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CosPa2016_Yamanaka

Masato Yamanaka (Maskawa Institute)
Collaborator: S. Okawa, M. Tanabashi
arXiv:1607.08520 [hep-ph]
Idea to control relic density of 𝑂 TeV DM by
mediator lifetime in cases that dark sector is
secluded from SM sector
Dark matter
Various gravitational
evidences, but no
direct evidences …
LUX collaboration (2016)
CMS collaboration (2016)
New scenarios secluded from SM
No interaction between DM and SM?
DM
mediator
Various scenarios in light of theoretical and
observational motivations
Secluded WIMP dark matter
M. Pospelov, A. Ritz, M. B. Voloshin, PLB (2007)
N. Arkani-Hamed, D. P. Finkbeiner, T. R. Slatyer, N. Weiner, PRD (2009)
SIMP dark matter
Y. Hochberg, E. Kuflik, T. Volansky, J. G. Wacker, PRL (2014)
Y. Hochberg, E. Kuflik, H. Murayama, T. Volansky, J. G. Wacker, PRL (2015)
Cannibal dark matter
E. D. Carlson, M. E. Machacek, L. J. Hall, APJ (1992)
D. Pappadopulo, J. T. Ruderman, G. Trevisan, PRD (2016)
Impeded dark matter
J. Kopp, J. Liu, T. Slatyer, X. Wang, W. Kue, arXiv1609.02174 (2016)
etc.
SM
New scenarios secluded from SM
No interaction between DM and SM?
DM
Various scenarios in light of theoretical and
observational motivations
Secluded WIMP dark
matterlifetime plays an important role toSM
Mediator
M. Pospelov, A. Ritz, M. B. Voloshin, PLB (2007)
N. Arkani-Hamed,
D. P. Finkbeiner,
T. R.
Slatyer,
N. Weiner,
PRD particularly
(2009)
determine
the
DM
relic
density,
SIMP dark matterin DM-mediator degenerated scenario
Y. Hochberg, E. Kuflik, T. Volansky, J. G. Wacker, PRL (2014)
Y. Hochberg, E. Kuflik, H. Murayama, T. Volansky, J. G. Wacker, PRL (2015)
Cannibal dark matter
E. D. Carlson, M. E. Machacek, L. J. Hall, APJ (1992)
D. Pappadopulo, J. T. Ruderman, G. Trevisan, PRD (2016)
Impeded dark matter
J. Kopp, J. Liu, T. Slatyer, X. Wang, W. Kue, arXiv1609.02174 (2016)
etc.
mediator
Aim and outline
Aim of work
Analysis of mediator lifetime dependence on
the relic density in secluded dark matter scenario
Toy model and analytic calculation
Outline
Numerical analysis
Summary
Toy model to illustrate new thermal relic scenario
Boltzmann Eq. in the new scenario
Parameter space wherein the mediator lifetime controls the relic density
Toy model
SMοΌ‹ dark matter πœ™π‘‘ οΌ‹ mediator πœ™π‘š
Dark sector with degenerated in mass: π‘šπ‘‘ ≃ π‘šπ‘š
Communicator between dark sector and SM: SM Higgs πœ™
Our idea holds for other scenarios in
which communicator is not SM Higgs
Toy model (important point)
SMοΌ‹ dark matter πœ™π‘‘ οΌ‹ mediator πœ™π‘š
Dark sector with degenerated in mass: π‘šπ‘‘ ≃ π‘šπ‘š
Communicator between dark sector and SM: SM Higgs πœ™
Important: strong interaction
between πœ™π‘‘ and πœ™π‘š
πœ™π‘‘ and πœ™π‘š go out of equilibrium
with SM at the same time, and
their densities interplay each other
Necessary to solve a system of
evolution equations
Evolution Eq. (Boltzmann Eq.)
Boltzmann Eqs. for 𝑛𝑑 and π‘›π‘š
𝐻: Hubble parameter
πœŽπ‘£ : thermal averaged cross section
Ξ“ : thermal averaged decay rate
Evolution Eq. (Boltzmann Eq.)
Boltzmann Eqs. for 𝑛𝑑 and π‘›π‘š
DM annihilation/creation
via πœ™π‘‘ πœ™π‘‘ ↔ πœ™πœ™
Our scenario holds even
in the absence of the term
Our relic scenario works
also in scenarios wherein
DM is secluded from SM
𝑑
πœ™
𝑑
πœ™
Evolution Eq. (Boltzmann Eq.)
Boltzmann Eqs. for 𝑛𝑑 and π‘›π‘š
Our scenario holds even
in the absence of the term
why???
Indirect equilibrium is
achieved by strong π‘”π‘‘π‘‘π‘šπ‘š
and equilibrium of πœ™π‘š -πœ™
𝑑
π‘š
π‘š
πœ™
+
𝑑
π‘š
𝑑
πœ™
𝑑
πœ™
indirectly
π‘š
πœ™
Evolution Eq. (Boltzmann Eq.)
Boltzmann Eqs. for 𝑛𝑑 and π‘›π‘š
π‘š
πœ™
π‘š
πœ™
Thermalize πœ™π‘š (πœ™π‘‘ ) with
SM
Ensuring (1) 𝑇dark = 𝑇𝑆𝑀
(2) formulation with
well-known distribution
function
𝑑
π‘š
𝑑
π‘š
DM density can vary through only this process
DM density is fixed when this process is frozen
Evolution Eq. (Boltzmann Eq.)
Boltzmann Eqs. for 𝑛𝑑 and π‘›π‘š
π‘’π‘ž
π‘›π‘š /π‘›π‘š β‰  1 once πœ™π‘š
goes out of equilibrium
DM density is sensitive
π‘’π‘ž
whether π‘›π‘š /π‘›π‘š β‰  1 or
π‘’π‘ž
π‘›π‘š /π‘›π‘š = 1
Important: πœ™π‘š can go
out of equilibrium or not
πœ™
Decreasing π‘›π‘š and 𝑛𝑑 indirectly
via πœ™π‘‘ πœ™π‘‘ ↔ πœ™π‘š πœ™π‘š
π‘š
πœ™
Parameter space where lifetime controls DM density
Condition to maintain the equilibrium of πœ™π‘š and SM
derived in our paper
πœ™π‘š cannot go out of equilibrium for π‘”π‘šπœ™β€  πœ™ ≳ 10βˆ’7
π‘’π‘ž
π‘›π‘š(𝑑) = π‘›π‘š(𝑑) ∼ 𝑒 βˆ’π‘šπ‘š(𝑑)/𝑇 , and are fixed when πœ™π‘‘ πœ™π‘‘ ↔ πœ™π‘š πœ™π‘š freezes out
Well-known thermal relic scenario (but, annihilation to πœ™π‘š , not SM particles)
πœ™π‘š goes out of equilibrium, and its lifetime controls DM density
for π‘”π‘šπœ™β€  πœ™ ≲ 10βˆ’7
Evolution of DM density
Relation of DM relic density and mediator lifetime
Evolution : stage 1
𝐻
πœŽπ‘£
Ξ“
π‘šπ‘šπœ™πœ™ π‘›π‘š
D
πœŽπ‘£
Ξ“
ID
πœŽπ‘£
π‘‘π‘‘π‘šπ‘š 𝑛𝑑
π‘šπ‘šπ‘‘π‘‘ π‘›π‘š
Evolution : stage 2
Fake freeze out
𝐻
πœŽπ‘£
Ξ“
π‘šπ‘šπœ™πœ™ π‘›π‘š
D
πœŽπ‘£
Ξ“
ID
πœŽπ‘£
π‘‘π‘‘π‘šπ‘š 𝑛𝑑
π‘šπ‘šπ‘‘π‘‘ π‘›π‘š
Evolution : stage 3
𝑛𝑑 traces π‘›π‘š and decreases
∴
𝐻
πœŽπ‘£
Ξ“
π‘šπ‘šπœ™πœ™ π‘›π‘š
Violation of detailed valance due to
D
πœŽπ‘£
Ξ“
ID
πœŽπ‘£
π‘‘π‘‘π‘šπ‘š 𝑛𝑑
π‘šπ‘šπ‘‘π‘‘ π‘›π‘š
Evolution : stage 4
𝐻
πœŽπ‘£
π‘šπ‘šπœ™πœ™ π‘›π‘š
True freeze out
Ξ“
D
πœŽπ‘£
Ξ“
ID
πœŽπ‘£
π‘‘π‘‘π‘šπ‘š 𝑛𝑑
π‘šπ‘šπ‘‘π‘‘ π‘›π‘š
π‘’π‘ž
Lifetime dependence and effect of π‘Œπ‘š /π‘Œπ‘š β‰  1
No lifetime dependence for
π‘”π‘šπœ™πœ™ ≳ 10βˆ’7 , because πœ™π‘š holds
in equilibrium with SM
Lifetime dependence
on DM relic density
consistent with the condition analytically derived
For π‘”π‘šπœ™πœ™ ≳ 10βˆ’7 , detailed balance
π‘’π‘ž
of πœ™π‘š ↔ πœ™πœ™ keeps π‘›π‘š /π‘›π‘š = 1
DM evolves regardless of mediator
Long-lived
=1
ηŸ­ε―Ώε‘½
Short-lived
π‘’π‘ž
Lifetime dependence and effect of π‘Œπ‘š /π‘Œπ‘š β‰  1
Timing of DM freeze out also
depends on the πœ™π‘š lifetime
Lifetime dependence
on DM relic density
π‘›π‘š exponentially drops, and
balanced πœ™π‘‘ πœ™π‘‘ ↔ πœ™π‘š πœ™π‘š proceeds
to β€œone-way” πœ™π‘‘ πœ™π‘‘ β†’ πœ™π‘š πœ™π‘š
πœ™π‘š lifetime : key ingredient for
DM relic density
Long-lived
ηŸ­ε―Ώε‘½
Short-lived
Summary
DM scenarios secluded from SM are activated from the viewpoint
of observational motivations/constraints
Theoretical viewpoint suggests 𝑂(TeV) DM with degenerated mediator
Over-abundant DM in previous scenarios with long-lived mediator
due to too small DM annihilation rate
New relic scenario wherein mediator decouples from SM with DM, and
the lifetime controls DM density via decaying before freeze out of DM
Toy model with Higgs communicator accounts for the observed density
Our idea holds for other scenarios in which communicator is not Higgs
Thank you very much!
γƒ€γƒΌγ‚―γ‚»γ‚―γ‚ΏγƒΌζΈ©εΊ¦γ―ζ¨™ζΊ–ζ¨‘εž‹γ‚»γ‚―γ‚ΏγƒΌγ¨εŒγ˜οΌŸ
Condition that lifetime controls DM density (derivation)
Only πœ™π‘š ↔ πœ™ † πœ™ for the process of πœ™π‘š and SM @ 𝑇 < π‘šπ‘š
Rewriting Boltzmann Eq. in terms of π‘‹π‘š = π‘›π‘š 𝑅3 (𝑅: scale factor)
π‘’π‘ž
πœ™π‘š goes out of equilibrium at 𝑑0 , then π‘‹π‘š = π‘‹π‘š + 𝐢𝑒 βˆ’ Ξ“ Δ𝑑/2 at 𝑑0 + Δ𝑑
πœ™π‘š immediately goes back to equilibrium as long as
Condition that lifetime controls DM density (derivation)
π‘’π‘ž
Assumption in this step β€œconstant π‘‹π‘š in Δ𝑑”
eq
eq
Requirement for justification: Ξ”Xm /Xm β‰ͺ 1 in Δ𝑑
π‘’π‘ž
Ξ”π‘‹π‘š
π‘’π‘ž
π‘‹π‘š
β‰ƒβˆ’
π‘šπ‘š
Δ𝑑𝐻 β‰ͺ 1
𝑇
Condition that lifetime controls DM density (derivation)
Condition to maintain the equilibrium of πœ™π‘š by combining inequalities
In other parameter cases
Lifetime can control DM density
even for different interaction
strength of πœ™π‘‘ -πœ™π‘š and/or πœ™π‘‘(π‘š) -πœ™
Holds for various models and
scenarios
Relic density in degenerated DM-mediator system
Previous scenarios can not
account for the observed density
in degenerated system (solid)
Our scenario successfully yields
the observed DM density even in
DM-Med. degenerated system
Novel possibility of DM model
buildings is introduced wherein
πœ™π‘‘ and πœ™π‘š are unified in a dark
symmetry multiplet
Contour of observed DM density
X: mass ratio of DM and mediator
Y: coupling of πœ™π‘‘ πœ™π‘‘ πœ™π‘š πœ™π‘š
Ex. 1: Secluded DM scenario
Framework : SM + DM + mediator
DM annihilates into only mediator
Mediator decays into SM particles
after freeze out of DM density
Requirement to account for observed DM density: π‘šDM ≫ π‘šm
DM density ∝ πœŽπ‘£DMβ†’M
βˆ’1
2
∝ 𝑠 βˆ’ 4π‘šπ‘š
βˆ’1
2
2
≃ 4π‘šπ·π‘€
βˆ’ 4π‘šπ‘š
βˆ’1
Feature: Cosmic ray anomaly can be reproduced by selecting
daughter particles with tuned π‘šπ‘š
Ex. 2: SIMP DM scenario
Framework : SM + DM + mediator
Decreasing DM density through
DM + DM + DM β†’ DM + DM
Getting cold daughter DM by
transporting DM energy to SM
Requirement to account for observed DM density: π‘šDM ∼ 𝑂(100MeV)
Reaction rate:
2
𝑛DM
πœŽπ‘£
2
3β†’2
3
≃ (π‘šDM 𝑇)
𝑒
βˆ’π‘šDM /𝑇 2
3
5
β‹… (𝛼𝑒𝑓𝑓
/π‘šDM
)
Feature: shortcoming of small scale structure can be explained by
strong self-interaction of DM
Scenario: Heavy DM with degenerated mediator
Can DM density be observed
one in such a scenario?
Seems to be impossible due to
small phase space and unitarity
bound on the coupling
Key ingredient:
Mediator lifetime, which can
make the impossible possible
Evolution : stage 1
1
10
Thermalization of dark
sector via scatterings
with SM particles
Reaction rate πœŽπ‘£ π‘šπ‘šπœ™πœ™ π‘›π‘š
becomes smaller than 𝐻
πœ™π‘‘ and πœ™π‘š decouple from
equilibrium with SM
𝐻
πœŽπ‘£
Ξ“
π‘šπ‘šπœ™πœ™ π‘›π‘š
D
πœŽπ‘£
Ξ“
𝑧 = π‘šπ‘‘ /𝑇
ID
πœŽπ‘£
π‘‘π‘‘π‘šπ‘š 𝑛𝑑
π‘šπ‘šπ‘‘π‘‘ π‘›π‘š
Evolution : stage 2
10
Mediator decay rate 𝛀
is smaller than 𝐻
𝐷
πœ™π‘‘ and πœ™π‘š densities are
temporarily frozen
(β€œterrace” structure)
102
𝐻
Mediator decay becomes
active, because 𝛀 𝐷 > 𝐻
Mediator density starts
to decrease exponentially
𝑧 = π‘šπ‘‘ /𝑇
πœŽπ‘£
Ξ“
π‘šπ‘šπœ™πœ™ π‘›π‘š
D
πœŽπ‘£
Ξ“
ID
πœŽπ‘£
π‘‘π‘‘π‘šπ‘š 𝑛𝑑
π‘šπ‘šπ‘‘π‘‘ π‘›π‘š
Evolution : stage 3
102
103
Due to large rate of
πœ™π‘‘ πœ™π‘‘ ↔ πœ™π‘š πœ™π‘š ,
πœ™π‘‘ density tracks
decreasing πœ™π‘š density
𝛀 𝐷 exceeds interaction
rates πœŽπ‘£ π‘‘π‘‘π‘šπ‘š 𝑛𝑑 and
πœŽπ‘£ π‘šπ‘šπ‘‘π‘‘ π‘›π‘š
Large gap of πœ™π‘‘ and πœ™π‘š
density breaks detailed
balance of πœ™π‘‘ πœ™π‘‘ ↔ πœ™π‘š πœ™π‘š
𝑧 = π‘šπ‘‘ /𝑇
Detail will be illustrated soon
𝐻
πœŽπ‘£
Ξ“
π‘šπ‘šπœ™πœ™ π‘›π‘š
D
πœŽπ‘£
Ξ“
ID
πœŽπ‘£
π‘‘π‘‘π‘šπ‘š 𝑛𝑑
π‘šπ‘šπ‘‘π‘‘ π‘›π‘š
Evolution : stage 4
103
πœŽπ‘£ π‘šπ‘šπ‘‘π‘‘ π‘›π‘š < 𝐻, and
πœ™π‘š πœ™π‘š β†’ πœ™π‘‘ πœ™π‘‘ is frozen
πœŽπ‘£ π‘‘π‘‘π‘šπ‘š 𝑛𝑑 < 𝐻, and
πœ™π‘‘ πœ™π‘‘ β†’ πœ™π‘š πœ™π‘š is also frozen
104
𝑧 = π‘šπ‘‘ /𝑇
True freeze out of DM
via the decoupling from
mediator
Observed DM density is
obtained in DM-mediator
degenerated system
𝐻
πœŽπ‘£
Ξ“
π‘šπ‘šπœ™πœ™ π‘›π‘š
D
πœŽπ‘£
Ξ“
ID
πœŽπ‘£
π‘‘π‘‘π‘šπ‘š 𝑛𝑑
π‘šπ‘šπ‘‘π‘‘ π‘›π‘š

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