1. Georg G. Raffelt, Max-Planck-Institut für Physik, München
Solar Axions
Globular Cluster
Supernova 1987A
TeV Gamma Rays
Gravity Waves
Axions in the Skies
Georg G. Raffelt, Max-Planck-Institut für Physik, München

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
Cosmic rays
High-Energy Frontier
CERN
22 mg
Low-E Frontier
“Intensity Frontier”
(feeble interactions)

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)
Axion dark matter (related to Peccei-Quinn symmetry)
𝒇 𝒂
𝒎 𝒂 ∼ 𝒎 𝝅 𝒇 𝝅 𝒇 𝒂
𝒎 𝝅 , 𝒇 𝝅

4. 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
Black Hole
Super-Radiance
AxDM
Experimental & Astro Limits
Allowed fa SR
Axion dark matter (related to Peccei-Quinn symmetry)
𝒇 𝒂
𝒎 𝒂 ∼ 𝒎 𝝅 𝒇 𝝅 𝒇 𝒂
𝒎 𝝅 , 𝒇 𝝅

5. Super-Radiance
Masha Baryakhtar, Talk at Invisibles 2016,

6. Super-Radiance
Masha Baryakhtar, Talk at Invisibles 2016,

7. Gravitational Wave Signals
Arvanitaki, Baryakhtar, Dimopoulos, Dubovsky & Lasenby, arXiv:
Masha Baryakhtar, Talk at Invisibles 2016,

8. 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
Grav.Waves
from BHs
AxDM
Experimental & Astro Limits
Allowed fa SR
Axion dark matter (related to Peccei-Quinn symmetry)
𝒇 𝒂
𝒎 𝒂 ∼ 𝒎 𝝅 𝒇 𝝅 𝒇 𝒂
𝒎 𝝅 , 𝒇 𝝅

9. Solar Axions and Axion-Like Particles
Solar Models
Solar Axions and
Axion-Like Particles

10. Phenomenological Axion Properties
Gluon coupling (generic), defines normalization of axion scale 𝑓 𝑎
ℒ 𝑎𝐺 = 𝛼 𝑠 8𝜋 𝑎 𝑓 𝑎 𝐺 𝐺
Mass (generic) depends on up/down quark masses
𝑚 𝑎 = 𝑚 𝑢 𝑚 𝑑 𝑚 𝑢 + 𝑚 𝑑 𝑚 𝜋 𝑓 𝜋 𝑓 𝑎 ≈ 6 𝜇eV 𝑓 𝑎 GeV
Axion-photon coupling (model dependent)
ℒ 𝑎𝛾 =− 𝑔 𝑎𝛾 4 𝐹 𝐹 𝑎= 𝑔 𝑎𝛾 𝐄⋅𝐁 𝑎= 𝛼 2𝜋 𝐸 𝑁 −1.92 𝑎 𝑓 𝑎 𝐄⋅𝐁
Generic from 𝑎-𝜋-𝜂 mixing γ 𝑎
Model-dependent,
E/N = 0 (KSVZ), 8/3 (DFSZ), many others γ
Axion-nucleon coupling (model-dependent numerical factors 𝐶 𝑁 )
ℒ 𝑎𝑁 = 𝐶 𝑁 Ψ 𝑁 𝛾 𝜇 𝛾 5 Ψ 𝑁 𝜕 𝜇 𝑎 2 𝑓 𝑎
Axion-electron coupling in non-hadronic models is analogous with 𝐶 𝑒 𝑓
• Axial-vector current
• Spin-dependent int’n 𝑎 𝑓

11. First discussion of Primakoff
effect for WW axions ( 𝑚 𝑎 ≫𝑇)
For “invisible axions” ( 𝑚 𝑎 ≪𝑇)
screening effects crucial
(G.R., PRD 33, 897:1986)

12. Solar Observables Modified by Axion Losses
New
opacity
Old
opacity
Surface He abundance
Depth Convective Zone
Boron neutrinos
Beryllium neutrinos
Vinyoles, Serenelli, Villante, Basu, Redondo & Isern, arXiv:

13. Solar Sound-Speed Variation
New opacity
New energy loss makes
disagreement with seismic
observations worse,
especially in the central regions
Vinyoles, Serenelli, Villante, Basu, Redondo & Isern, arXiv:

14. Global Fit from Solar Observables
Allow all input parameters to float, including chemical composition,
and marginalize except for axion losses
𝑔 10 = 𝑔 𝑎𝛾 × GeV
Vinyoles, Serenelli, Villante, Basu, Redondo & Isern, arXiv:

15. 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

16. 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 ...)

17. LHC Magnet Mounted as a Telescope to Follow the Sun

18. CAST Results

19. 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

20. Parameter Space for Axion-Like Particles (ALPs)
Maximal mixing
(“coherent”, small 𝑚 𝑎 )
End of solar
spectrum
Large 𝑚 𝑎 , 𝑎-𝛾-oscillations
suppressed
𝑎-𝛾-oscillations enhanced
with He filling ( 𝑚 𝛾 ∼ 𝑚 𝑎 )
CAST exclusion range

21. Next Generation Axion Helioscope (IAXO)
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. Axion Dark Matter from Topological Defects
Editor’s suggestion
Diversity of scenarios for
cosmic axion production
depending on
domain-wall index NDW
and phase parameter δ
of the bias term

24. Historical Neutrino Dark Matter Lessons
Early 1980s
- If neutrinos have mass, probably they are dark matter ( 𝒎 𝝂 ~𝟏𝟎 𝐞𝐕)
(“Neutrinos are known to exist”, only SM candidate)
- Detection of 𝒎 𝝂 𝒆 ∼𝟑𝟎 𝐞𝐕 at ITEP, Moscow (PRL 58:2019, 1987)
- Dedicated oscillation experiments
(NOMAD 1995–1998 and CHORUS 1994–1997)
Status 2015
- 70% of gravitating “mass” is dark energy
- Dark matter must be mostly “cold” (structure formation)
- Neutrinos have sub-eV masses (oscillations, cosmo limits)
- Sub-dominant dark matter component
History does not always repeat itself, but …
- If axions (or similar) exist, MUST be ALL of dark matter?

25. Gamma-ALP Conversion in Astrophysical B-Fields
Credit: SLAC National Accelerator Laboratory/Chris Smith

26. Axion-Photon-Conversion from SN 1987A
in transverse galactic B-field
SN 1987A
SMM
Primakoff
production
in SN core
No excess g rays
in coincidence
with SN 1987A
Galactic
B-field
models
Payez, Evoli, Fischer, Giannotti, Mirizzi & Ringwald, arXiv:

27. Astrophysical ALP-Photon Conversion
Galactic and cluster fields (mG range) or intergalactic (nG) can cause
significant conversion over kpc–Mpc scales: Low-mass ALPs
Manuel Meyer, arXiv:

28. Hillas Plot ALP-g conversion 𝒈 𝒂𝜸 𝟏𝟎 𝟏𝟐 𝐆𝐞𝐕 𝑩𝑳∼𝟏
A. M. Hillas
Ann. Rev. Astron. Astrophys.
22, 425 (1984)
Size and B field strength
of possible sites for
particle acceleration.
Objects below the
line cannot accelerate
protons to 1020 eV
ALP-g conversion
𝒈 𝒂𝜸 𝟏𝟎 𝟏𝟐 𝐆𝐞𝐕 𝑩𝑳∼𝟏

29. Galactic Globular Cluster M55

30. Color-Magnitude Diagram for Globular ClustersH He
C O
Asymptotic Giant H He
Red Giant H He
Horizontal Branch H
Main-Sequence
Particle emission reduces
helium burning lifetime,
i.e. number of HB stars
C O
White
Dwarfs
Hot, blue
cold, red
Color-magnitude diagram synthesized from several low-metallicity globular
clusters and compared with theoretical isochrones (W.Harris, 2000)

31. New ALP Limits from Globular Clusters
Helium abundance and energy loss rate
from modern number counts HB/RGB
in 39 globular clusters
Planck
Ayala, Dominguez, Giannotti, Mirizzi & Straniero, arXiv:

32. Parameter Space for Axion-Like Particles (ALPs)

33. Axion-Electron Interaction
• Axions can interact with electrons, notably in GUT models,
e.g. DFSZ model
• Strong constraints from stars
Electrons
𝐶 𝑒 2 𝑓 𝑎 Ψ 𝑒 𝛾 𝜇 𝛾 5 Ψ 𝑒 𝜕 𝜇 𝑎
Compton
Pair
Annihilation
Electromagnetic
Bremsstrahlung

34. Color-Magnitude Diagram of Globular Cluster M5
Brightest red giant
measures nonstandard energy loss
CMD (a) before and (b) after cleaning
CMD of brightest 2.5 mag of RGB
Viaux, Catelan, Stetson, Raffelt, Redondo, Valcarce & Weiss, arXiv:

35. Limits on Axion-Electron Coupling from GC M5
I-band brightness
of tip of red-giant brach
[magnitudes]
Detailed account of theoretical and observational uncertainties
• Uncertainty dominated
by distance
• Can be improved in
future (GAIA mission)
Axion-electron Yukawa 𝑔 𝑎𝑒 × 10 13
Limit on axion-electron Yukawa
Mass limit in DFSZ model
𝑔 𝑎𝑒 < 2.6× 10 −13 (68% CL) 4.3× 10 −13 (95% CL)
𝑚 𝑎 cos 2 𝛽 < meV (68% CL) 15.4 meV (95% CL)
Viaux, Catelan, Stetson, Raffelt, Redondo, Valcarce & Weiss, arXiv:

36. Axion Bounds from WD Luminosity Function
Limits on axion-electron coupling and mass limit in DFSZ model:
𝑔 𝑎𝑒 ≲3× 10 − 𝑚 𝑎 cos 2 𝛽 ≲10 meV
Miller Bertolami, Melendez, Althaus & Isern, arXiv: ,

37. Period Change of Variable White Dwarfs
Period change Π of pulsating white darfs depends on cooling speed
White dwarf G117−B15A
White dwarf PG
Favored by Π
Limited by Π
Córsico et al., arXiv:
Battich et al., arXiv:

38. Summary of White Dwarf Bounds
Tip of RGB
Luminosity Function
Period
Change
Variable
White
Dwarfs
Córsico et al., arXiv:

39. Neutrinos from Thermal Processes
Photo (Compton)
Plasmon decay
Pair annihilation
Bremsstrahlung
These processes were first
discussed in
after V-A theory

40. Neutrino-Photon-Coupling in a Plasma
Neutrino effective in-medium coupling
𝐿 eff =− 2 𝐺 F Ψ 𝛾 𝛼 − 𝛾 5 Ψ Λ 𝛼𝛽 𝐴 𝛽
Λ V 𝜇𝜈 𝐾 = 𝐶 V 𝑒 Π V 𝜇𝜈 (𝐾)
Λ 𝜇ν
For vector current it is analogous
to photon polarization tensor
Emission almost purely electron flavor sin 2 Θ W =0.2312
𝐶 V 2 = sin 2 Θ W 2 = for 𝜈 𝑒
𝐶 V 2 = − sin 2 Θ W 2 = for 𝜈 𝜇 and 𝜈 𝜏

41. Sanduleak
Supernova 1987A
23 February 1987
Sanduleak

42. Supernova 1987A Energy-Loss Argument
SN 1987A neutrino signal
Neutrino
sphere
Volume emission
of new particles
Neutrino
diffusion
Emission of very weakly interacting
particles would “steal” energy from the
neutrino burst and shorten it.
(Early neutrino burst powered by accretion,
not sensitive to volume energy loss.)
Late-time signal most sensitive observable

43. Three Phases of Neutrino Emission
Explosion
triggered
Cooling on neutrino
diffusion time scale
Shock breakout
De-leptonization of
outer core layers
Shock stalls ~ 150 km
Neutrinos powered by
infalling matter
Spherically symmetric Garching model (25 M⊙) with Boltzmann neutrino transport

44. Cooling Time Scale
Exponential cooling model: T = T0 e-t/4, constant radius, L = L0 e-t/
Fit parameters are T0, , radius, 3 offset times for KII, IMB & BST detectors
Loredo and Lamb, Bayesian analysis
astro-ph/

45. Long-Term Cooling of EC SN (Garching 2009)
Neutrino opacities with strong
NN correlations and nucleon
recoil in neutrino-nucleon scattering.
Exponential cooling with 𝜏=2.6 s
Barely allowed by SN 1987A
Neutrino opacities without these effects
Much longer cooling times
L. Hüdepohl et al. (Garching Group), arXiv:

46. Axion Emission from a Nuclear Medium
Axion-nucleon interaction: ℒ int = 𝐶 𝑁 2 𝑓 𝑎 Ψ 𝑁 𝛾 𝜇 𝛾 5 Ψ 𝑁 𝜕 𝜇 𝑎= 𝐶 𝑁 2 𝑓 𝑎 𝐽 𝜇 𝐴 𝜕 𝑎 𝜇 a N N
Energy-loss rate (erg c m −3 s −1 )
𝑄=∫𝑑 Γ 𝑎 ∫𝑑 Γ Nucleons ℳ 2 𝜔 (axion energy 𝜔)
= 𝐶 𝑁 2 𝑓 𝑎 𝑛 𝐵 4 𝜋 ∞ 𝑑𝜔 𝜔 4 𝑆(−𝜔)
Dynamical structure function, in nonrelativistic limit correlator of nucleon spin density operator
𝑆 𝜔,𝑘 = 4 3 𝑛 𝐵 −∞ +∞ 𝑑𝑡 𝑒 𝑖𝜔𝑡 〈𝝈 𝑡,𝑘 ⋅𝝈 0,𝑘 〉
+ ... V N N
Nucleon-Nucleon
Bremsstrahlung
Early calculations using one-pion exchange potential without many body effects or
multiple-scattering effects over-estimated emission rate, see e.g.
• Janka, Keil, Raffelt & Seckel, PRL 76:2621,1996.
• Hanhart, Phillips & Reddy, PLB 499:9, 2001.
• Bacca, Hally, Liebendörfer, Perego, Pethick & Schwenk, ApJ 758: 34 (2012).
• Bartl, Pethick & Schwenk, PRL 113: (2014).

47. Axion-Nucleon Couplings
Axion-nucleon coupling (model-dependent numerical factors 𝐶 𝑁 )
ℒ 𝑎𝑁 = 𝐶 𝑁 Ψ 𝑁 𝛾 𝜇 𝛾 5 Ψ 𝑁 𝜕 𝜇 𝑎 2 𝑓 𝑎
Axion-electron coupling in non-hadronic models is analogous with 𝐶 𝑒 𝑓
• Axial-vector current
• Spin-dependent int’n 𝑎 𝑓
Values from
Grilli di Cortona et al.
arXiv:
Coupling to neutron could be very small!

48. Axion Bounds and Searches
103
106
109
1012
[GeV] fa eV
keV
meV ma
neV
1015
Microwave
Searches
CASPEr
Experiments
Tele
scope
CAST
Hadronic axions
Too much
hot dark matter
String DW
Too much cold dark matter
(re-alignment with Qi = 1)
Too much CDM
(misalignment)
Helium-burning stars
(a-g-coupling, hadronic axions)
SN 1987A
Too many events
Too much
energy loss
Globular clusters (He ignition), WD cooling
(a-e coupling)

49. Diffuse Supernova Axion Background (DSAB)
Neutrinos from all core-collapse SNe comparable to photons from all stars
Diffuse Supernova Neutrino Background (DSNB) similar energy density as
extra-galactic background light (EBL), approx 10% of CMB energy density
DSNB probably next astro neutrinos to be measured
Axions with 𝑚𝑎 ~ 10 meV
near SN 1987A energy-loss limit
Provide DSAB with compable
energy density as DSNB and EBL
No obvious detection channel
Raffelt, Redondo & Viaux
work in progress (2011)

50. Cooling of Neutron Star in Cas A
Chandra
x-ray
image of
non-pulsar
compact
remnant
𝐶 𝑛 𝑚 𝑎 ∼2.4 meV
Measured surface temperature over 10 years reveals unusually fast cooling rate
• Neutron Cooper pair breaking and formation (PBF) as neutrino emission process?
• Evidence for extra cooling (by axions)?
Leinson, arXiv:

51. CP-Violating Forces 𝑔 𝑠 𝑁 𝑔 𝑠 𝑁 𝑔 𝑠 𝑁 𝑔 𝑝 𝑒 𝑔 𝑝 𝑒 𝑔 𝑝 𝑒 𝑎 𝑎 𝑎
bulk
bulk
bulk
spin
spin
spin 𝑎 𝑎 𝑎
Tests of Newton’s law
& equivalence principle:
Scalar axion coupling 𝑔 𝑠 𝑁 2
Torsion balance using
polarized electron spins
Axion couplings 𝑔 𝑠 𝑁 𝑔 𝑝 𝑒
T-violating force
Spin-spin forces
hard to measure
Axion couplings 𝑔 𝑠 𝑒 2

52. Long-Range Force Experiments
Long-range force limits from tests of
Newton’s law and equivalence principle
(Mostly from Eöt-Wash Group, Seattle)
Limits from long-range 𝑔 𝑠 𝑁 limits times
astrophysical 𝑔 𝑝 𝑁 limits, compared with
direct 𝑔 𝑠 𝑁 𝑔 𝑝 𝑁 constraints
Raffelt, arXiv:
Raffelt, arXiv:
Experimental
Exp+astro
bulk
bulk
bulk
spin 𝑎 𝑎

53. ARIADNE: Axion Resonant InterAction DetectioN Experiment
NMR Experiment
meV
ARIADNE: Axion Resonant InterAction DetectioN Experiment
A.Geraci, A.Arvanitaki, A.Kapitulnik, Chen-Yu Liu, J.Long, Y.Semertzidis, M.Snow

54. Axion Dark Matter Density
Partly excluded by
cosmic HDM bounds
& Euclid sensitivity
[arXiv: ]
Hot DM
Cold DM
Javier Redondo 2014
Realignment
Cosmic Strings & Domain Walls

55. Thermal Axion Density and EUCLID Sensitivity
Hot dark matter sensitivity of future surveys (EUCLID) is around minimal 𝑚 𝜈
Can probe axions down to 𝑚 𝑎 ∼0.15 eV
Archidiacono, Basse, Hamann, Hannestad, Raffelt & Wong, arXiv:

56. Axion Bounds and Searches
103
106
109
1012
[GeV] fa eV
keV
meV ma
neV
1015
Microwave
Searches
CASPEr
Experiments
Tele
scope
CAST
Hadronic axions
Too much
hot dark matter
Future
EUCLID
ARIADNE
String DW
Too much CDM
(misalignment)
Too much cold dark matter
(re-alignment with Qi = 1)
IAXO
Helium-burning stars
(a-g-coupling, hadronic axions)
SN 1987A
Too many events
Too much
energy loss
Globular clusters (He ignition), WD cooling
(a-e coupling)

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