeV
]
0.079
cm
0.079
0.307
0.033 region
0.033
of0.307
theexcluded
galaxies,
theDM
influenceofthe distribudensity.
the ]current
withthebaryons
cuspedonDM
density
FIG. 1. Dark matter density as a function of the distancetion
matter 28.4
is not yet resolved. The formation
10
rs [kpc] rs [kpc]
20.0
20.0
21.0 of dark
21.0
28.4
for the cusped
DMdensity
profile.
The coreradius,rc , depends
onH.E.S.S.
the modeltoofthe Galactic center. The parametrizations
nthe
thecored
analysisof theH.E.S.S.
collaboration[30].
The sensitivity
ofcenterthe
CoredEinastoofpronounced
density
cusps
towards
theofgalaxEinasto
104 and NFW profiles are taken from [12]. The cored↵s↵s 0.17
0.17
–
–0.17
0.17
([14],
and,recently,
theOFF1
predictionthat cored
Einasto and NFW density profiles follow theCored
respective
cuspedand forcores
to rincies
⇠
5 kpc
can
potentiallybe[34]. DM
The
NFW
died
theextending
cored profiles
Ref.
[35],[15])which
is morefocusing
on obtained
the
pure
Wino
profiles at distances to the Galactic center that are larger than5
the dark matter
density in the central few hundred pc is
Cusped Einasto
the coreradius of 500 pc.
ofile
is
asdefined
shown
below.
as shown
below.
constant[4], [6]havediscussed.
lat3
sfinedstudy,
the upper
bound
onalmost
the linecross [5],sectionwill
be beenweakenedby aThefactor10
Cuspedprofile:Enhancement
flux darkfor small
angle
8
8
ter
predictionof anmodels.
almostinconstant
matterdensity
Cusped NFW
redicted in the context
oftheextra-dimensional
See
Ref.
[31]
for
the
discussion
in the<we use the cored<DM
density
profile.
⇢
(r)
⇢
for
(r)
r
>
r
for
,
r
>
r
,
0
in
the
centralregionofthe
Galaxyisconsidered
in
this
c
c
EinastoEinastoNumerical impact → several
ordersensions. ⇢(r) = ⇢(r) =
(4.7)
(4.7)
constructed.
The construction of the background region:⇢: ) work.
for (rrc<) rcfor, r < rc ,Signal Region
102
Einasto (rc⇢Einastomust be performed such that the ratio of the acceptanceThe current strongest constraints on the velocity averSignal Region
for background
events in the signal and the background-5profile,→(4.5).
Huge
uncertainty
density
profilesaged
cross
sectionforDM
self-annihilationof valuedark matdefined(r) isindefinedEq.
in Eq.
For(4.5).
the
cored
For
the
profile,
cored
⇢from
⇢sthe
is
to chosen
realizetotherealize
value
the
t from
gamma-rayline
signaturess is chosen
astoregion is known from instrumental characteristics. The
ter particles with massesOFF2
in the range ofBackground∼ 400
GeV toRegion
10
to
probe
DM
indirectdetectionalnsity.
DM We
density.
showespeciallyWe
the showcurrent
theexcluded
current
excludedregion with
regionthein
withcuspedtheDMcuspeddensity
DM density
Regiondefinition ofBackgroundthe backgroundregion enables a compari∼ 10 TeV result from a search for an extended emission
son between the number of events that are detected in-10
of between
γ-raysinour
thecentralregionoftheMilky
Way-10with
hepredicted
analysisin theofanalysis
the H.E.S.S.
of thecollaboration
H.E.S.S.
collaboration
[30].
The
[30].
sensitivity
The
sensitivityofthe
H.E.S.S.
ofthe
H.E.S.S.
eumed
line
cross
sectionspin-1
DM
and
the
Wino
system.
In
10
5
0
-5
( We needglobalDM density
profile)10-1
the signal
region and 1the number of 10background events
Galactic
Longitude(deg) only if the
H.E.S.S.
[7]. However,the constraints
apply
line
Angular Distance (deg)thed isforpredictedstudiedthe cored
for theprofilescoredinprofiles
Ref.
[35],
in
Ref.
which
[35],
is
focusing
which
is
on
focusing
the
pure
on
Wino
the
pure
DM
Wino
DM
value of h vreldark
i ,Zmatterand density
experimental
upperinbounds.
The
solid
that are expected in the signal region. The acceptance
distribution
the central
∼ 500
pc
FIG.
2.Way
The
signalregionclose
thelines
Galactic
center1).
and forbackground
eventsof H.E.S.S.
in generalstronglyrom
tudy,thisthestudy,
upperthe
bound
upper
on boundthe line
crosstheMilky
line
sectioncross
will
sectionweakenedwill
beweakenedbydotted
atofactor
bya factorofontheisbecusped(seein Fig.
FIG.
3. Line of sightintegralover the issquareddark matve shows the line cross section
includingSommerfeld
enhancementfor
ourspin-1the two background regions with a symmetric right ascension influenced
byaatmospheric
the between
pointing
ter density as
function of theconditions,angular distancethezenith•

Galactic Latitude (deg)•∵J (GeV 2/cm6 kpc)

3

Dark Matter Density (GeV/cm )Cusp vs CoreDM candidatesDM candidates (1/2)[Chapline (1975)] [Meszaros (1975)]

Primordial blackhole (PBH)

Villanueva-Domingo et al.

•
•
•
•

cs : speed of sound[Villanueva-Domingo, Mena, Palomares-Ruiz [review] (2021)]

Primordia

Compact object formed in early universe(density fluctuation)> (critical value) ≃ cs2→ Corresponding region collapse(BH scale) ~Universe @collapse time

Villanueva-Domingo et al.

BH mass can be flexible

Primordial Black HolesFIGURE 1 | Sketch of the formation of PBHs from overdensities for three different successive moments. When ﬂuctuations larger than a critical threshold δcenter the horizon, i.e., their wavelength λ ! 2π/k (which characterizes the size of the perturbation) is of the order of the Hubble horizon (aH)− 1 , the overden
collapses and a PBH is produced. As can be seen in Eqs 1, 2, longer modes (large λ, low k) enter the horizon later and lead to more massive PBHs.

[although broad spectra have also been argued not to produce
M⊙ et al., 2019)].
(stelar (Moradinezhad
BH mass) ∼Dizgah
appreciable cf.
clustering
Depending on the speciﬁc mechanism of forvariance σ 2 (M) at a mass scale M, the initial abundance, deﬁned
population of PBHs with different masses could beas β(MH ) ! ρPBH (tf )/ρtot (tf ), is given by (Sasaki et al., 2018;
Anyway, PBHs could become bounded as the Universe
Green and Kavanagh, 2021)
The speciﬁc shape of the enhancement of ﬂuctuations"#
evolves. A proper determination of their clustering properties
the mass distribution function. Sharp peaks in the powe∞2 σ(MPBH )δ2c
imply approximately monochromatic distributions. Fo
exp$ − 2β(MPBH )xc ! P(δ) dδxc%,
at later times is of great−16
importance, for instance, in order toπ
2 σ (MPBH )δcδchaotic new inﬂation may give rise to relatively nar
M
≲
10
M
:
(Yokoyama, 1998; Saito et al., 2008). However, inﬂati(3)
estimate their merger
rates (Desjacquesand Riotto, 2018; De Luca
BH⊙
with an inﬂection point in a plateau of the potenti
where in the last equality, σ(MH ) ≪ δ c has been assumed. For the
et al., 2020a).
Indeed,the formationof clusters
could alleviate
PBH
evaporates
in current
universe
Bellido, 2017; García-Bellido and Ruiz Morales, 2017)
standard cosmological scenario with an initial scale invariant
inﬂation (Clesse and García-Bellido, 2015), predic
some constraints on the PBH abundance (Belotsky et al., 2019).
power spectrum, at CMB scales, the amplitude of the ﬂuctuations
extended mass functions, which can span over a larg
−16PBHs−12
is around σ(MPBH ) ∼ 10− 5 , leading to β ∼ 10− 5 exp(−1010 ),On another
hand,
since
would
be
formedfrom
the
PBHs masses. In this review, we focus on mono
MBH ∈ [10 ,10 ]M⊙:
which is completely negligible (Green, 2014). Therefore, in
distributions for simplicity, although it is possible t
collapse of high density peaks relatively spherically symmetric,order to have a relevant population of PBHs, larger values of
constraints to extended mass functions, which ca
100% DM is possible but some constraints
the initial power spectrum are needed. On the other hand, thestringent despite the fact of having more parameters
their torques and angular momentum are expected to be small
assumption of a Gaussian distribution may not be consistent withet al., 2017; Bellomo et al., 2018). Nonetheless, even iunder 2017;
debateenhanced ﬂuctuations and the presence of PBHs, so deviations(Chiba and are
Yokoyama,
Mirbabayi et al., 2020). It is usuallybounds that exclude fPBH ∼ 1 in the monochromatic cas
are unavoidable (Franciolini et al., 2018; De Luca et al., 2019b)
choices for the mass function which allow PBHs to consquantiﬁedwith the −12dimensionless spin parameter,[except for speciﬁc inﬂation models presenting an inﬂection pointor all of the DM abundance (Lehmann et al., 2018; A
2MBH ≳ 10
Atal and Germani (2019)]. Non-gaussianities could have a great), where S is M
the⊙:spin. Estimations of for PBHs
S ! S/(GMPBH
et al., 2020; Sureda et al., 2020).
impact on the initial fraction and lead to a larger population, asshow that it constrained
is a small quantity,equal or lower than
0.01 etc(De Luca
by Microlensing,
CMB,
well as leaving detectable signatures in gravitational waves (Caiet al., 2019). Finally, note that the above formula follows theet al., 2019a). In contrast, astrophysical BHs are expected to have
4 ACCRETION ONTO PBHS
simple Press-Schechter approach, whereas to account for the
non-universalFIGURE
nature of 2thethreshold, theofuse
of peak theory
substantially larger spins, since angular momentum must be| Compilation
constraints
on the One
PBHoffraction(with respect
the consequencesof the existence of PBHs w

Current status

•

c

•
•

provides more accurate results (Green et al., 2004; Germani andDM candidates (2/2)
Particle DM••

Even if we focus on particle DM candidates, we have vast possibilities for DM→ DM identification is ultimately a challenging task
What kind of information do we need for DM identification?

• DM mass• Coupling w/ SM particles

Concrete candidates

•
•
•
•
•
•

Weakly Interacting Massive Particle (WIMP)
Sterile neutrino
Axion
Feebly Interacting Massive Particle
Strongly Interacting Massive Particles
Self-interacting DM …

Plot in “Observational and theoretical motivation for particle dark matter”

Weakly Interacting Massive Particle
Assumption

DM Annihilation

Features•••

DM is thermalized in early universe
WIMP candidate often appears
if we extend the SM frame work
We have various channels to test(& crosscheck) DM property

DM Scattering

DM is an unknown elementary particle
that “weakly” interacts w/ SM particles

DM

SM

DM

SM

DM Production

Let’s see what happen once we assume this hypothetical unknown particle
in the expanding universe

Annihilation rateχχ…

DM pair annihilation:

final particlesℳχχ→final : Annihilation amplitude of DM- related to probability of each process- highly depends on individual model
Phase space (x, p), internal d.o.f.
Definition:2

χ 2∫ | ℳχχ→final | ( f eq) d(phase space)⟨σannv⟩ =
χ 2
∑
∫
(
f
)
d(phasespace)eq
final
Adding all the possible modes

distribution function of DM @ equilibrium

feq,i =

1
e

Ei
T

±1

⇠e

Ei
T

Ei : energy of particle

T : temperatureBoltzmann equation
Time evolution of DM number density
Change of DM # in time evolutionof expanding universe

dnχ

•
•
•

dt

Change of DM #due to particle processes22+ 3Hnχ = − ⟨σannv⟩(nχ − nχ,eq)

Annihilation rate control process → ∝ ⟨σannv⟩
Pair annihilation process→ ∝ (DM # density)2

No change @equilibrium2→ ∝ (nχ2 − nχ,eq)Solve this equation → prediction on DM energy density observed today
CMB observation→ Observationally favored DM energy density

We can test this scenario by comparing theoretical prediction in light of observation

DM density per coming volume

Thermal historytimeDM density per coming volume

Thermal history

time

Production
eg1. DM production from SM particles
produced during reheatingeg2. DM production directly from inflaton※ Many possibilities for initial condition

SM

SM

DM

SM

SM

DM

inflatonDM
inflatonDMDM density per coming volume

Thermal history

time

Equilibrium

Production

DM

SM

DM is in thermal equilibrium through the interaction w/ SM particles→ Physics after equilibrium can “forget” about initial condition
We can derive general predictions independent of initial condition DM

SM

Annihilation

g: internal d.o.f

DM density per coming volume

Thermal history

d 3p − kEχTnχ,eq = ge B =3
∫ (2π)gmχT( 2π )

32em− k χTB

gT 3
π2(mχ ≫ T )(mχ ≪ T )time

Annihilation

Production

DM

SM

DM

SM

During cosmic expansion, temperature keep decreasing→ Thermal bath can no longer produce DM pair
→ DM # density decrease exponentially

Annihilation

H: Hubble constant

DM density per coming volume

Thermal history

To explain correct DM energy density,

Thermal relic⟨σannv⟩ ≃ 3 × 10−26 cm3 /stime
Production

Freeze-out
DM cannot meet with annihilation partner due to expansion(cosmic age) vs (typical scale of DM annihilation)
!

1/H

≃

1/(nχ,eq⟨σannv⟩)

DM

SM

DM

SM

Annihilation

WIMP Scenario
よく見る図
D. Hooper, lecture note [arXiv:0901.4090]
0.01
0.001

DM density per coming volume0.0001

Decoupling of DM
from thermal bath

Thermal relic

1

DM

SM

DM

SM
10

time

100

1000

Implication of WIMP scenario
h ann vi ⇠ 3 ⇥ 10 26 cm3 /s = 1 pb · c

c = 3 ⇥ 108 m/s
1 b = 10 24 cm2= Typical cross section for weak process

What happen in weak process? (eg. Decay of charged pion)

d

µ

µ

d
W

ū

DM

DM

⌫¯µ

SM

SM

ū

?

⌫¯µ

DM

SM
?

DM

Electroweak boson(W boson, mW = 80.4 GeV)
mediates interaction

SM

Mediator in electroweak scale?
- Higgs boson?
- Z boson?
- new particles?
…

DM search directions
Focusing on WIMP DM

How to probe WIMP DM?
DM pair production
Collider experiment

DM

SM

DM

SM

DM scattering w/ SM particle
Direct detection

DM pair annihilation
Indirect detection

[Slide of P. Pani’s talk @TAUP2019]

Collider search (overview)
Theoretical framework

Parameter for analysis

DM

6

DM

DM

SM

DM

SM

SM
- Mediator-SM particle interaction- Mediator mass
- Mediator’s decay width?

- DM-SM particle interaction- DM mass

productionSMAxial-vector mediator

DM search @LHC

¯

q

q g
ZV F CZB

Typical event: Large missing ET

pp→ missing + X

ZV /A

ZB

u

u

h

q̄

(b)

Figure 3: Diagram 3

production
DM
¯f/ū
¯

u

SM

SM

DM

Z

/t

t

X = gluon, photon, … q̄(c)FigureDiagram2
Figure4: 2:Diagram
4

X + ssimTE

gq = 0.25, glep = 0, gDM = 1

(a)

u

f

Figure 1: Schematic representation of the dominant production and de

DM passes through the detector due to small interaction
w/ the SM particles

2m

EDTMmiss=m

Invisiblepq

Figure 1: Diagram 1

¯

q

¯

DM

(b)

Figure 3: Diagram 3

q

?

ZV /A

ZV /A

ZB

Z’

ZB

p
SM

(a)

q̄ q̄ g/ /V
X

h

DM
q̄

visibleATLAS DRAFTJHEP 05 (2019) 142
q
What we observe: Large missing transverse momentum ETmisspin-1 mediators - masses

We need X so that we can read out transverse momentum for reconstruction

ZV /AIndirect detection
Implication of WIMP scenario

h ann vi ⇠ 3 ⇥ 10 26 cm3 /s

DM

SM

DM

SM

annihilation→ Possibility to probe DM through annihilation→ Direct test of WIMP scenarioDM

SM

Fragments

DM

SM

Fragments

Annihilationh, Z, W, t, ⌧, · · ·Fragmentation

2e, p, ⌫, , H, · · ·What we observe: Fragment (stable particles) from DM annihilation

Photon flux from DM annihilation
20

Diﬀerential # of photon (eg. χχ → γγ)

2!

18

Thermal Wino Spectrum

16

2

dA
dtdEdV4πℓ 2( mχ )

γ/dE [1/TeV]dEρχeg. of dNγ /dE [Rinchiuso, et al. (2018)]

14

line

12

endpoint

10
8

d

dNγ =

dNγ (σχχ→γγ v)

5

6
4

• dN

2

Energy spectrum of photon
γ

dE

•
•

0
2.7

= 2δ(E − mχ ) for χχ → γγ

2.75

2.8
2.85
E [TeV]

2.9

2.95

FIG. 2: Left: A schematic of the key physical contributions for the precision calculation as relevant for a H.E.S.S. search forheavy wino annihilation. DM particles, , annihilate to the detected photon (in red), which recoils against a jet (in blue), i.e.
a collimated spray of electroweak radiation. Low energy isotropic radiation (in green) also yields important physical e↵ects.
The winos collide with non-relativistic velocity, and the exchange of electroweak gauge bosons gives rise to the Sommerfeld
enhancement (in purple). Right: The spectral shape of the endpoint contribution at NLL (orange solid line), as compared to
the line which is a pure delta function (black dashed line). The theoretical spectrum is shown for a thermal wino of mass
mDM = 2.9 TeV.

→ Forming line-like (monochromatic) spectrum
Rate of annihilation

probability for χχ → γγ to occur within [E, E + dE]ℓ: line-of-sight length

Ratio of observable
photons
files with flattened
density within 100 parsec or more ofin [5], the unaccounted-for presence of lower-energy sigthe GC. In order to avoid this limitation, one can exnal photons could potentially bias the background model.
(Eﬀective areaforobservation)/(Fullemotionarea)
dA: eﬀectivearea
tract the residual background energy distribution fromThus to obtain precise
and accurate
constraints, it isextragalactic observations [57]. In this case, the residual
background is extracted from blank fields at high Galactic latitudes in the same observation conditions as for theimportant to have a theoretical prediction for the full
photon spectrum to compare with the data, rather thansimply comparing constraints on an isolated line to a the-Flux formula
2
(σ
v)
ρ
dN
1
χχ→γγ
χ
γ
=
=
dV
2
2
dE
dtdEdA 4π 2!mχ dE ∫ ℓ

dΦγ

•

dNγ

Particle physics• DM mass• Annihilation cross section• Energy spectrum•

cf. (σannv) ≃ 3 × 10−26 cm3 /s for WIMP scenario

Astrophysics• DM density profile

Source of uncertainty to test prediction• Region of integral→ Characterized by J-factor (see backup slide)

We can directly test WIMP scenario by probing annihilation process

Scattering

Direct detection (idea)

DM

SM

DM

SM

Sketch of direct detection
WIMP’s windXe

Milky way galaxy (from north pole side)

230 km/s
earth

230 km/s

DM

NucleusAstrophysics

1 ⇢DM
dR
=
dER
mT mDM

Z vescScattering

Direct detection (event rate)

DM

SM

DM

SM

- DM density profile- velocity distributiond scatd ~v vf (~v , ~vE )(v, ER )
dER
vmin
3

Particle physics

Depending on particle nature of DM- DM mass- DM-nucleon cross section
Naive dimensional analysis
for DM w/ electroweak charge

vmin =smT Eth2µ2vesc : Escape velocity of DMµ⌘

mN mDM
⇠ mN : Reduced mass
mN + mDM(N = n, p)

GF ⇠ 10 5 GeV 2

1 2 2
4
40
2
GF µ ⇠ 4 ⇥ 10 pb ⇠ 4 ⇥ 10cm
scat ⇠
32⇡

Scattering

Neutrino background

DM

SM

DM

SM

Pros & Cons•••

Underground experiment can control background well
Less uncertainty from DM profile (we only need local info. on density & velocity dist.)
Serious background due to neutrino scattering eﬀects

White region:
We can probe DM-nucleon scattering

n)
o
r
t
u
e
SD, n
(
T
1
N
XENO

Naive estimation

Gray dashed curve:
Prospect of next generation exp.
Orange region:
Coherent neutrino scattering is expected→ We may not probe DM in this region
How to probe DM-nucleon scatteringin this neutrino background region?
(→ next slide)

T (SI)
4
−
X
Panda
ect)
p
s
o
r
p
(SI,
T
n
N
XENO
ν floorSummary: Part 1
DM in our universe••

10 kpcDark unknown gravitational source are independently implied
Necessary component to provide density fluctuation in early universe The cosmic pie

DM candidates••

Compact object:eg. Primordial blackhole

Particle candidate: eg. Weakly Interacting Massive particle (WIMP)
Exp./Astrophys. information is indispensable for DM identification

WIMP DM search•••

Collider search: Direct production by injecting energy
Indirect detection: Direct test of WIMP scenario
Direct detection: Background is well-controled but neutrino w/ BG

Developing new direction to probe DM is mandatory!

https://sci.esa.int/web/planck/-/51557-planck-new-cosmic-recipe