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QCD axion, and Dark energy

QCD axion, and Dark energy. Jihn E. Kim Kyung Hee Univ. & Seoul National Univ. 10 th PATRAS Workshop, CERN, 30 June 2014. JEK, Phys. Rev. Lett. 111 (2013) 031801; JEK, Phys. Lett. B726 (2013) 450; JEK+H. P. Nilles, Phys. Lett. B730 (2014) 53 ;

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QCD axion, and Dark energy

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  1. QCD axion, and Dark energy Jihn E. Kim Kyung Hee Univ. & Seoul National Univ. 10th PATRAS Workshop, CERN, 30 June 2014 JEK, Phys. Rev. Lett. 111 (2013) 031801; JEK, Phys. Lett. B726 (2013) 450; JEK+H. P. Nilles, Phys. Lett. B730 (2014) 53 ; JEK, arXiv:1311.4545[hep-ph] ; arXiv:1404.4022[hep-ph]; JEK, PLB734 (2014) 68 [arXiv:1405.0221[hep-th]]; JEK, PLB735 (2014) 95 [arXiv:1405.6175]

  2. 1. Introduction 2. Axions and the strong CP problem 3. Pseudo-goldstone bosons from discrete symmetries 4. Dark energy from U(1)de 5. Gravity waves from U(1)de 6. PQ symmetry breaking below HI

  3. 1. Introduction

  4. Cosmic pie CC Follows the cold dark matter Responsible for galaxy formation We discuss DE of order 10-47 GeV4 and CDM axion.

  5. Axion detection scheme 5/45 J E Kim “QCD axion, and DE”, 10th PATRAS, CERN, 30 June 2014

  6. ★Axion detection is based on the bosonic coherent motion (BCM) can account for CDM. ★Higgs boson is a fundamental scalar. Higgs portal: In the age of fundamental scalars, can these explain both DE and CDM? In the age of GUT scale vacuum energy observed, can these explain all of DE and CDM and inflation-finish? 6/45 J E Kim “QCD axion, and DE”, 10th PATRAS, CERN, 30 June 2014

  7. Quantum gravity problem ★But quantum gravity effects are known to break global symmetries: the Planck scale wormholes connect observable universe O to the shadow world S. They can take out the global charges from O. ★ We can think of two possibilities of discrete symmetries realized from string compactification, below MP: • The discrete symmetry arises as a part of a gauge symmetry. • [Krauss-Wilczek, PRL 62 (1989) 1211] (ii) The string selection rules directly give the discrete symmetry. [JEK, PRL 111 (2013) 031801] ★ So, we start with discrete gauge symmetries. 7/45 J E Kim “QCD axion, and DE”, 10th PATRAS, CERN, 30 June 2014

  8. Exact and approximate symmetries Vertical, exact sym.: gauged U(1), or string dictated. The global symmetry violating terms. A few low order W’s respected by discrete symmetry defines a global symmetry. 8/45 J E Kim “QCD axion, and DE”, 10th PATRAS, CERN, 30 June 2014

  9. 2. Axions and Strong CP

  10. Strong CP The strongly interacting θ(Gluon)μν(Gluon-dual)μν term gives a nEDM. Neutron EDM is measured very accurately. dnth = (1.2-14.5)x10-16θe cm dnexp = 2.9 x10-26 e cm, Baker et al (2006) “Why is nEDM so small?” is the strong CP problem. 10/45 J E Kim “QCD axion, and DE”, 10th PATRAS, CERN, 30 June 2014

  11. U(1) breaking potential For gauge symmetry breaking, exactly flat. For global symmetry breaking, ALWAYS a potential is generated: Approximate

  12. Cosmology of axion models 1. BCM: Preskill-Wise-Wilczek, Abbott-Sikivie, Dine-Fischler 2. Axion DW problem: Zel'dovich-Kobzarev-Okun (1975); Vilenkin-Everett (1982); P. Sikivie (1982). 3. N=1 numerical simulation: Florida group (Sikivie-Chang-Hagmann), Cambridge group (Battye-Shellard), KEK group (Kawasaki-Hiramatsu-Saikawa-Sekiguchi) 4. Solutions: Works for discrete groups. Lazarides-Shafi, PLB115, 21 (1982), Choi-Kim, PRL55, 2637 (1985), JEK, PLB734, 68 (2014) [arXiv:1405.0221[hep-th]]. 12/45 J E Kim “QCD axion, and DE”, 10th PATRAS, CERN, 30 June 2014

  13. It is very flat if the axion decay constant is large, CP conserving point 10-20 In the evolving universe, at some temperature, say T1, a starts to roll down to end at the CP conserving point sufficiently closely. This analysis constrains the axion decay constant (upper bound) and the initial VEV of a at T1. Still oscillating nEDM was suggested to be measured 20 years ago: Hong-Kim-Sikivie, PRD42, 1847 (1990), Hong-Kim PLB265, 197 (1991), Hong-Kim-Nam-Semertzdis, 1403.1576. The axion oscillation is just one example of Bosonic Coherent Motion (BCM). 13/45 J E Kim “QCD axion, and DE”, 10th PATRAS, CERN, 30 June 2014

  14. The Lagrangian is invariant under changing θ → θ-2α.But θ becomes dynamical and the θ=a/Fapotential becomes The true vacuum chooses θ=a/Faat Vafa-Witten(1983) 14/45 J E Kim “QCD axion, and DE”, 10th PATRAS, CERN, 30 June 2014

  15. A recent calculation of the cosmic axion density is, 109 GeV < Fa < {1012 GeV ?} Turner (86), Grin et al (07), Giudice-Kolb-Riotto (08), Bae-Huh-K (JCAP 08, [arXiv:0806.0497]): recalculated including the anharmonic term carefully with the new data on light quark masses. It is the basis of using the anthropic argument for a large Fa. Without string radiation Reheating after inflation: Visinelli+Gondolo, Marsh et al. 15/45 J E Kim “QCD axion, and DE”, 10th PATRAS, CERN, 30 June 2014

  16. Many lab. searches were made, and we hope the axion be discovered . BICEP2: Gondolo+Vissinelli, Marsh et al. Only string calculation: JEK, PLB735 (2014) 95 [1405.6175[hep-ph]] Oscillating nEDM was suggested to be measured 20 years ago: Hong-Kim-Sikivie, PRD42, 1847 (1990), Hong-Kim PLB265, 197 (1991). Rate calculation: Hong-Kim-Nam-Semertzidis, arXiv:1403.1576[hep-ph].

  17. Only string calculation: JEK, PLB 735(2014)95, 1405.6175[hep-ph] 100% axion CDM is ruled out. 17/45 J E Kim “QCD axion, and DE”, 10th PATRAS, CERN, 30 June 2014

  18. KSVZ axion: The Peccei-Quinn symmetry by renormalizable couplings to heavy quarks. Why are we restricted to renormalizable interactions only at the EW scale? Definition of a global symmetry can be non- renormalizable terms also: DFSZ. Here, Higgs doublets are neutral under PQ. If they are not neutral, then it is not necessary to introduce heavy quarks [DFSZ axion]. In any case, the axion is the phase of the SM singlet S, if the VEV of S is much above the electroweak scale. Kim-Nilles term Because Fa can be in the intermediate scale, axions can live up to now (m<24 eV) and constitute DM of the Universe. 18/45 J E Kim “QCD axion, and DE”, 10th PATRAS, CERN, 30 June 2014

  19. Pseudo-goldstone bosons from discrete symmetries

  20. [JEK, PRL111, 031801 arXiv:1303.1822].

  21. In string theory, matter fields are from E8 x E8 representations. Not from BMN . Kim-Nilles μ-term arises from Where do X and X–bar belong? Probably, in matter reps. Anyway, BMN fields: decay constant is very large F>1016 GeV [Choi-Kim (1984), Svrcek-Witten(2006)] 21/45 J E Kim “QCD axion, and DE”, 10th PATRAS, CERN, 30 June 2014

  22. The d=4 example is the θ term of Callan-Dashen-Gross and Jackiw-Rebbi. The d=5 examples are Weinberg operator and KN operator(with SUSY). The global symmetry violating terms is The red part. A few low order W’s are respected by discrete symmetry. 22/45 J E Kim “QCD axion, and DE”, 10th PATRAS, CERN, 30 June 2014

  23. The PQ breaking diagram is 23/45 J E Kim “QCD axion, and DE”, 10th PATRAS, CERN, 30 June 2014

  24. But the dominant breaking is by the QCD anomaly term: 24/45 J E Kim “QCD axion, and DE”, 10th PATRAS, CERN, 30 June 2014

  25. Dominantly by the QCD anomaly term: 25/45 J E Kim “QCD axion, and DE”, 10th PATRAS, CERN, 30 June 2014

  26. 4. Dark energy from U(1)de

  27. DE magnitude ★There exists a tiny DE of order 10-47 GeV4. ★We propose to relate this DE scale to a pseudo-Goldstone boson mass scale. ★The breaking scale of U(1)de is trans-Planckian, and the intermediate scale PQ symmetry breaking of U(1)de just adds the decay constant only by a tiny amount. 27/45 J E Kim “QCD axion, and DE”, 10th PATRAS, CERN, 30 June 2014

  28. ★The discrete and global symmetries below MP are the consequence of the full W. So, the exact symmetries related to a discrete gauge symmetry or to string compactification are respected by the full W. Considering only W(3), we can consider approximate symmetries too. In particular, the approximate PQ symmetry. ★In string compactification, the bottom-up approach constraints [Lee et al, NPB 850, 1] toward a discrete gauge symmetry need not be considered. They are automatically satisfied with suitable massless singlets. ★For the MSSM interactions supplied by R-parity, one needs to know all the SM singlet spectrum. Z2 needed for a WIMP candidate. 28/45 J E Kim “QCD axion, and DE”, 10th PATRAS, CERN, 30 June 2014

  29. ★Because the Higgs scalar is known to be a fundamental scalar, fundamental SM singlet scalar VEVs at the PQ symmetry breaking scale are considered, The DE potential height is The singlets must couple to Hu Hd : Then, to remove the U(1)de-QCD anomaly , U(1)PQ must be introduced for one linear combination is free of the QCD anomaly. The needed discrete symmetry must be of high order such that some low order W are forbidden. 29/45 J E Kim “QCD axion, and DE”, 10th PATRAS, CERN, 30 June 2014

  30. ★ But, if QCD anomaly coupling to U(1)de is present, then we have the usual QCD axion. ★ U(1)de should not have QCD anomaly. ★ We need one more U(1) such that one linear combination U(1)de does not have the QCD anomaly. We must introduce to global U(1)s, of course approximate: U(1)de and U(1)PQ . ★ We have the scheme to explain both 68% of DE and 28% of CDM via approximate global symmetries. With SUSY, axino may contribute to CDM also. Hilltop inflation 30/45 J E Kim “QCD axion, and DE”, 10th PATRAS, CERN, 30 June 2014

  31. Typical example ★ The height of the potential is highly suppressed and we can obtain 10-47 GeV4 from discrete symmetry Z10R, without the gravity spoil of the global symmetry breaking term. ★ The discrete symmetry Z10R charges are the gauge charges of the mother U(1) gauge symmetry. ★ As a byproduct of the Mexican hat potential, Fig. (b), we also have a model of inflation, the so-called ‘hilltop inflation’. It is a small field inflation, consistent with the recent PLANCK data. Written before BICEP2

  32. 5. Gravity waves from U(1)de

  33. DE magnitude ★There exists a tiny DE of order 10-47 GeV4. ★ What is the form of the U(1)de breaking V? ★We propose to relate this DE scale to a pseudo-Goldstone boson mass scale. ★The breaking scale of U(1)de is trans-Planckian, and the intermediate scale PQ symmetry breaking of U(1)de just adds the decay constant only by a tiny amount. The height is (GUT scale)4 ★It is by closing the green circle of (a):

  34. Natural inflation starting at 0 is here. Natural inflation starting at π is here. Freese-Kinney: 1403.5277.

  35. 35/45 J E Kim “QCD axion, and DE”, 10th PATRAS, CERN, 30 June 2014

  36. U(1)de inflation with ‘chaoton’ X, more range. 36/45 J E Kim “QCD axion, and DE”, 10th PATRAS, CERN, 30 June 2014

  37. ★One condition to have a large e-folding is the Lyth bound, in our case fDE > 15 MP[D. Lyth, PRL 78 (1997) 1861] ★It is possible if the potential energy density is lower than MP4 .. One method is natural inflation: [Freese-Frieman-Olinto, PRL 65 (1990) 3233]. But, trans-Planckian needed two axions at least: [Kim-Nilles-Peloso, JCAP 01 (2005) 005]

  38. U(1)de inflation with ‘chaoton’ X, more range. 38/45 J E Kim “QCD axion, and DE”, 10th PATRAS, CERN, 30 June 2014

  39. Kim-Nilles, PLB 730 (2014) 53 [arXiv:1311.0012]. Kim [arXiv:1404.4022].

  40. Lyth, 1403.7323 [hep-ph]

  41. Trans-Planckian decay constant ★ Fundamental theory suppressed by MP, ★ ZnR example: ZnR quantum number 41/45 J E Kim “QCD axion, and DE”, 10th PATRAS, CERN, 30 June 2014

  42. Trans-Planckian decay constant ★ ψ /MP ≈ 0.01, Φ /MP≈31=103/2 Lyth, 1403.7323 [hep-ph] For Φ104 /Mp100 , we need 10-127 . 42/45 J E Kim “QCD axion, and DE”, 10th PATRAS, CERN, 30 June 2014

  43. 43/45 J E Kim “QCD axion, and DE”, 10th PATRAS, CERN, 30 June 2014

  44. 6. PQ symmetry breaking below HI JEK, PLB734, 68 (2014), 1405.0221[hep-th]

  45. HI≈1014 GeV imply most probably that the PQ symmetry breaking has occurred after (at the end phase of) inflation. Reheating may go close to HI, maybe suppressed by a factor of 50-100 [Buchmuller et al, 1309.7788]. So, the method of inflating away strings and domain walls of spontaneously broken U(1)PQ is out. The DW number must be one. The horizon size wall(s) is the problem. The domain wall problem: Zeldovich-Kobzarev-Okun (1974); Sikivie (1982). DW number = 1:

  46. For the DW number = 2:

  47. Choi-Kim mechanism Choi-Kim, PRL55 (1985) 2637 N1 Flat direction. Max. common divisor of 2 and 3 is NDW= 1. Identification by torus. Identification by torus. N2

  48. Model-independent axion with U(1)anom ★ The MI-axion has NDW =1 [Witten, PLB 153, 243 (1985)]. Basically, it is due to the Green-Schwarz condition, with the unit coefficient. It is in 10D and SU(3)-color is in the fundamental of E8 which will become the fundamental of SU(3)-color. For MI axion, we have NDW =1. 48/45 J E Kim “QCD axion, and DE”, 10th PATRAS, CERN, 30 June 2014

  49. U(1)PQ broken at an intermediate scale ★ Three families arise in addition from comp’n with those in the twisted sectors. Then, we have to check all the colored fields, including those from twisted sectors. The necessary condition to have DW number 1 is the U(1)PQ below U(1)anom scale has the coupling with common N ★ This form is necessary to allow a Goldstone boson direction ∂2a=0. Then, we obtain NDW =1by the CK mechanism. 49/45 J E Kim “QCD axion, and DE”, 10th PATRAS, CERN, 30 June 2014

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