Axions

1. Georg G. Raffelt, Max-Planck-Institut für Physik, München Axions Axions Motivation, Cosmological Role and Experimental Searches Seminar, University of New South Wales, 5 March 2014

2. Axions as Cold Dark Matter of the Universe Dark Energy ~70% (Cosmological Constant) Neutrinos 0.1-2% Ordinary Matter ~5% (of this only about 10% luminous) Dark Matter ~25%

3. Periodic System of Elementary Particles Quarks Leptons Charge +2/3 Charge -1/3 Charge -1 Charge 0 d e ne u Up Electron 1stFamily Down e-Neutrino d e ne Up u Electron Down e-Neutrino s m nm 2ndFamily Strange Charm Muon m-Neutrino c b t nt 3rd Family Bottom Top Neutron t Tau t-Neutrino Higgs Strong Interaction (8 Gluons) Electromagnetic Interaction (Photon) Proton Weak Interaction (W and Z Bosons) Gravitation (Gravitons?)

4. Three-Flavor Neutrino Parameters e e m m t t e e m m t t m m t t Three mixing angles ,, (Euler angles for 3D rotation), , a CP-violating “Dirac phase” , and two “Majorana phases” and v Relevant for 0n2b decay Reactor Solar/KamLAND Atmospheric/LBL-Beams Normal Inverted • Tasks and Open Questions • Precision for all angles • CP-violating phase d? • Mass ordering? • (normal vs inverted) • Absolute masses? • (hierarchical vs degenerate) • Dirac or Majorana? 72–80 meV2 2 3 Sun Atmosphere 1 Atmosphere 2180–2640 meV2 2 Sun 1 3

5. Antineutrino Oscillations Different from Neutrinos? Dirac phase causes different 3-flavor oscillations for neutrinos and antineutrinos same as Distance [1000 km] for E = 1 GeV

6. 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 violated by weak interactions 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

7. Cabbibo-Kobayashi-Maskawa (CKM) Matrix Quark interaction with W boson (charged-current electroweak interaction) Unitary Cabbibo-Kobayashi-Maskawa matrix relates mass eigenstates to weak interaction eigenstates VCKM depends on three mixing angles and one phase d, explaining all observed CP-violation Precision tests use “unitarity triangles” consisting of products of measured components of VCKM, for example:

8. Measurements of CKM Unitarity Triangle UTfit Collaboration http://www.utfit.org CKMfitter Group http://ckmfitter.in2p3.fr

9. The CP Problem of Strong Interactions Phase from Yukawa coupling Angle variable CP-odd quantity Real quark mass Remove phase of mass term by chiral transformation of quark fields • can be traded between quark phases and term • No physical impact if at least one • Induces a large neutron electric dipole moment (a T-violating quantity) Experimental limits: Why so small?

10. Neutron Electric Dipole Moment Violates time reversal (T) and space reflection (P) symmetries Natural scale Experimental limit Limit on coefficient

11. Strong CP Problem QCD vacuum energy Equivalent Equivalent • CP conserving vacuum has (Vafa and Witten 1984) • QCD could have any , is “constant of nature” • Energy can not be minimized: not dynamical Peccei-Quinn solution: Make dynamical, let system relax to lowest energy

12. 35 Years of Axions

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

14. Axion as a Nambu-Goldstone Boson Periodic variable (angle) • New U(1) symmetry, spontaneously broken at a large scale • Axion is “phase” of new Higgs field: angular variable • By construction couples to term with strength , • e.g. triangle loop with new heavy quark (KSVZ model) • Mixes with -- mesons • Axion mass • (vanishes if or )

15. From Standard Model to Invisible Axions Standard Model “Standard Axion” Weinberg 1978, Wilczek 1978 Invisible Axion Kim 1979, Shifman, Vainshtein, Zakharov 1980, Dine,Fischler,Srednicki1981 Zhitnitsky 1980 All Higgs degrees of freedom are used up • Peccei-Quinn scale • fa = fEW • (electroweak scale) • Two Higgs fields, • separately giving mass • to up-type quarks and • down-type quarks • Additional Higgs with • fa≫fEW • Axions very light and • and very weakly • interacting No room for Peccei-Quinn symmetry and axions Standard axion quickly ruled out experimentally • New scale required • Axions can be • cold dark matter • Can be detected

16. Simplest Invisible Axion: KSVZ Model Ingredients: Scalar field , breaks U(1)PQ spontaneously Very heavy colored quark with coupling to, provides term Invariant under chiral phase transformations (Peccei Quinn symmetry) , , Mexican hat potential , expand fields as Low-energy Lagrangian , where Lowest-order interaction term induces term Couples axion to QCD sector

17. Axion Properties Gluon coupling (generic) G a G Mass (generic) Photon coupling g a g Pion coupling p p p a Nucleon coupling (axial vector) N a N Electron coupling (optional) e a e

18. High- and Low-Energy Frontiers in Particle Physics QCD scale Planck mass Cosmological constant Electroweak scale GUT scale eV Heavy right-handed neutrinos (see-saw mechanism) WIMP dark matter (related to EW scale, perhaps SUSY) Axion dark matter(related to Peccei-Quinn symmetry)

19. Sanduleak -69 202 Sanduleak -69 202 Supernova 1987A 23 February 1987 Tarantula Nebula Large Magellanic Cloud Distance 50 kpc (160.000 light years)

20. 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

21. SN 1987A Axion Limits Excluded Neutrino diffusion Neutrino diffusion Trapping Free streaming Volume emission of new particles Axion diffusion

22. Axion Bounds and Searches [GeV] fa 103 106 109 1012 1015 keV eV meV meV neV ma Experiments Tele scope CAST Direct searches ADMX (Seattle & Yale) Too much hot darkmatter Too much CDM (misalignment) Too much cold dark matter (re-alignment with Qi = 1) Globular clusters (a-g-coupling) Classic region Anthropic region SN 1987A Too many events Too much energy loss Globular clusters (helium ignition) (a-e coupling)

23. Do White Dwarfs Need Axion Cooling? White dwarf luminosity function (number of WDs per brightness interval) No axions With axion cooling ( near SN1987A limit) Isern et al., arXiv:1204.3565

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

25. Limits on CP Violation from Long-Range Forces Raffelt, arXiv:1205.1776 Assume axion scalar CP-violating force with nucleons Eöt-Wash constraint provides best limit around [Hoedl et al. PRL 106 (2011) 041801]

26. 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 limits times astrophysical limits, compared with directconstraints Raffelt, arXiv:1205.1776 Raffelt, arXiv:1205.1776 Torsion (bulk-spin) Torsion+astro bulk bulk bulk spin

27. Searching for Solar Axions Searching for Axion-Like Particles

28. Axion and Relatives WISPs (Weakly Interacting Slim Particles) Axions (1 parameter or ) - Solve strong CP problem - Could be dark matter String axions (almost massless pseudoscalars in string theory) Need not solve CP problem Axion-like particles (ALPs) Generic two-photon vertex (2 parameters and ) Hidden photons Low-mass gauge boson from U’(1) (Parameters: kinetic mixing, mass)

29. Parameter Space for Axion-Like Particles (ALPs) Axion Line Invisible axion (DM)

30. Experimental Tests of Invisible Axions Primakoff effect: Axion-photon transition in external static E or B field (Originally discussed for 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

31. Search for Solar Axions Axion Helioscope (Sikivie 1983) Primakoff production N Axion flux a a g g MagnetS 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 ...)

32. CAST at CERN

33. Photon Regeneration Experiments Ehret et al. (ALPS Collaboration), arXiv:1004.1313 • 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)

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

35. Parameter Space for Axion-Like Particles Laser Experiments CAST Solar Axions CAST Solar Axions HB Stars HB Stars HB Stars How to make progress? TeV g rays Axion Line Axion Line Axion Line Axion Line Invisible axion (DM) Invisible axion (DM) Invisible axion (DM) Invisible axion (DM)

36. Next Generation Axion Helioscope (IAXO) at CERN Need new magnet w/ – Much bigger aperture: per bore – Lighter (no iron yoke) – Bores at Troom • Irastorza et al.: Towards a new generation axion helioscope, arXiv:1103.5334 • Armengaud et al.: Conceptual Design of the International Axion Observatory (IAXO), arXiv:1401.3233

37. Axions as Cold Dark Matter of the Universe Dark Energy ~70% (Cosmological Constant) Neutrinos 0.1-2% Ordinary Matter ~5% (of this only about 10% luminous) Dark Matter ~20%

38. Creation of Cosmological Axions (very early universe) • UPQ(1) spontaneously broken • Higgs field settles in • “Mexican hat” • Axion field sits fixed at (eV) • Axion mass turns on quickly • by thermal instanton gas • Field starts oscillating when • Classical field oscillations • (axions at rest) Axions are born as nonrelativistic, classical field oscillations Very small mass, yet cold dark matter

39. Axion Cosmology in PLB 120 (1983)

40. Cosmic Axion Density Modern values for QCD parameters and temperature-dependent axion mass imply (Bae, Huh & Kim, arXiv:0806.0497) If axions provide the cold dark matter: • implies GeV and meV (“classic window”) • GeV (GUT scale) or larger (string inspired) requires (“anthropic window”)

41. Cold Axion Populations Case 1 Inflation after PQ symmetry breaking Case 2 Reheating restores PQ symmetry Homogeneous mode oscillates after Dependence on initial misalignment angle • Cosmic strings of broken UPQ(1) • form by Kibble mechanism • Radiate long-wavelength axions • independent of initial conditions • or else domain wall problem Dark matter density a cosmic random number (“environmental parameter”) • Inhomogeneities of axion field large, • self-couplings lead to formation of • mini-clusters • Typical properties • Mass • Radius cm • Mass fraction up to several 10% • Isocurvature fluctuations from large • quantum fluctuations of massless • axion field created during inflation • Strong CMB bounds on isocurvature • fluctuations • Scale of inflation required to be small

42. Creation of Adiabatic vs. Isocurvature Perturbations Inflaton field Axion field De Sitter expansion imprints scale invariant fluctuations De Sitter expansion imprints scale invariant fluctuations Slow roll Reheating Inflaton decay  matter & radiation Both fluctuate the same: Adiabatic fluctuations Inflaton decay  radiation Axion field oscillates late  matter Matter fluctuates relative to radiation: Entropy fluctuations

43. Power Spectrum of CMB Temperature Fluctuations Planck Sky map of CMBR temperature fluctuations Multipole expansion Angular power spectrum Provides “acoustic peaks” and a wealth of cosmological information Acoustic Peaks

44. Adiabatic vs. Isocurvature Temperature Fluctuations Adapted from Fox, Pierce & Thomas, hep-th/0409059

45. Isocurvature Forecast Hubble scale during inflation Axion decay constant Hamann, Hannestad, Raffelt & Wong, arXiv:0904.0647

46. Axion Production by Domain Wall and String Decay Recent numerical studies of collapse of string-domain wall system Implies a CDM axion mass of Hiramatsu, Kawasaki, Saikawa& Sekiguchi, arXiv:1202.5851 (2012) Remains to be confirmed, interpretation of numerical studies not entirely straightforward

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

48. Searching for Axion Dark Matter Searching for Axion Dark Matter

49. Search for Galactic Axions (Cold Dark Matter) Power ma Frequency Dark matter axions Velocities in galaxy Energies therefore ma = 1-100 meV va 10-3 c Ea (1 10-6) ma Microwave Energies (1 GHz  4 meV) Axion Haloscope(Sikivie1983) Axion Signal Bext 8 Tesla Thermal noise of cavity & detector Microwave Resonator Q  105 Power of galactic axion signal Primakoff Conversion g a Cavity overcomes momentum mismatch Bext

50. Axion Dark Matter Experiment (ADMX), Seattle Adapted from Gianpaolo Carosi