Radiative dark matter
Polarization state of photons
Asymmetric dark matter
Conclusions
Polarisation of photons emitted by decaying dark matter
A. Tokareva (EPFL, Lausanne) in collaboration with M. Shaposhnikov
(EPFL, Lausanne) and D. Gorbunov (INR, Moscow)
September, 5
A. Tokareva (EPFL, Lausanne) in collaboration with M. Shaposhnikov
Polarisation
(EPFL,
of photons
Lausanne)
emitted
and by
D.decaying
Gorbunovdark
(INR,
matter
Mosco
Radiative dark matter
Polarization state of photons
Asymmetric dark matter
Conclusions
1
Radiative dark matter
The observational status of 3.5 keV line
Models
2
Polarization state of photons
Scalar
Fermion
Atomic transition
How to distinguish?
3
Asymmetric dark matter
4
Conclusions
A. Tokareva (EPFL, Lausanne) in collaboration with M. Shaposhnikov
Polarisation
(EPFL,
of photons
Lausanne)
emitted
and by
D.decaying
Gorbunovdark
(INR,
matter
Mosco
Radiative dark matter
Polarization state of photons
Asymmetric dark matter
Conclusions
The observational status of 3.5 keV line
Models
Indications of the unidentified X-ray line
E.Bulbul et al., Astrophys.J. 789 (2014) 13,
A.Boyarsky et al., Phys.Rev.Lett. 113 (2014) 251301,
arXiv:1402.4119
0.36
-1
3.57 keV
XMM - PN
Rest of the Sample
(69 Clusters)
1. 8 M
s
0.5
M31 ON-center
0.34
[cts/sec/keV]
0.75
Normalized count rate
-1
Flux (cnts s keV )
arXiv:1402.2301
No line at 3.5 keV
0.32
0.30
0.28
0.26
0.24
0.22
[cts/sec/keV]
0
No line at 3.5 keV
Line at 3.5 keV
8⋅10-3
0.02
Data - model
Residuals
1⋅10-2
6⋅10-3
4⋅10-3
2⋅10-3
0⋅100
-2⋅10-3
-0.02
3
3.2
3.4
3.6
Energy (keV)
3.8
4
-4⋅10-3
3.0
3.2
3.4
3.6
3.8
4.0
Energy [keV]
A. Tokareva (EPFL, Lausanne) in collaboration with M. Shaposhnikov
Polarisation
(EPFL,
of photons
Lausanne)
emitted
and by
D.decaying
Gorbunovdark
(INR,
matter
Mosco
Radiative dark matter
Polarization state of photons
Asymmetric dark matter
Conclusions
The observational status of 3.5 keV line
Models
X-ray line non-confirmed by Hitomi
Hitomi Collaboration (Felix A. Aharonian et al.),
arXiv:1607.07420
X-ray telescope Hitomi (Astro-H) destroyed 26th of
March 2016. It worked 37 days instead of 3 years planned.
The next mission is needed...
A. Tokareva (EPFL, Lausanne) in collaboration with M. Shaposhnikov
Polarisation
(EPFL,
of photons
Lausanne)
emitted
and by
D.decaying
Gorbunovdark
(INR,
matter
Mosco
Radiative dark matter
Polarization state of photons
Asymmetric dark matter
Conclusions
The observational status of 3.5 keV line
Models
Radiative keV dark matter models
Sterile neutrino (νMSM)
Axion or axion-like particle
SUSY: axino, gravitino
Majoron
Excited dark matter
Annihilating dark matter
... about 300 papers explaining 3.5 keV line!
How to choose?
A. Tokareva (EPFL, Lausanne) in collaboration with M. Shaposhnikov
Polarisation
(EPFL,
of photons
Lausanne)
emitted
and by
D.decaying
Gorbunovdark
(INR,
matter
Mosco
Radiative dark matter
Polarization state of photons
Asymmetric dark matter
Conclusions
Scalar
Fermion
Atomic transition
How to distinguish?
Two polarization states
|Li
|Ri
Spin projection:
(sk) = −1
(sk) = 1
Which particles may emit polarized photons?
A. Tokareva (EPFL, Lausanne) in collaboration with M. Shaposhnikov
Polarisation
(EPFL,
of photons
Lausanne)
emitted
and by
D.decaying
Gorbunovdark
(INR,
matter
Mosco
Radiative dark matter
Polarization state of photons
Asymmetric dark matter
Conclusions
Scalar
Fermion
Atomic transition
How to distinguish?
Scalar and pseudoscalar decay
1
φFµν F µν ,
Λ
γ
γ
a
L=
1
aFµν F̃ µν , Λ ∼ MP
Λ
ρ=(|L><L|+|R><R|)/2
ρ= 1_
entangled _ _
_
(|LL>+|RR>)/√2
(1 0
(
L=
2 0 1
A. Tokareva (EPFL, Lausanne) in collaboration with M. Shaposhnikov
Polarisation
(EPFL,
of photons
Lausanne)
emitted
and by
D.decaying
Gorbunovdark
(INR,
matter
Mosco
Radiative dark matter
Polarization state of photons
Asymmetric dark matter
Conclusions
Scalar
Fermion
Atomic transition
How to distinguish?
Fermion effective interaction with photon
Higgs portal:
LνMSM = f l¯L N H̃ + h.c. .
ν
N
h
l
l
L=
γ
v
ν̄L σµν N F µν + h.c.
Λ2
A. Tokareva (EPFL, Lausanne) in collaboration with M. Shaposhnikov
Polarisation
(EPFL,
of photons
Lausanne)
emitted
and by
D.decaying
Gorbunovdark
(INR,
matter
Mosco
Radiative dark matter
Polarization state of photons
Asymmetric dark matter
Conclusions
Scalar
Fermion
Atomic transition
How to distinguish?
Dirac fermion decay
νL
sz=-1/2
ψ
γ
A. Tokareva (EPFL, Lausanne) in collaboration with M. Shaposhnikov
Polarisation
(EPFL,
of photons
Lausanne)
emitted
and by
D.decaying
Gorbunovdark
(INR,
matter
Mosco
Radiative dark matter
Polarization state of photons
Asymmetric dark matter
Conclusions
Scalar
Fermion
Atomic transition
How to distinguish?
Dirac fermion decay
νL
sz=-1/2
ψ
γ
sz=-1 ?
- wrong because
sz(ψ)=-3/2 - impossible
No |R> state!
A. Tokareva (EPFL, Lausanne) in collaboration with M. Shaposhnikov
Polarisation
(EPFL,
of photons
Lausanne)
emitted
and by
D.decaying
Gorbunovdark
(INR,
matter
Mosco
Radiative dark matter
Polarization state of photons
Asymmetric dark matter
Conclusions
Scalar
Fermion
Atomic transition
How to distinguish?
Dirac fermion decay
νL
sz=-1/2
ψ
γ
sz=1
pure |L> state
A. Tokareva (EPFL, Lausanne) in collaboration with M. Shaposhnikov
Polarisation
(EPFL,
of photons
Lausanne)
emitted
and by
D.decaying
Gorbunovdark
(INR,
matter
Mosco
Radiative dark matter
Polarization state of photons
Asymmetric dark matter
Conclusions
Scalar
Fermion
Atomic transition
How to distinguish?
Dirac fermion decay
νL
sz=-1/2
_
νR
_
ψ
ψ
γ
sz= 1/2
sz=1
pure |L> state
γ
sz=-1
pure |R> state
A. Tokareva (EPFL, Lausanne) in collaboration with M. Shaposhnikov
Polarisation
(EPFL,
of photons
Lausanne)
emitted
and by
D.decaying
Gorbunovdark
(INR,
matter
Mosco
Radiative dark matter
Polarization state of photons
Asymmetric dark matter
Conclusions
Scalar
Fermion
Atomic transition
How to distinguish?
Majorana fermion decay
Each particle may decay both to ν and ν̄
The state of photon is defined by the state of N which depends on the
production mechanism
Thermal production or inflaton decay:
1
ρ = (|RihR| + |LihL|).
2
Resonant production (Shi, Fuller, Phys. Rev. Lett. 82, 2832 (1999)):
common pure state
√
√
1 − β|Li + √βe iα |Ri, with probability 12 ,
|γi = √
1 − β|Ri + βe iα |Li, with probability 12 .
A. Tokareva (EPFL, Lausanne) in collaboration with M. Shaposhnikov
Polarisation
(EPFL,
of photons
Lausanne)
emitted
and by
D.decaying
Gorbunovdark
(INR,
matter
Mosco
Radiative dark matter
Polarization state of photons
Asymmetric dark matter
Conclusions
Scalar
Fermion
Atomic transition
How to distinguish?
Polarisation of photon from atomic transition
Dipolar transition:
s
p
m=0
m=-1
|R>
Right
m=0
_
(|R>+eiα|L>)/√2
Linear
m=1
|L>
Left

1
|Ri, with probability 3 ,
1
|γi = |Li, with probability 3 ,
 √1 (|Ri + e iα |Li), with probability 1 .
3
2
A. Tokareva (EPFL, Lausanne) in collaboration with M. Shaposhnikov
Polarisation
(EPFL,
of photons
Lausanne)
emitted
and by
D.decaying
Gorbunovdark
(INR,
matter
Mosco
Radiative dark matter
Polarization state of photons
Asymmetric dark matter
Conclusions
Scalar
Fermion
Atomic transition
How to distinguish?
Pure or mixed state?
=|L>
=(|R><R|+|L><L|)/2=ρ1
=|R>
?
=
pure state
mixed state
measured:
<Ψ|O1(x1)...On(xn)|Ψ>
Tr[ρN O1(x1)...On(xn)]
O - any gauge invariant operator containing photon field
A. Tokareva (EPFL, Lausanne) in collaboration with M. Shaposhnikov
Polarisation
(EPFL,
of photons
Lausanne)
emitted
and by
D.decaying
Gorbunovdark
(INR,
matter
Mosco
Radiative dark matter
Polarization state of photons
Asymmetric dark matter
Conclusions
Scalar
Fermion
Atomic transition
How to distinguish?
Dispersion of correlators
Theorem: (S.LLoyd)
Difference between measurement for pure and mixed state is smaller than
the dispersion (mistake) for mixed state.
h(hΨ|A|Ψi − Tr(ρA))2 i|Ψi =
Tr(ρA2 ) − (Tr(ρA))2
N +1
A = O1 ...On – product of gauge invariant operators
N – number of considering photons
ρ ∼ 1 – maximally mixed state
Conclusion: all discussed cases provide equivalent result.
A. Tokareva (EPFL, Lausanne) in collaboration with M. Shaposhnikov
Polarisation
(EPFL,
of photons
Lausanne)
emitted
and by
D.decaying
Gorbunovdark
(INR,
matter
Mosco
Radiative dark matter
Polarization state of photons
Asymmetric dark matter
Conclusions
Asymmetric Dirac fermionic dark matter
nψ 6= nψ̄ ⇒ circular polarization
1
1
n̄ 0
ρ=
= (1 − ηψ σ3 ) ,
n + n̄ 0 n
2
The example of model:
Dirac sterile neutrino instead of Majorana.
Production:
Resonant conversion of SM neutrinos to sterile (Shi, Fuller)
The SM lepton asymmetry (if large enough) directly goes to DM
asymmetry
Natural to have ηψ ∼ 1.
A. Tokareva (EPFL, Lausanne) in collaboration with M. Shaposhnikov
Polarisation
(EPFL,
of photons
Lausanne)
emitted
and by
D.decaying
Gorbunovdark
(INR,
matter
Mosco
Radiative dark matter
Polarization state of photons
Asymmetric dark matter
Conclusions
Summary
Polarization of photons from DM line may give some information
about the dark sector
CP-symmetric dark matter will always provide unpolarized flux of
photons. It is impossible to distinguish between scalar, spinor, dark
transition, self-annihilation models.
Asymmetric Dirac fermionic DM will emit circularly polarized line
Circular polarization of X-ray photons may be a smoking gun of CP
asymmetry in the dark sector
It looks as a good motivation for future observations sensitive to the
circular polarization
A. Tokareva (EPFL, Lausanne) in collaboration with M. Shaposhnikov
Polarisation
(EPFL,
of photons
Lausanne)
emitted
and by
D.decaying
Gorbunovdark
(INR,
matter
Mosco
Radiative dark matter
Polarization state of photons
Asymmetric dark matter
Conclusions
Thanks for your attention!
A. Tokareva (EPFL, Lausanne) in collaboration with M. Shaposhnikov
Polarisation
(EPFL,
of photons
Lausanne)
emitted
and by
D.decaying
Gorbunovdark
(INR,
matter
Mosco