1. Cosmological mass bounds on hot-dark matter axions Alessandro MIRIZZI (MPI, Munich) NOW 2008- Neutrino Oscillation Workshop Conca Specchiulla, September 6-13 2008 [based on works in collaboration with S.Hannestad, G.G. Raffelt, Y.Y.Y. Wong]

2. OUTLINE Strong CP problem and the axions Axions and large-scale structures Cosmological mass limit Implication for axion search (CAST experiment) Conclusions Alessandro Mirizzi NOW 2008 Conca Specchiulla, 6-13 September 2008

3. THE STRONG CP PROBLEM The QCD Lagrangian includes a term which violates CP (and T) where Prediction of an electric dipole moment for the neutron: Present experimental limit : Why so small ? Alessandro Mirizzi NOW 2008 Conca Specchiulla, 6-13 September 2008

4. THE PECCEI-QUINN MECHANISM Introduction of a new global U(1) PQ simmetry, spontaneously broken at a scale f a. Existence of a massless pseudoscalar field a(x), the axion, interacting with the gluon field. Peccei & Quinn 1977, Wilczek 1978, Weinberg 1978 Re-interpret  as a dynamical variable: PQ Symmetry Introduce a symmetry that results in a term which dynamically minimize . Alessandro Mirizzi NOW 2008 Conca Specchiulla, 6-13 September 2008

5. a V(a) Potential (mass term) induced by L a drives a(x) to CP-conserving minimumCP-symmetry dynamically restored At low energy (  QCD ) the gga vertex generates the potential V(a) which has its minimum at a 0 =0, restoring dynamically CP-simmetry. Axions pick up a small mass Axions generically couple Axions generically couple to gluons and mix with  0 to gluons and mix with  0 gluon a gluon Alessandro Mirizzi NOW 2008 Conca Specchiulla, 6-13 September 2008

6. AXION PROPERTIES Nucleon coupling (axial vector) N N a Electron coupling (optional absent for hadronic axions) e e a Gluon coupling (Generic property) a G G Photon coupling   a Pion coupling a  

7. Alessandro Mirizzi NOW 2008 Conca Specchiulla, 6-13 September 2008 This talk Hadronic axion window m a ~ O(eV), f a ~10 6 GeV COSMOLOGICAL AND ASTROPHYSICAL AXION LIMITS

8. DARK MATTER CANDIDATES Alessandro Mirizzi NOW 2008 Conca Specchiulla, 6-13 September 2008

9. DARK-MATTER AXIONS log(  a ) log(m a ) MMMM 30 eV 100 meV CDM HDM Axions Thermal Relics Non-ThermalRelics log(  ) log(m ) MMMM 30 eV CDMHDM 3 GeV Neutrinos Thermal Relics

10. THERMAL PRODUCTION OF AXIONS If f a < 1.2 ×10 12 GeV there would be a primordial population of axions produced in hot thermal plasma [Turner (1987), Masso’ (2002)] Freeze-out temperature If axions were sufficiently strong interacting (f a 0.2 eV) they decouple after QCD phase transition (T < 200 MeV). The most generic interaction process involves hadrons rather than quarks and gluons that would be relevant at earlier epochs. There would be a background of low-mass ( ~ eV) relic axions

11. Massive neutrinos affect Large Scale Structures. They smooth out the distribution: no small scale structures. Cold Dark Matter (no neutrino mass) Hot + Cold Dark Matter (non-zero neutrino mass) S. Dodelson, ‘04 Low mass thermal relics affect structure formation because they are source of hot dark matter Alessandro Mirizzi NOW 2008 Conca Specchiulla, 6-13 September 2008

12. POWER SPECTRUM OF MATTER DENSITY FLUCTUATIONS Density contrast Power spectrum Alessandro Mirizzi NOW 2008 Conca Specchiulla, 6-13 September 2008

13. Neutrinos affect the Power Spectrum of the 2-point density correlation function. P(k)=A k n T 2 (k) T 2 (k) = Transfer function It is possible to obtain constraints on m  Neutrino Free Streaming  P(k)/P(k) = -8  /  m (Hu et al. 1998) 0 eV 0.3 eV 1 eV Power suppression for FS ≲ 100 Mpc/h S.Hannestad,hep-ph/0404239 Alessandro Mirizzi NOW 2008 Conca Specchiulla, 6-13 September 2008

14. NEUTRINO MASS LIMITS [Fogli et al., arXiv: 0805.2517] Alessandro Mirizzi NOW 2008 Conca Specchiulla, 6-13 September 2008

15. THERMALIZATION OF HADRONIC AXIONS The Lagrangians relevant for axion decoupling processes are the following Pion-axion interaction   a  Contact interaction Choi & Chang, PLB 316, 51(1993); Hannestad, Mirizzi & Raffelt, JCAP 07 (2005) 02 Alessandro Mirizzi NOW 2008 Conca Specchiulla, 6-13 September 2008

16. Freeze-out temperature Cosmic thermal degrees of freedom at axion freeze-out Present-day axion density AXION HOT-DARK MATTER

17. AXION HOT-DARK MATTER LIMIT FROM PRECISION DATA Credible regions for neutrinos plus axions HDM (WMAP-5, LSS, BAO; SN-Ia) Hannestad, Mirizzi, Raffelt & Wong [arXiV: 0803.1585] Dashed (red) curves: Same with WMAP-3 HMRW [arXiv: 0706.4198] Marginalizing over unknown neutrino hot-dark matter component WMAP5, LSS, BAO, SN Ia Hannestad, Mirizzi, Raffelt & Wong [arXiV:0803.1585] WMAP3, small-scale CMB, HST, BBN, LSS, Ly  Melchiorri, Mena & Slosar [arXiV: 0705.2695]

18. NEW AXION MASS LIMIT Our limit m a 5.7 × 10 6 GeV, is comparable with the one obtained with the globular-cluster. However, the globular cluster limit depends on axion-photon coupling that is rather model dependent. Our limit closes the “hadronic axion window” left open by SN1987A arguments New cosmological mass limit Alessandro Mirizzi NOW 2008 Conca Specchiulla, 6-13 September 2008

19. IMPLICATION FOR AXION SEARCHES Searches for solar axions: Axion helioscopes Axion-photon oscillation Primakoff process Tokyo axion helioscope Results since 1998 CERN Axion Solar Telescope (CAST) Data since 2003 Sun Laboratory

21. CAST PHASE II AND OUR COSMOLOGICAL AXION MASS LIMIT PROBABLY CONNECT. g a  < 8.8 x 10 -11 GeV -1 at 95% CL for m a < 0.02 eV LIMITS FROM CAST-I AND CAST-II CAST-I g a  < 2.2 x 10 -10 GeV -1 at 95% CL for m a < 0.39 eV CAST-II (Preliminary)

22. CONCLUSIONS For hadronic axions we find a new mass limit m a 5.7×10 6 GeV. It is comparable with the (model-dependent) limit obtained with the globular clusters. It closes the “hadronic axion” window. It is nicely complementary with the CAST search. If neutrino masses are detected in laboratory (KATRIN) : Less room for axions in the dark matter inventory. Observations of the cosmological large-scale structure provide well- estabilished neutrino mass limit. We extend this argument to thermal relic axions: Alessandro Mirizzi NOW 2008 Conca Specchiulla, 6-13 September 2008

23. Thank you!