1. Max Planck Institute for Physics, Munich
Solar Axions
Supernova 1987A
Early Universe
Dark Matter
Long-Range Force
Axion Landscape
Georg Raffelt
Max Planck Institute for Physics, Munich

2. High- and Low-Energy Frontiers in Particle Physics
10 27 eV
Planck
mass
GUT
scale
Electroweak
QCD
Cosmological
constant
10 24
10 21
10 18
10 15
10 12
10 9
10 6
10 3 1
10 −3
10 −6
“for the theoretical discovery of a mechanism that contributes to our understanding of the origin of mass of subatomic particles, and which recently was confirmed through the discovery of the predicted fundamental par-ticle, by the ATLAS and CMS experiments at CERN’s Large Hadron Collider”
P. Higgs
F. Englert
2013
22 mg
“for the discovery of neutrino oscillations, which shows that neutrinos have mass”
T. Kajita
A. McDonald
2015

3. High- and Low-Energy Frontiers in Particle Physics
10 27 eV
Planck
mass
GUT
scale
Electroweak
QCD
Cosmological
constant
10 24
10 21
10 18
10 15
10 12
10 9
10 6
10 3 1
10 −3
10 −6
𝒎 𝑫
𝒎 𝑫 𝟐 𝑴 𝑴
Heavy right-handed
neutrinos
(see-saw mechanism)
WIMP dark matter
(related to EW scale, perhaps SUSY)
Axion dark matter (related to Peccei-Quinn symmetry)
𝒇 𝒂
𝒎 𝒂 ∼ 𝒎 𝝅 𝒇 𝝅 𝒇 𝒂
𝒎 𝝅 , 𝒇 𝝅

4. Bestiarium of Low-Mass Bosons
Weakly Interacting Sub-eV Particles (WISPs)
• Axion (1 parameter family 𝑚 𝑎 𝑓 𝑎 ∼ 𝑚 𝜋 𝑓 𝜋 )
Solves strong CP problem
Could be dark matter
• String axions
(almost massless pseudoscalars in string theory)
One of them may solve CP problem
• Axion-like particles (ALPs)
Generic two-photon vertex, could be dark matter
(2 parameters 𝑚 𝑎 and 𝑔 𝑎𝛾 )
• Hidden photons
Low-mass gauge bosons from 𝑈′(1)
(kinetic mixing parameter 𝜒 and mass 𝑚 𝛾′ )
• Chameleons
Scalars in certain models of scalar-tensor gravity
Motivated by dark energy
Environment-dependent properties

5. CP Violation in Particle Physics
Discrete symmetries in particle physics
C – Charge conjugation, transforms particles to antiparticles
violated by weak interactions
P – Parity, changes left-handedness to right-handedness
T – Time reversal, changes direction of motion (forward to backward)
CPT – exactly conserved in quantum field theory
CP – conserved by all gauge interactions
violated by three-flavor quark mixing matrix
All measured CP-violating effects derive
from a single phase in the quark mass matrix
(Kobayashi-Maskawa phase),
i.e. from complex Yukawa couplings
Cosmic matter-antimatter asymmetry
requires new ingredients
M. Kobayashi
T. Maskawa
Physics Nobel Prize 2008

6. The CP Problem of Strong Interactions
Real quark
mass
Phase from
Yukawa coupling
Angle
variable
CP-odd
quantity ∼𝐄⋅𝐁
ℒ QCD = 𝑞 𝜓 𝑞 i𝐷− 𝑚 𝑞 𝑒 i 𝜃 𝑞 𝜓 𝑞 − 𝐺 𝜇𝜈𝑎 𝐺 𝑎 𝜇𝜈 −Θ 𝛼 s 8𝜋 𝐺 𝜇𝜈𝑎 𝐺 𝑎 𝜇𝜈
Remove phase of mass term by chiral transformation of quark fields
𝜓 𝑞 → 𝑒 −𝑖 𝛾 5 𝜃 𝑞 /2 𝜓 𝑞
ℒ QCD = 𝑞 𝜓 𝑞 i𝐷− 𝑚 𝑞 𝜓 𝑞 − 𝐺𝐺− Θ−arg det 𝑀 𝑞 −𝜋 ≤ Θ ≤+𝜋 𝛼 s 8𝜋 𝐺 𝐺
Θ can be traded between quark phases and 𝐺 𝐺 term
No physical impact if at least one 𝑚 𝑞 =0
Induces a large neutron electric dipole moment (a T-violating quantity)
Experimental limits: 𝚯 < 𝟏𝟎 −𝟏𝟏 Why so small?

7. Strong CP Problem QCD vacuum energy 𝑉(Θ) Λ QCD 4 Equivalent Equivalent
Peccei-Quinn solution:
Make 𝚯 dynamical, let system relax to lowest energy Θ
−2𝜋 −𝜋 +𝜋
+2𝜋
• CP conserving vacuum has Θ=0 (Vafa and Witten 1984)
• QCD could have any −𝜋≤Θ≤+𝜋, is “constant of nature”
• Energy can not be minimized: Θ not dynamical

8. The Pool Table Analogy (Pierre Sikivie 1996)
Gravity
Pool table
Symmetric
relative
to gravity
Axis
Symmetry
dynamically
restored
(Peccei & Quinn 1977)
New degree
of freedom
 Axion 𝚯
(Weinberg 1978, Wilczek 1978) fa
Symmetry
broken
Floor
inclined

9. 37 Years of Axions

10. The Cleansing Axion “I named them after a laundry
Frank Wilczek
“I named them after a laundry
detergent, since they clean up
a problem with an axial current.”
(Nobel lecture 2004)

11. Arthur Godfrey

12. Opportunities for detection
Axion Bounds
mPlanck fa
1018
1015
1012
109
106
GeV eV
meV ma
neV
peV
Astrophysical Bounds
(Energy loss of stars)
Supernova 1987A
Globular Cluster
Opportunities for detection

13. Experimental Tests of Invisible Axions
Primakoff effect:
Axion-photon transition in external
static E or B field
(Originally discussed for 𝜋 0
by Henri Primakoff 1951)
Pierre Sikivie:
Macroscopic B-field can provide a
large coherent transition rate over
a big volume (low-mass axions)
Axion helioscope:
Look at the Sun through a dipole magnet
Axion haloscope:
Look for dark-matter axions with
a microwave resonant cavity
Two-photon vertex generic for
𝜋 0 , 𝜂, axion-like particles (ALPs), gravitons

14. Search for Solar Axions
Axion Helioscope
(Sikivie 1983)
Primakoff
production
Axion flux N a g a g
Magnet S
Axion-Photon-Oscillation
Sun
Tokyo Axion Helioscope (“Sumico”)
(Results since 1998, up again 2008)
CERN Axion Solar Telescope (CAST)
(Data since 2003)
Alternative technique:
Bragg conversion in crystal
Experimental limits on solar axion flux
from dark-matter experiments
(SOLAX, COSME, DAMA, CDMS ...)

15. CERN Axion Solar Telescope (CAST)

16. CAST Results

17. Parameter Space for Axion-Like Particles (ALPs)
Two parameters:
- ALP mass 𝑚 𝑎
- ALP-𝛾 coupling 𝑔 𝑎𝛾
Weinberg Wilczek
“standard axion”
Model dependence
(KSVZ, DFSZ, …) broadens
the “axion line”
Γ 𝑎→𝛾𝛾 = 𝑔 𝑎𝛾 2 𝑚 𝑎 3 64𝜋

18. Parameter Space for Axion-Like Particles (ALPs)
CAST exclusion range

19. Parameter Space for Axion-Like Particles (ALPs)
ALPS-II at DESY

20. Shining TeV Gamma Rays through the Universe
Figure from a talk by Manuel Meyer (Univ. Hamburg)

21. Next Generation Axion Helioscope (IAXO) at CERN
Need new magnet w/
– Much bigger aperture:
~1 m2 per bore
– Lighter (no iron yoke)
– Bores at Troom
• Irastorza et al.: Towards a new generation axion helioscope, arXiv:
• Armengaud et al.:
Conceptual Design of the International Axion Observatory (IAXO), arXiv:

22. Parameter Space for Axion-Like Particles (ALPs)
- Improvement by
a factor of 30
- Leaping into
uncharted territory
Pushing generic
ALP frontier
QCD Axion
meV frontier

23. Pie Chart of Dark Matter of the Universe
Dark Energy 70%
(Cosmological Constant)
Neutrinos %
Ordinary Matter 5%
(of this only about
10% luminous)
Dark Matter
25%

24. Creation of Cosmological Axions by Re-alignment
𝑻 ~ 𝒇 𝒂 (very early universe)
UPQ(1) spontaneously broken
Higgs field settles in “Mexican hat”
Axion field sits fixed at 𝑎𝑖 =Θ𝑖 𝑓 𝑎 𝑎
𝑉(𝑎)
𝑻 ~ 𝟏 GeV (𝑯 ~ 𝟏𝟎 −𝟗 eV)
Axion mass turns on quickly
by thermal instanton gas
Field starts oscillating when
𝑚𝑎 ≳ 3𝐻
Classical field oscillations (axions at rest)
𝑉(𝑎) 𝑎
Θ =0
Axions are born as nonrelativistic, classical field oscillations
Very small mass, yet cold dark matter

25. Axion Cosmology in PLB 120 (1983)

26. Galactic WIMP vs Axion Dark Matter
Local dark matter density around 0.4 GeV/cm3
WIMPs: Typical mass 100 GeV
• Local number density:
𝟒𝟎𝟎𝟎 𝐦 −𝟑 𝟏𝟎𝟎 𝐆𝐞𝐕 𝒎 𝐖𝐈𝐌𝐏
Dilute gas of particles
Axions: Typical mass 10 meV
• Local number density:
𝟒×𝟏 𝟎 𝟏𝟗 𝐦 −𝟑 𝟏𝟎 𝛍𝐞𝐕 𝒎 𝒂
• Typical galactic virial velocity:
𝒗 𝐠𝐚𝐥 ∼𝟏 𝟎 −𝟑 𝒄
• Typical de Broglie wavelength
(“localisation”)
𝝀∼ 𝟐𝝅 𝒎 𝒂 𝒗 𝐠𝐚𝐥 ∼𝟏𝟎𝟎 𝐦 𝟏𝟎 𝛍𝐞𝐕 𝒎 𝒂
• Typical occupation number
𝒇∼𝟏 𝟎 𝟐𝟓 𝟏𝟎 𝛍𝐞𝐕 𝒎 𝒂 𝟒
Highly degenerate Bose gas!

27. Axion Dark Matter Driving Oscillators
Relic oscillations of QCD Q term
• Drives oscillating neutron EDM
• Drives oscillating E-field in
microwave cavity w/ B-field +𝜋 −𝜋
Λ QCD 4
Θ=a/ f a n
Axion-induced
electric field
oscillating with
𝝎= 𝒎 𝒂
External
static
B-field
Neutron electric dipole moment
oscillating with 𝝎= 𝒎 𝒂

28. Cold Axion Populations
Scenario 1
• Cosmic inflation first
• PQ symmetry breaking at 𝑇∼ 𝑓 𝑎
• Every causal patch has different random Θ 𝑖
• Topological defects at interfaces
• Axion dark matter from
- average re-alignment
- cosmic-string (CS) & domain-wall (DW) decay
Cosmic axion
string
Random
Θ 𝑖 values
0.01
1.12
0.37
1.93
0.63
2.01
3.14
0.17
1.57
Scenario 2
• Cosmic inflation after PQ symmetry breaking
• All axions from re-alignment of one random
Θ i in our patch of the universe
• Allows large 𝑓 𝑎 if Θ 𝑖 ≪1 (“anthropic” case)
Θ 𝑖 =1.57
𝛺 𝑎 ℎ 2 =0.20 Θ 𝑖 𝑓 𝑎 GeV =0.11 Θ 𝑖 𝜇eV 𝑚 𝑎

29. Axion Production by Domain Wall and String Decay
Recent numerical studies of collapse
of string-domain wall system
Ω 𝑎 ℎ 2 = 8.4± 𝑓 𝑎 GeV
× 𝑔 ∗, − Λ 400 MeV
Implies a CDM axion mass of
𝑚 𝑎 ∼300 𝜇eV
Hiramatsu, Kawasaki, Saikawa &
Sekiguchi, arXiv: (2012)
More recently by the same group
𝑚 𝑎 ∼90−140 𝜇eV
Kawasaki, Saikawa & Sekiguchi,
arXiv: (PRD 2015)

30. Axion Dark Matter Parameters
mPlanck fa
1018
1015
1012
109
106
GeV eV
meV ma
neV
peV
kHz
MHz
GHz
THz na
Too much dark matter in
re-aligment scenario with 𝚯 𝐢 =𝟏
Axion DM
Astrophysical Bounds
(Energy loss of stars)
Too much dark matter in
cosmic string and domain wall scenario
Axion DM

31. Search for Galactic Axions (Cold Dark Matter)
Dark matter axions
Velocities in galaxy
Energies therefore
ma = meV
va  10-3 c
Ea  (1  10-6) ma
Microwave Energies
(1 GHz  4 meV)
Axion Haloscope (Sikivie 1983)
Power
Frequency ma
Axion Signal
Bext  8 Tesla
Thermal noise of
cavity & detector
Microwave
Resonator
Q  105
Power of galactic axion signal
Primakoff Conversion g
4× 10 −21 W 𝑉 m 𝐵 8.5 T 2 𝑄 × 𝑚 a 2𝜋 GHz 𝜌 𝑎 5× 10 −25 g/cm 3 a
Cavity
overcomes
momentum
mismatch
Bext

32. Axion Dark Matter Experiment (ADMX) – Seattle
Adapted from Gray Rybka

33. SQUID Microwave Amplifiers in ADMX
Adapted from Gianpaolo Carosi

34. ADMX Gen 2

35. Axion Dark Matter Parameters
mPlanck fa
1018
1015
1012
109
106
GeV eV
meV ma
neV
peV
kHz
MHz
GHz
THz na
Too much dark matter in
re-aligment scenario with 𝚯 𝐢 =𝟏
Axion DM
Astrophysical Bounds
(Energy loss of stars)
Too much dark matter in
cosmic string and domain wall scenario
Axion DM
ADMX
Taking data

36. Axion Dark Matter Search with Transition Radiation
Dark matter axion field producing photons at dielectric interface (in B-field!)
(Jaeckel & Redondo, PRD 88 (2013) , arXiv: )
“Seed project” at MPI Physics:
Test practical boost factor with a setup
that contains up to five exchangeable
discs (diameter ~200 mm) with
high-ε material that can be positioned
using motor drives with a precision of
a few μm

37. Center for Axion and Precision Physics (CAPP)
Yannis
Semertzidis
15 Oct 2013
The plan is to launch a competitive Axion Dark Matter Experiment in Korea, participate in state-of-the-art axion experiments around the world, play a leading role in the proposed proton electric-dipole-moment (EDM) experiment and take a significant role in storage-ring precision physics involving EDM and muon g–2 experiments.

38. Searching for Axions in the Anthropic Window
CASPEr experiment
Precise magnetometry to measure
tiny deviations from Larmor frequency
Graham & Rajendran, arXiv:
Budker, Graham, Ledbetter, Rajendran & Sushkov, arXiv:

39. ARIADNE: Axion Resonant InterAction DetectioN Experiment
NMR Experiment
ARIADNE: Axion Resonant InterAction DetectioN Experiment
A.Geraci, A.Arvanitaki, A.Kapitulnik, Chen-Yu Liu, J.Long, Y.Semertzidis, M.Snow
(to be supported by NSF and/or DoE?)

40. Axion Searches mPlanck fa 1018 1015 1012 109 106 GeV eV meV ma neV peV
kHz
MHz
GHz
THz na
Taking
data
IAXO
CASPEr
ARIADNE
Astrophysical Bounds
(Energy loss of stars)

41. Axion and Axion-Like Particle Searches
ARIADNE
Center for Axion & Precision Physics (Daejon, Korea)
WISP
DMX
(DESY)
MAGIC
ADMX-HF
(Yale)
Axion Dark Matter
Experiment
(UW, Seattle)
H.E.S.S.
IAXO Proposal
(CERN)
CASPEr, HIM (Mainz)
Fermi LAT
CERN

42. Dow Jones Index of Axion Physics
It’s a bull market,
buy shares!
Dow Jones Index of Axion Physics
inSPIRE: Citation of Peccei-Quinn papers or title axion (and similar)