String theoretic QCD axions in the light of PLANCK and BICEP2

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Article

Abstract

The QCD axion solving the strong CP problem may originate from antisymmetric tensor gauge fields in compactified string theory, with a decay constant around the GUT scale. Such possibility appears to be ruled out now by the detection of tensor modes by BICEP2 and the PLANCK constraints on isocurvature density perturbations. A more interesting and still viable possibility is that the string theoretic QCD axion is charged under an anomalous U(1)A gauge symmetry. In such case, the axion decay constant can be much lower than the GUT scale if moduli are stabilized near the point of vanishing Fayet-Illiopoulos term, and U(1)A-charged matter fields get a vacuum value v ~ (mSUSYMPln)1/(n + 1) (n ≥ 0) induced by a tachyonic SUSY breaking mass mSUSY. We examine the symmetry breaking pattern of such models during the inflationary epoch with HI ≃ 1014 GeV, and identify the range of the QCD axion decay constant, as well as the corresponding relic axion abundance, consistent with known cosmological constraints. In addition to the case that the PQ symmetry is restored during inflation, i.e. v(tI) = 0, there are other viable scenarios, including that the PQ symmetry is broken during inflation with v(tI) ∼ (4πHIMPln)1/(n + 1) ~ 1016–1017 GeV due to the Hubble-induced D-term DA ~ 8π2HI2, while v(t0) ~ (mSUSYMPln)1/(n + 1) ~ 109–5 × 1013 GeV in the present universe, where v(t0) above 1012 GeV requires a fine-tuning of the axion misalignment angle. We also discuss the implications of our results for the size of SUSY breaking soft masses.

Keywords

Cosmology of Theories beyond the SM Compactification and String Models 

References

  1. [1]
    J.E. Kim and G. Carosi, Axions and the strong CP problem, Rev. Mod. Phys. 82 (2010) 557 [arXiv:0807.3125] [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    A. Ringwald, Exploring the role of axions and other WISPs in the dark universe, Phys. Dark Univ. 1 (2012) 116 [arXiv:1210.5081] [INSPIRE].CrossRefGoogle Scholar
  3. [3]
    M. Kawasaki and K. Nakayama, Axions: theory and cosmological role, Ann. Rev. Nucl. Part. Sci. 63 (2013) 69 [arXiv:1301.1123] [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    R.D. Peccei and H.R. Quinn, CP conservation in the presence of instantons, Phys. Rev. Lett. 38 (1977) 1440 [INSPIRE].ADSCrossRefGoogle Scholar
  5. [5]
    R.D. Peccei and H.R. Quinn, Constraints imposed by CP conservation in the presence of instantons, Phys. Rev. D 16 (1977) 1791 [INSPIRE].ADSGoogle Scholar
  6. [6]
    S. Weinberg, A new light boson?, Phys. Rev. Lett. 40 (1978) 223 [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    F. Wilczek, Problem of strong p and t invariance in the presence of instantons, Phys. Rev. Lett. 40 (1978) 279 [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    J.E. Kim, Weak interaction singlet and strong CP invariance, Phys. Rev. Lett. 43 (1979) 103 [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    M.A. Shifman, A.I. Vainshtein and V.I. Zakharov, Can confinement ensure natural CP invariance of strong interactions?, Nucl. Phys. B 166 (1980) 493 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  10. [10]
    M. Dine, W. Fischler and M. Srednicki, A simple solution to the strong CP problem with a harmless axion, Phys. Lett. B 104 (1981) 199 [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    A.R. Zhitnitsky, On possible suppression of the axion hadron interactions (in Russian), Sov. J. Nucl. Phys. 31 (1980) 260 [Yad. Fiz. 31 (1980) 497] [INSPIRE].
  12. [12]
    L.F. Abbott and M.B. Wise, Wormholes and global symmetries, Nucl. Phys. B 325 (1989) 687 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  13. [13]
    S.R. Coleman and K.-M. Lee, Wormholes made without massless matter fields, Nucl. Phys. B 329 (1990) 387 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  14. [14]
    R. Kallosh, A.D. Linde, D.A. Linde and L. Susskind, Gravity and global symmetries, Phys. Rev. D 52 (1995) 912 [hep-th/9502069] [INSPIRE].ADSMathSciNetGoogle Scholar
  15. [15]
    T. Banks and N. Seiberg, Symmetries and strings in field theory and gravity, Phys. Rev. D 83 (2011) 084019 [arXiv:1011.5120] [INSPIRE].ADSGoogle Scholar
  16. [16]
    S.M. Barr and D. Seckel, Planck scale corrections to axion models, Phys. Rev. D 46 (1992) 539 [INSPIRE].ADSGoogle Scholar
  17. [17]
    M. Kamionkowski and J. March-Russell, Planck scale physics and the Peccei-Quinn mechanism, Phys. Lett. B 282 (1992) 137 [hep-th/9202003] [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    R. Holman et al., Solutions to the strong CP problem in a world with gravity, Phys. Lett. B 282 (1992) 132 [hep-ph/9203206] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    E. Witten, Some properties of O(32) superstrings, Phys. Lett. B 149 (1984) 351 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  20. [20]
    M.B. Green, J.H. Schwarz and E. Witten, Superstring theory, vol. 2, Cambridge University Press, Cambridge U.K. (1987).MATHGoogle Scholar
  21. [21]
    L.E. Ibanez and A.M. Uranga, String theory and particle physics: an introduction to string phenomenology, Cambridge University Press, Cambridge U.K. (2012).Google Scholar
  22. [22]
    K. Choi and J.E. Kim, Harmful axions in superstring models, Phys. Lett. B 154 (1985) 393 [Erratum ibid. B 156 (1985) 452] [INSPIRE].
  23. [23]
    K. Choi and J.E. Kim, Compactification and axions in E 8 × E 8 superstring models, Phys. Lett. B 165 (1985) 71 [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    P. Svrček and E. Witten, Axions in string theory, JHEP 06 (2006) 051 [hep-th/0605206] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    T. Banks and M. Dine, Couplings and scales in strongly coupled heterotic string theory, Nucl. Phys. B 479 (1996) 173 [hep-th/9605136] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  26. [26]
    K. Choi, Axions and the strong CP problem in M-theory, Phys. Rev. D 56 (1997) 6588 [hep-th/9706171] [INSPIRE].ADSGoogle Scholar
  27. [27]
    J. Preskill, M.B. Wise and F. Wilczek, Cosmology of the invisible axion, Phys. Lett. B 120 (1983) 127 [INSPIRE].ADSCrossRefGoogle Scholar
  28. [28]
    L.F. Abbott and P. Sikivie, A cosmological bound on the invisible axion, Phys. Lett. B 120 (1983) 133 [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    M. Dine and W. Fischler, The not so harmless axion, Phys. Lett. B 120 (1983) 137 [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    M. Axenides, R.H. Brandenberger and M.S. Turner, Development of axion perturbations in an axion dominated universe, Phys. Lett. B 126 (1983) 178 [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    D. Seckel and M.S. Turner, Isothermal density perturbations in an axion dominated inflationary universe, Phys. Rev. D 32 (1985) 3178 [INSPIRE].ADSGoogle Scholar
  32. [32]
    A.D. Linde, Generation of isothermal density perturbations in the inflationary universe, Phys. Lett. B 158 (1985) 375 [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    D.H. Lyth, A limit on the inflationary energy density from axion isocurvature fluctuations, Phys. Lett. B 236 (1990) 408 [INSPIRE].ADSCrossRefGoogle Scholar
  34. [34]
    M.S. Turner and F. Wilczek, Inflationary axion cosmology, Phys. Rev. Lett. 66 (1991) 5 [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    P. Fox, A. Pierce and S.D. Thomas, Probing a QCD string axion with precision cosmological measurements, hep-th/0409059 [INSPIRE].
  36. [36]
    K.J. Mack and P.J. Steinhardt, Cosmological problems with multiple axion-like fields, JCAP 05 (2011) 001 [arXiv:0911.0418] [INSPIRE].ADSCrossRefGoogle Scholar
  37. [37]
    K.J. Mack, Axions, inflation and the anthropic principle, JCAP 07 (2011) 021 [arXiv:0911.0421] [INSPIRE].ADSCrossRefGoogle Scholar
  38. [38]
    M.B. Green and J.H. Schwarz, Anomaly cancellation in supersymmetric D = 10 gauge theory and superstring theory, Phys. Lett. B 149 (1984) 117 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  39. [39]
    S.M. Barr, Harmless axions in superstring theories, Phys. Lett. B 158 (1985) 397 [INSPIRE].ADSCrossRefGoogle Scholar
  40. [40]
    J.E. Kim, The strong CP problem in orbifold compactifications and an SU(3) × SU(2) × U(1)n model, Phys. Lett. B 207 (1988) 434 [INSPIRE].ADSCrossRefGoogle Scholar
  41. [41]
    K. Choi, K.S. Jeong, K.-I. Okumura and M. Yamaguchi, Mixed mediation of supersymmetry breaking with anomalous U(1) gauge symmetry, JHEP 06 (2011) 049 [arXiv:1104.3274] [INSPIRE].ADSCrossRefGoogle Scholar
  42. [42]
    G. Honecker and W. Staessens, On axionic dark matter in type IIA string theory, Fortsch. Phys. 62 (2014) 115 [arXiv:1312.4517] [INSPIRE].CrossRefMathSciNetGoogle Scholar
  43. [43]
    M. Cvetič, G. Shiu and A.M. Uranga, Chiral four-dimensional N = 1 supersymmetric type 2A orientifolds from intersecting D6 branes, Nucl. Phys. B 615 (2001) 3 [hep-th/0107166] [INSPIRE].ADSCrossRefGoogle Scholar
  44. [44]
    D. Cremades, L.E. Ibáñez and F. Marchesano, SUSY quivers, intersecting branes and the modest hierarchy problem, JHEP 07 (2002) 009 [hep-th/0201205] [INSPIRE].ADSCrossRefGoogle Scholar
  45. [45]
    G. Honecker and T. Ott, Getting just the supersymmetric Standard Model at intersecting branes on the Z 6 orientifold, Phys. Rev. D 70 (2004) 126010 [Erratum ibid. D 71 (2005) 069902] [hep-th/0404055] [INSPIRE].
  46. [46]
    G. Villadoro and F. Zwirner, D terms from D-branes, gauge invariance and moduli stabilization in flux compactifications, JHEP 03 (2006) 087 [hep-th/0602120] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  47. [47]
    F. Gmeiner and G. Honecker, Millions of Standard Models on Z 6 ?, JHEP 07 (2008) 052 [arXiv:0806.3039] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  48. [48]
    R. Blumenhagen, G. Honecker and T. Weigand, Loop-corrected compactifications of the heterotic string with line bundles, JHEP 06 (2005) 020 [hep-th/0504232] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  49. [49]
    R. Blumenhagen, G. Honecker and T. Weigand, Supersymmetric (non-)Abelian bundles in the type I and SO(32) heterotic string, JHEP 08 (2005) 009 [hep-th/0507041] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  50. [50]
    L.B. Anderson, J. Gray, A. Lukas and B. Ovrut, Stability walls in heterotic theories, JHEP 09 (2009) 026 [arXiv:0905.1748] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  51. [51]
    H. Murayama, H. Suzuki and T. Yanagida, Radiative breaking of Peccei-Quinn symmetry at the intermediate mass scale, Phys. Lett. B 291 (1992) 418 [INSPIRE].ADSCrossRefGoogle Scholar
  52. [52]
    K. Choi, E.J. Chun and J.E. Kim, Cosmological implications of radiatively generated axion scale, Phys. Lett. B 403 (1997) 209 [hep-ph/9608222] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  53. [53]
    BICEP2 collaboration, P.A.R. Ade et al., Detection of B-mode polarization at degree angular scales by BICEP2, Phys. Rev. Lett. 112 (2014) 241101 [arXiv:1403.3985] [INSPIRE].ADSCrossRefGoogle Scholar
  54. [54]
    D.J.E. Marsh, D. Grin, R. Hlozek and P.G. Ferreira, Tensor detection severely constrains axion dark matter, Phys. Rev. Lett. 113 (2014) 011801 [arXiv:1403.4216] [INSPIRE].ADSCrossRefGoogle Scholar
  55. [55]
    L. Visinelli and P. Gondolo, Axion cold dark matter in view of BICEP2 results, Phys. Rev. Lett. 113 (2014) 011802 [arXiv:1403.4594] [INSPIRE].ADSCrossRefGoogle Scholar
  56. [56]
    A.G. Dias, A.C.B. Machado, C.C. Nishi, A. Ringwald and P. Vaudrevange, The quest for an intermediate-scale accidental axion and further ALPs, JHEP 06 (2014) 037 [arXiv:1403.5760] [INSPIRE].ADSCrossRefGoogle Scholar
  57. [57]
    Planck collaboration, P.A.R. Ade et al., Planck 2013 results. XXII. Constraints on inflation, arXiv:1303.5082 [INSPIRE].
  58. [58]
    K.S. Jeong and F. Takahashi, Suppressing isocurvature perturbations of QCD axion dark matter, Phys. Lett. B 727 (2013) 448 [arXiv:1304.8131] [INSPIRE].ADSCrossRefGoogle Scholar
  59. [59]
    T. Higaki, K.S. Jeong and F. Takahashi, Solving the tension between high-scale inflation and axion isocurvature perturbations, Phys. Lett. B 734 (2014) 21 [arXiv:1403.4186] [INSPIRE].ADSCrossRefGoogle Scholar
  60. [60]
    T. Hiramatsu, M. Kawasaki, K. Saikawa and T. Sekiguchi, Production of dark matter axions from collapse of string-wall systems, Phys. Rev. D 85 (2012) 105020 [Erratum ibid. D 86 (2012) 089902] [arXiv:1202.5851] [INSPIRE].
  61. [61]
    T. Hiramatsu, M. Kawasaki, K. Saikawa and T. Sekiguchi, Axion cosmology with long-lived domain walls, JCAP 01 (2013) 001 [arXiv:1207.3166] [INSPIRE].ADSCrossRefGoogle Scholar
  62. [62]
    L.J. Hall, Y. Nomura and S. Shirai, Grand unification, axion and inflation in intermediate scale supersymmetry, JHEP 06 (2014) 137 [arXiv:1403.8138] [INSPIRE].ADSCrossRefGoogle Scholar
  63. [63]
    K.-W. Choi, A QCD axion from higher dimensional gauge field, Phys. Rev. Lett. 92 (2004) 101602 [hep-ph/0308024] [INSPIRE].ADSCrossRefGoogle Scholar
  64. [64]
    I.-W. Kim and J.E. Kim, Modification of decay constants of superstring axions: effects of flux compactification and axion mixing, Phys. Lett. B 639 (2006) 342 [hep-th/0605256] [INSPIRE].ADSCrossRefGoogle Scholar
  65. [65]
    M. Cicoli et al., Explicit de Sitter flux vacua for global string models with chiral matter, JHEP 05 (2014) 001 [arXiv:1312.0014] [INSPIRE].ADSCrossRefGoogle Scholar
  66. [66]
    R. Allahverdi, M. Cicoli, B. Dutta and K. Sinha, Correlation between dark matter and dark radiation in string compactifications, arXiv:1401.4364 [INSPIRE].
  67. [67]
    Y. Kawamura, Model independent analysis of soft masses in heterotic string models with anomalous U(1) symmetry, Phys. Lett. B 446 (1999) 228 [hep-ph/9811312] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  68. [68]
    K. Choi and K.S. Jeong, Supersymmetry breaking and moduli stabilization with anomalous U(1) gauge symmetry, JHEP 08 (2006) 007 [hep-th/0605108] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  69. [69]
    M.S. Turner, Cosmic and local mass density of invisible axions, Phys. Rev. D 33 (1986) 889 [INSPIRE].ADSGoogle Scholar
  70. [70]
    D.H. Lyth, Axions and inflation: sitting in the vacuum, Phys. Rev. D 45 (1992) 3394 [INSPIRE].ADSMathSciNetGoogle Scholar
  71. [71]
    K.J. Bae, J.-H. Huh and J.E. Kim, Update of axion CDM energy, JCAP 09 (2008) 005 [arXiv:0806.0497] [INSPIRE].ADSCrossRefGoogle Scholar
  72. [72]
    L. Visinelli and P. Gondolo, Dark matter axions revisited, Phys. Rev. D 80 (2009) 035024 [arXiv:0903.4377] [INSPIRE].ADSGoogle Scholar
  73. [73]
    T. Kobayashi, R. Kurematsu and F. Takahashi, Isocurvature constraints and anharmonic effects on QCD axion dark matter, JCAP 09 (2013) 032 [arXiv:1304.0922] [INSPIRE].ADSCrossRefGoogle Scholar
  74. [74]
    M. Kawasaki, K. Nakayama, T. Sekiguchi, T. Suyama and F. Takahashi, Non-Gaussianity from isocurvature perturbations, JCAP 11 (2008) 019 [arXiv:0808.0009] [INSPIRE].ADSCrossRefGoogle Scholar
  75. [75]
    A.D. Linde, Axions in inflationary cosmology, Phys. Lett. B 259 (1991) 38 [INSPIRE].ADSCrossRefGoogle Scholar
  76. [76]
    M. Kawasaki, M. Yamaguchi and T. Yanagida, Natural chaotic inflation in supergravity, Phys. Rev. Lett. 85 (2000) 3572 [hep-ph/0004243] [INSPIRE].ADSCrossRefGoogle Scholar
  77. [77]
    R. Kallosh and A.D. Linde, Landscape, the scale of SUSY breaking and inflation, JHEP 12 (2004) 004 [hep-th/0411011] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar

Copyright information

© The Author(s) 2014

Authors and Affiliations

  1. 1.Center for Theoretical Physics of the Universe, IBSYuseong-guKorea
  2. 2.Department of Physics, KAISTYuseong-guKorea
  3. 3.DESYHamburgGermany

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