1. Astrophysical and Cosmological Axion Limits
Sun
Globular Cluster
Supernova 1987A
Dark Matter
Astrophysical and Cosmological Axion Limits
Georg G. Raffelt, Max-Planck-Institut für Physik, München

2. Axion Bounds and Searches
103
106
109
1012
[GeV] fa eV
keV
meV ma
neV
1015
ADMX Search
(Seattle & Yale)
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)
Anthropic
Range
SN 1987A
Too many events
Too much
energy loss
Globular clusters (He ignition), WD cooling
(a-e coupling)

3. Axion Properties g g p p p a e e G Gluon coupling
(generic)
ℒ 𝑎𝐺 = 𝛼 𝑠 8𝜋 𝑓 𝑎 𝐺 𝐺 𝑎 G a G
Mass (generic)
𝑚 𝑎 = 𝑚 𝑢 𝑚 𝑑 𝑚 𝑢 + 𝑚 𝑑 𝑚 𝜋 𝑓 𝜋 𝑓 𝑎 ≈ 6 𝜇eV 𝑓 𝑎 GeV
Photon coupling
ℒ 𝑎𝛾 =− 𝑔 𝑎𝛾 4 𝐹 𝐹 𝑎= 𝑔 𝑎𝛾 𝐄⋅𝐁 𝑎
𝑔 𝑎𝛾 = 𝛼 2𝜋 𝑓 𝑎 𝐸 𝑁 −1.92 g a g
Pion coupling p p
ℒ 𝑎𝜋 = 𝐶 𝑎𝜋 𝑓 𝜋 𝑓 𝑎 𝜋 0 𝜋 + 𝜕 𝜇 𝜋 − +… 𝜕 𝜇 𝑎 p a
Nucleon coupling
(axial vector)
ℒ 𝑎𝑁 = 𝐶 𝑁 2 𝑓 𝑎 Ψ 𝑁 𝛾 𝜇 𝛾 5 Ψ 𝑁 𝜕 𝜇 𝑎 N a N
Electron coupling
(optional)
ℒ 𝑎𝑒 = 𝐶 𝑒 2 𝑓 𝑎 Ψ 𝑒 𝛾 𝜇 𝛾 5 Ψ 𝑒 𝜕 𝜇 𝑎 e a e

4. Globular Cluster
Supernova 1987A
Dark Matter
Sun
Solar Axions

5. 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

6. 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 ...)

7. Pointing a Magnet to the Sun
By CAST student Sebastian Baum

8. Tokyo Axion Helioscope (“Sumico”)
Moriyama, Minowa, Namba, Inoue, Takasu & Yamamoto
PLB 434 (1998) 147
Inoue, Akimoto, Ohta, Mizumoto, Yamamoto & Minowa
PLB 668 (2008) 93

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

10. CERN Axion Solar Telescope (CAST)

11. Helioscope Limits First experimental crossing of the KSVZ line
CAST-I results: PRL 94: (2005) and JCAP 0704 (2007) 010
CAST-II results (He-4 filling): JCAP 0902 (2009) 008
CAST-II results (He-3 filling): PRL 107: (2011) and in preparation (2013)

12. Fore-CAST (2013–2015) CAST 2013 (Preliminary) CAST 2014 (Preliminary)
Renewed CAST running in vacuum mode with new detectors
and in future new x-ray telescopes
CAST 2013 (Preliminary)
CAST 2014 (Preliminary)
Sensitivity forecast

13. Parameter Space for Axion-Like Particles (ALPs)
ℒ 𝑎𝛾𝛾 =− 𝑔 𝑎𝛾𝛾 4 𝐹 𝐹 𝑎
= 𝑔 𝑎𝛾𝛾 𝑬⋅𝑩 𝑎
Γ 𝑎→𝛾𝛾 = 𝑔 𝑎𝛾 2 𝑚 𝑎 3 64𝜋

14. Parameter Space for Axion-Like Particles (ALPs)
ℒ 𝑎𝛾𝛾 =− 𝑔 𝑎𝛾𝛾 4 𝐹 𝐹 𝑎
= 𝑔 𝑎𝛾𝛾 𝑬⋅𝑩 𝑎
Γ 𝑎→𝛾𝛾 = 𝑔 𝑎𝛾 2 𝑚 𝑎 3 64𝜋

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

16. 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:

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

18. Photon Regeneration Experiments
Ehret et al. (ALPS Collaboration), arXiv:
Recent “shining-light-through-a-wall” or vacuum birefringence experiments:
ALPS
BMV
BFRT
GammeV
LIPPS
OSQAR
PVLAS
(DESY, using HERA dipole magnet)
(Laboratoire National des Champs Magnétiques Intens, Toulouse)
(Brookhaven, 1993)
(Fermilab)
(Jefferson Lab)
(CERN, using LHC dipole magnets)
(INFN Trieste)

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

20. PVLAS Collaboration, arXiv:1410.4081 (15 Oct 2014)
Latest PVLAS Limit
PVLAS seeks B-field induced birefringence (QED effect)
Searching for induced ellipticity of linearly polarized laser beam
PVLAS Collaboration, arXiv: (15 Oct 2014)

21. Any Light Particle Search II (ALPS-II) at DESY
ALPS-I (finished)
ALPS-IIa (2014)
ALPS-IIb (2015)
ALPS-IIc (2017)
ALPS-II Technical Design Report, arXiv:

22. 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:

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

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

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

26. Axions from Normal Stars
Sun
Supernova 1987A
Dark Matter
Globular Cluster
Axions from Normal Stars

27. Galactic Globular Cluster M55

28. 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)

29. Helium-Burning Lifetime of Horizontal-Branch Stars
Number ratio of HB-Stars/Red Giants in 15 galactic globular clusters
(Buzzoni et al. 1983)
Helium-burning lifetime established within 10%

30. 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:

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

32. Blue-Loop Suppression by Axion Emission
Blue loop at the end of helium burning
No axions
Axion emission near limit
Evolution of massive stars with Primakoff axion emission
(Friedland et al. arXiv: )

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

34. 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

35. Color-Magnitude Diagram for Globular ClustersH He
C O
Asymptotic Giant H He
Red Giant
Particle emission
delays He ignition, i.e.
core mass increased H He
Horizontal Branch H
Main-Sequence
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)

36. 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:

37. 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:

38. White Dwarf Luminosity Function
Stars formed in the past Gyr
Systematic deviations between
WDLFs beyond stated errors
Miller Bertolami, Melendez, Althaus & Isern, arXiv:

39. 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: ,

40. Period Change of Variable White Dwarfs
Period change Π of pulsating white darfs depends on cooling speed
White dwarf G117−B15A
White dwarf R548
Favored by Π
Favored by Π
Córsico et al., arXiv:
Córsico et al., arXiv:

41. Axion Bounds and Searches
103
106
109
1012
[GeV] fa eV
keV
meV ma
neV
1015
ADMX Search
(Seattle & Yale)
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)
Anthropic
Range
SN 1987A
Too many events
Too much
energy loss
Globular clusters (He ignition), WD cooling
(a-e coupling)

42. SN 1987A Neutrino Signal Supernova 1987A Sun Globular Cluster
Dark Matter
Supernova 1987A
SN 1987A Neutrino Signal

43. Sanduleak
Supernova 1987A
23 February 1987
Sanduleak

44. 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

45. 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/

46. 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
(~ Basel case?)
Much longer cooling times
L. Hüdepohl et al. (Garching Group), arXiv:

47. Operational Detectors for Supernova Neutrinos
SNO+
(300)
HALO
(tens)
LVD (400)
Borexino (100)
Baksan
(100)
Super-K (104)
KamLAND (400)
Daya Bay
(100)
In brackets events
for a “fiducial SN”
at distance 10 kpc
IceCube (106)

48. 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, arXiv: (2011).

49. Axion Bounds and Searches
103
106
109
1012
[GeV] fa eV
keV
meV ma
neV
1015
ADMX Search
(Seattle & Yale)
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)
Anthropic
Range
SN 1987A
Too many events
Too much
energy loss
Globular clusters (He ignition), WD cooling
(a-e coupling)

50. 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)

51. 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:

52. 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

53. 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 𝑒 limits, compared with
direct 𝑔 𝑠 𝑁 𝑔 𝑝 𝑒 constraints
Raffelt, arXiv:
Raffelt, arXiv:
Torsion
(bulk-spin)
Torsion+astro
bulk
bulk
bulk
spin 𝑎 𝑎

54. Cosmological Constraints
Sun
Globular Cluster
Supernova 1987A
Dark Matter
Cosmological Constraints

55. Lee-Weinberg Curve for Axions
Javier Redondo 2014
Realignment
Cosmic Strings & Domain Walls

56. Axion Hot Dark Matter from Thermalization after LQCDp p
𝐿 𝑎𝜋 = 𝐶 𝑎𝜋 𝑓 𝑎 𝑓 𝜋 𝜋 0 𝜋 + 𝜕 𝜇 𝜋 − + 𝜋 0 𝜋 − 𝜕 𝜇 𝜋 + −2 𝜋 + 𝜋 − 𝜕 𝜇 𝜋 0 𝜕 𝜇 𝑎
Chang & Choi, PLB 316 (1993) 51 p a
Hannestad, Mirizzi
& Raffelt,
hep-ph/

57. Neutrino and Axion HDM Limits After Planck
After marginalising over 𝑚 𝜈
𝑚 𝑎 <0.67 eV (95% CL)
𝑚 𝑎 <0.86 eV (95% CL) without local H0 measurement
Archidiacono, Hannestad, Mirizzi, Raffelt & Wong, arXiv:

58. 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, work in progress (2014)

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

60. Dow Jones Index of Axion Physics
inSPIRE: Citation of Peccei-Quinn papers or title axion (and similar)