Thermal history of thedark matter in thehidden gauge theory
N. Yamanaka(RIKEN, iTHES Research Group)
In collaboration with
S. Fujibayashi, S. Gongyo, and H. Iida2014.09.03
熱場の量子論理研

Dark matter : 27% of the energy component of the Universe
Dark matter
Neutral, collisionless, nonrela, WIMP
Dark matter halo:
Our galaxy is surrounded
by a halo of dark matter

Cosmic "makeup". Credit: ESA/Planck

Suggested by:
Galactic rotation curve
N-body simulation
Galactic bullet clusters
Cosmic microwave background…

DM Halo20kpc
DM density at the Earth: 0.3GeV/cm3

Need to explain dark matter in particle physics
Dark matter seems to be WIMP … Are there candidates in Standard model ?

→ No!
→ We need to introduce some new physics beyond Standard model.

What is a good candidate of new physics beyond standard model ?
Not in conﬂict with phenomenologyNaturalness← 当たり前ですね (́ ｀;)What is natural?

Uniﬁed theories, eﬀective theories (example : GUT)No ﬁne-tuning, explain hierarchy problem(Massive parameters should have reasonable reasons)
Example of massive parameters :Higgs mass, neutrino mass, QCD scale, cosmological constants,dark matter mass, early inﬂation parameters, etc.

Hidden gauge theory (HGT)

The idea is to introduce additional gauge theory(ies)
We consider SU(Nc) gauge theory very weakly coupled to Standard model (SM)HGT and SM uniﬁes near GUT scale
In hidden gauge theory, the dark matter is• a pion
if current (dark) quark mass < scale parameter• a glue ball
if current (dark) quark mass > scale parameter• a baryon
if CP violation and quarks exists in HGT sector(We do not consider this scenario today)

What is natural in HGT ?
Mass scale controlled by the running coupling (input : Nc, Nf)
Many gauge forces (4th, 5th, …) uniﬁed at GUT scaleObject of study
As the HGTʼs exist since the GUT scale, particles in the HGT participate
in the thermal evolution of the Universe.
How about the observational constraints?

Object of study:
Study HGT’s thermal evolution andits phenomenological constraints.
• Propose a scenario for dark matter.
•We do not discuss the following topics:
How gauge theories are uniﬁed at the GUT scaleSupersymmetry

Dynamics of expanding Universe
Freedman equation (Einstein equation in homogeneous isotropic Universe)✏ : energy densityppd✏+ 2 6⇡G(✏ + p) ✏ = 0dt rda8⇡G pa ✏=0dt
3

p : pressurea : scale factor

G : Newton constant

Important cases of evolution:Radiation dominant Universe1✏(T ) / 4
T

1a(T ) /T

Temperature decreases as the Universe expands
Expansion decelerates in time

Matter dominant Universe1✏(T ) / 3TSlower decrease of energy density than radiationde Sitter Universe (inﬂation)a(t) / eKt

Vacuum energy
Negative pressure induces exponentially accelerating expansion

Relic density of dark matter in HGTWe assume
Entropy of the radiation is conserved: equilibrium in the comoving frame (adiabatic)
DM Hadron mass = temperature of freeze-out
DM QGP/hadron phase transition is a quasi-equilibrium process

Hadron number density at freeze-out temperature:⇣(DM)n(DM) TFO

⌘(DM)

= gFO

(DM)
TFO mDM2⇡! 32mDM(DM)
TFOe' O(m3DM )Extrapolation from the current DM relic density:n(DM)

⇣(DM)
TFO

⌘

⇢m01
⇢m0=
⇥ 3 =
⇥mDM
aFO
mDM

(DM)
gFO
(DM)

geq

⇣⇣

(SM)
TFO

(SM)

Teq

⌘3

⌘3a3eqentropy conservation⇢m0 ' 10 47 GeV4
aeq = 3 ⇥ 10 4

(SM)
Teq
= 1 ⇥ 104 K ' 1eV

(DM)
(SM)
If HGT and SM were not disturbed since the GUT time, TFO = TFO(=entropy is conserved)

mDM ' 108GeV(́ ｀;) BBN …

Constraint on DM mass from the stability of the DM halo
DM particle in the halo is nonrelativistic and bound by gravitational force
Annihilation processes can reduce the DM number
Relativistic products are ejected from the halo : decay of DM haloππLeading process:
φπDM HaloDM Haloφππφπππφφππ

Current DM halo is stable

φπDark pion 4 → 2 process

Dark glueball 3 → 2 process

Constraint on the mass scale of HGTSimple dimensional analysis estimates

mDM > 1 TeV(for pure Yang-Mills)

mDM > 1 GeV(with light quarks)

In conﬂict with previous naive evolution
We must decrease
the dark sector temperature
relative to SM sectorConstraint on the unification scale from high energy cosmic ray
DM particles can decay to SM particles via GUT forceqN cπNcfSMXDecay products can be observed
as cosmic rays at EarthfSM

qN c

Constraint on uniﬁcation scale

We have used 2 probes:

Neutrino:

R(E)Electron/positron:Diﬀusion in the galaxy
Data from AMS-02.

1mDM = 100 TeV, oDM = 1026s
background
AMS-02 data (PRL110,141102)

0.1

AMS-02 Collaboration, PRL 110, 141102 (2013).

No diﬀusion, data from IceCube

0.01
1101001000

E (GeV)

Positron fraction from DM decay

IceCube Collaboration, arXiv:1405.5303.

Constraint on GUT scale:

ΛGUT> 10 -14 GeV(for mDM ~ 1, 10 TeV, from AMS-02)(for mDM ~ 1 PeV, from Icecube)

All couplings were set to 1
• DM decay only to electron/neutrino•

How to resolve ?
DM relic density obtained by entropy conservation is in conﬂictwith the limit of halo stability
We must increase the entropy of SM sector by order of magnitude
By the way … Higgs sector is still unknown:
The Higgs eﬀective potential may induce inﬂation and increase the entropy

Let us introduce a mini-inﬂation to the Higgs scale
By introducing a mini-inﬂation of Δa = 103, we expect
Reduction of the DM density by ~109
• Reduction of baryon number density by 109 (current nB/s ~ 10-10 ! )• No notable change of energy density in SM sector, due to reheating•

Thermal history of the scenario we are proposing
Inﬂation at Higgs scale resizes
DM and baryon number
GUT SSB

Dandarkrdsecmotordelbaryon numberBBN

QCD phase transition

Leptogenesis

GUT SSB→sphaleroninducedbaryogenesis→

Higgs phase transition

ctorDM phase transition

fascale←radiation
dominant
Universe←→
matterdominant
Universe→

RecombinationSta→
structureformation→→
dark energy
dominant
Universe→t
Now

Higgs scale mini-inﬂation (Δa~103) is needed!

Prospective observations
B-modes:

Probe of Higgs mini-inﬂation (and other mini-inﬂation sources…)
BICEP2, Planck.

Gravitational wave backgrounds:

Probe of 1st order phase transition (Higgs & DM)

Y. Kikuta, K. Kohri, E. So, arXiv:1405.4166.

Precision tests of Higgs sector:Probe the Higgs potential : Need precision test such as ILC!!
ILC

Decay of dark matter to SM particles:
Probe the uniﬁcation scale

AMS-02, Icecube.

Accurate knowledge of DM halo density proﬁleProbe interactions among hadrons

M. Rocha et al., Mon. Not. R. Astron. Soc. 430, 81 (2013);
A. H. G. Peter et al., Mon. Not. R. Astron. Soc. 430, 105 (2013).

Summary

Summary:• We have introduced the hidden gauge theory to explain darkmatter.
• Phenomenology : thermal history, halo stability, cosmic rays.
• DM thermal history with entropy conservation contradicts
with halo stability: need to increase SM sector entropy.
• We have proposed a new scenario with mini-inflation at theHiggs scale: consistent with the present baryon number.
• Many observational probes will be soon available
Precise study of Higgs sector is neededILC!!

Future prospects:•••

Lattice study of thermal quantities in HGT.
HGT with spontaneous symmetry breaking.
HGT with SUSY.