ダークマターとCTAKazunori Kohri （郡和範）

Physics Department, Tohoku University

Dark Matter?

Ωi ≡

ρi
ρc 0

ΩCDM h 2 ∼ 0.1

http://map.gsfc.nasa.gov/media/060916

What is Dark Matter?
• It is massive (ρ∝a-3)• It is stable (τ>> 10 18 sec)
• It does not scatter off photons so much
( Is it a bound-state?)• It is neutral(from experiments of sea water m<106 GeV)
• The velocity dispersion is small [cold dark matter (CDM)]

Candidate of particle (cold) darkmatter• Stable or long-lived new particle•••••Neutralino
Gravitino
Right-handed sneutrino
Axino…

• Oscillating scalar field•••

AxionModuli…

Another candidates• Primordial black hole
• Brown dwarf• WIMPZILLA• Integral constant in Horava-Lifshitz gravity• Quark nugget (strange-quark matter)• Solutions in (relativistic-) Modified
Newtonian Dynamics (MOND)• …

Rotation curve

Dark HaloStars (visible component)gas
二間瀬敏史著 「なっとくする宇宙論」

M (r ) ∝ rBegeman, Broils,Sandars etal (91)Gravitational lens in colliding clusterof galaxies• Red: Baryonobserved by X-ray
produced by bremsof thermal electron• Blue: DM observed
by gravitational lens

(2007)

Time-evolution of fluctuation III(II) Horizon reentry before matter-radiation equality epoch-6-5-4-3
aEQ-2-1

∝a∝a２

Log a
Ma and Bertschinger (95)
See also 松原隆彦 「シリーズ 現代の天文学3 宇宙論 ＩＩ宇宙の進化」

Cluster baryon fraction• Cluster can have a representative distribution
in the Universe of both baryon and DM• Ωbh2 is independently known, fgas wasobserved by X-ray from OxygenΩm~ 0.2

Combined FigureRiess et al (98), Lahav-Liddle PDG (09)Introduction to SUSY
Supersymmetry (SUSY)
Solving “Hierarchy Problem”
Realizing “Coupling constant unification in GUT”

neutralino

Fermion

Boson

quark

squarkleptonsleptonphotinophotongravitino

graviton

Depending on SUGRA models

Hierarchy Problems
GUT-scaleMX ≈ 1014 - 1015GeV

12-13 orders ofmagnitude !!!

Weak-scale

MW ≈ 10 -10 GeV
2Higgs mass

32dVϕ222mϕ 0 =OM
≈λυ
≈(W )
2dϕVϕ

where Higgs’s potential

Vϕ = λ (ϕ ϕ − υ /2 )†22c.f) Masses of fermions and vector bosonsmψ ~ hψ ϕ , mZ ~ g ϕ~υ ϕRadiative correction to Higgs massin Quantum Field TheoryWϕϕ+λϕϕ

δ mϕ2 ~ λΛ2 + g 2 Λ2g ϕ

g

Quadratic divergence

Cut off scale Λ ~ MX ~ 1015 GeV

δ mϕ ~ (10 GeV ) ?
2152

How can we resolve the problem?
Weak scale in the tree level,~ (10 GeV )m2ϕ022

δ mϕ ~ (10 GeV )2In total,

152mϕ ~ mϕ 0 + δ mϕ ~ (10 GeV ) ?
222152To retain the hierarchy, we require an accidental cancellation,

mϕ 0 + δ mϕ 1 + δ mϕ 2 + δ m + ... ~ (10 GeV ) ?
2222ϕ3⎡⎣O (10 GeV) ⎤⎦15GDP in USA (2002)?

2

2$ 10,110,087,734,958.95-) $ 10,110,087,734,957.70$ 1.25Fine tuning!

2Solution in SUSY
In exact SUSY, the quadratic divergence iscanceled by both boson and fermion loops.

tt
ϕht
−2hΛ
2t

Even if SUSY,(4π )22= 0ϕht211(4π )+ ϕϕhtht2 Λ 2

Exact SUSY2⎛⎞Λ
22 2
δ mϕ ∼
h mt ln ⎜⎜ 2 ⎟⎟2 t(4π )⎝ mt ⎠1)∼2WM(O∼.
.
.

∼2bm2tmWe don’t need a fine tuning whenSUSY GUTThe coupling constants
are unified at

MX ≈ 10 GeV
16

A lot of newparticles ,which do not obey
the asymptotic free, appearatμ ≥ 102 GeVMartin, ”A Supersymmetry Primer”

Lightest SUSY particle (LSP)• R-parity conservationi)Decay

τ → χ +τ(-1)(-1)× (+1)ii) Pair annihilation/production

f + f ↔χ+χ(+1) ×(+1)(-1)× (-1)

Thermal freezeout
Boltzmann equation

3Hnχ ∼σ v frezeout
TFreezeout ∼ mχ / 30⎛⎞σv⎜⎟
2Ω χ h ∼ 0.1⎜
2 ⎟0.1
⎜
⎟
TeV ⎠
⎝

()

Ωχ does not depend on mχPredicting TeV Physics!!!

Kolb & Turnerσv = 3 × 10 −26cm 3 / sPositron Excess(PAMELA satellite reported)e + / e − ∝ E −δ (δ ~0.6 proton diffusion)

Adriani et al, arXiv:0810.4995v1 [astro-ph]Electron and positron flux by ATIC2

Chang et al (08)

Electron and positron flux by Fermi

Abdo et al, Fermi LAT Collaboration, arXiv:0905.0025, PRL102 (09) 181101

Positron excess
in DM annihilation
Hisano, Kawasaki,Kohri, Moroi, Nakayama (09)Diffusion model
Fitted to B/C ratio

σv ∼ 10 −24 − 10 −23cm 3 / sElectron/positron cutoff
in DM annihilation
Hisano, Kawasaki,Kohri, Moroi, Nakayama (09)σv ∼ 10 −23cm 3 / s

Gamma-ray signal from GC by DM annihilation
Kawasaki, Kohri, Nakayama (09)Extragalactic diffuse Gamma-ray by DM annihilation
Kawasaki, Kohri, Nakayama (09)Fitting by Papucci and Strumia

Papucci, Strumia, arXiv:0912.0742 [hep-ph]See also Chen, Mandal and F. Takahashi, arXiv:0910.2639 [hep-ph]CTA?

Courtesy of Kazunori Nakayama

Result of Papucci and Strumia

Papucci, Strumia, arXiv:0912.0742v1 [hep-ph]Extragalactic diffuse-gamma

CTA?

Direct detection by CDMSII

arXiv:0912.3592v1 [astro-ph.CO]
Background
0.8 ±0.1(stat) ±0.2(syst)

mGemDM

1 2
Erecoil ~ μ v ~ O(10)keV
2v ~ 220km/s (v/c~10-3 )mGemDM
μ~mGe + mDM

mGe = 72.6 u

M < O(100) GeV? (Farina et al)Marco Farina, Duccio Pappadopulo, Alessandro Strumia

arXiv:0912.5038v1 [hep-ph]Conclusion• Fermi may not exclude the possible scenarios
for the positron/electron excess by the DM
annihilation/decay because of the upper limiton the sensitivity (<300 GeV)• CTA will be able to verify those scenarios• CTA may have a sufficient sensitivity todetect gamma-rays associated with DM
annihilation even with its canonicalannihilation cross section (~3×10-26 cm3/s)