The quest for an intermediate-scale accidental axion and further ALPs

Journal of High Energy Physics

Volumn 2014, Issue 6, 2014, Pages

  Dias, A G ^a   Machado, A C B ^b   Nishi, C C ^a   Ringwald, A ^c   Vaudrevange, P ^d  

^a UNIVERSIDADE FEDERAL DO ABC   (Brazil)

^b SÃO PAULO STATE UNIVERSITY UNESP   (Brazil)

^c DESY   (Germany)

^d EXCELLENCE CLUSTER UNIVERSE   (Germany)

Author keywords

Beyond Standard Model; Discrete and Finite Symmetries; Global Symmetries

Indexed keywords

EID: 84904283512     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1007/JHEP06(2014)037     Document Type: Article

References (162)

1. R.D. Peccei and H.R. Quinn, CP conservation in the presence of instantons, Phys. Rev. Lett. 38 (1977) 1440.
2. S. Weinberg, A new light boson?, Phys. Rev. Lett. 40 (1978) 223.
3. F. Wilczek, Problem of strong p and t invariance in the presence of instantons, Phys. Rev. Lett. 40 (1978) 279.
4. J.E. Kim, Weak interaction singlet and strong CP invariance, Phys. Rev. Lett. 43 (1979) 103.
5. 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.
6. 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.
7. 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].
8. H. Georgi, D.B. Kaplan and L. Randall, Manifesting the invisible axion at low-energies, Phys. Lett. B 169 (1986) 73.
9. W.A. Bardeen and S.H.H. Tye, Current algebra applied to properties of the light Higgs boson, Phys. Lett. B 74 (1978) 229.
10. D.B. Kaplan, Opening the axion window, Nucl. Phys. B 260 (1985) 215.
11. M. Srednicki, Axion couplings to matter. 1. CP conserving parts, Nucl. Phys. B 260 (1985) 689.
12. A. Friedland, M. Giannotti and M. Wise, Constraining the axion-photon coupling with massive stars, Phys. Rev. Lett. 110 (2013) 061101 [ arXiv:1210.1271 ].
13. S. De Panfilis et al., Limits on the abundance and coupling of cosmic axions at 4.5μeV < m(a) < 5.0 μeV, Phys. Rev. Lett. 59 (1987) 839.
14. W. Wuensch et al., Results of a laboratory search for cosmic axions and other weakly coupled light particles, Phys. Rev. D 40 (1989) 3153.
15. C. Hagmann, P. Sikivie, N.S. Sullivan and D.B. Tanner, Results from a search for cosmic axions, Phys. Rev. D 42 (1990) 1297.
16. S.J. Asztalos et al., Large scale microwave cavity search for dark matter axions, Phys. Rev. D 64 (2001) 092003.
17. ADMX collaboration, S.J. Asztalos et al., A SQUID-based microwave cavity search for dark-matter axions, Phys. Rev. Lett. 104 (2010) 041301 [ arXiv:0910.5914 ].
18. G.G. Raffelt, Astrophysical axion bounds, Lect. Notes Phys. 741 (2008) 51 [ hep-ph/0611350 ].
19. J. Preskill, M.B. Wise and F. Wilczek, Cosmology of the invisible axion, Phys. Lett. B 120 (1983) 127.
20. L.F. Abbott and P. Sikivie, A cosmological bound on the invisible axion, Phys. Lett. B 120 (1983) 133.
21. M. Dine and W. Fischler, The not so harmless axion, Phys. Lett. B 120 (1983) 137.
22. P. Sikivie, Axion cosmology, Lect. Notes Phys. 741 (2008) 19 [ astro-ph/0610440 ].
23. K.J. Bae, J.-H. Huh and J.E. Kim, Update of axion CDM energy, JCAP 09 (2008) 005 [ arXiv:0806.0497 ].
24. L. Visinelli and P. Gondolo, Dark matter axions revisited, Phys. Rev. D 80 (2009) 035024 [ arXiv:0903.4377 ].
25. O. Wantz and E.P.S. Shellard, Axion cosmology revisited, Phys. Rev. D 82 (2010) 123508 [ arXiv:0910.1066 ].
26. T. Hiramatsu, M. Kawasaki, T. Sekiguchi, M. Yamaguchi and J. Yokoyama, Improved estimation of radiated axions from cosmological axionic strings, Phys. Rev. D 83 (2011) 123531 [ arXiv:1012.5502 ].
27. 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 ].
28. BICEP2 collaboration, P.A.R. Ade et al., BICEP2 I: detection of B-mode polarization at degree angular scales, arXiv:1403.3985.
29. P. Fox, A. Pierce and S.D. Thomas, Probing a QCD string axion with precision cosmological measurements, hep-th/0409059.
30. M. Beltrán, J. García-Bellido and J. Lesgourgues, Isocurvature bounds on axions revisited, Phys. Rev. D 75 (2007) 103507 [ hep-ph/0606107 ].
31. M.P. Hertzberg, M. Tegmark and F. Wilczek, Axion cosmology and the energy scale of inflation, Phys. Rev. D 78 (2008) 083507 [ arXiv:0807.1726 ].
32. J. Hamann, S. Hannestad, G.G. Raffelt and Y.Y.Y. Wong, Isocurvature forecast in the anthropic axion window, JCAP 06 (2009) 022 [ arXiv:0904.0647 ].
33. Planck collaboration, P.A.R. Ade et al., Planck 2013 results. XXII. Constraints on inflation, arXiv:1303.5082.
34. 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 ].
35. D.J.E. Marsh, D. Grin, R. Hlozek and P.G. Ferreira, Tensor detection severely constrains axion dark matter, arXiv:1403.4216.
36. L. Visinelli and P. Gondolo, Axion cold dark matter in view of BICEP2 results, arXiv:1403.4594.
37. S.J. Asztalos et al., Design and performance of the ADMX SQUID-based microwave receiver, Nucl. Instrum. Meth. A 656 (2011) 39 [ arXiv:1105.4203 ].
38. P.W. Graham and S. Rajendran, Axion dark matter detection with cold molecules, Phys. Rev. D 84 (2011) 055013 [ arXiv:1101.2691 ].
39. O.K. Baker et al., Prospects for searching axion-like particle dark matter with dipole, toroidal and wiggler magnets, Phys. Rev. D 85 (2012) 035018 [ arXiv:1110.2180 ].
40. I.G. Irastorza and J.A. Garcia, Direct detection of dark matter axions with directional sensitivity, JCAP 10 (2012) 022 [ arXiv:1207.6129 ].
41. D. Horns et al., Searching for WISPy cold dark matter with a dish antenna, JCAP 04 (2013) 016 [ arXiv:1212.2970 ].
42. P.W. Graham and S. Rajendran, New observables for direct detection of axion dark matter, Phys. Rev. D 88 (2013) 035023 [ arXiv:1306.6088 ].
43. D. Budker, P.W. Graham, M. Ledbetter, S. Rajendran and A. Sushkov, Cosmic Axion Spin Precession Experiment (CASPEr), Phys. Rev. X 4 (2014) 021030 [ arXiv:1306.6089 ].
44. J. Jaeckel and J. Redondo, An antenna for directional detection of WISPy dark matter, JCAP 11 (2013) 016 [ arXiv:1307.7181 ].
45. J. Jaeckel and J. Redondo, From resonant to broadband searches for WISPy cold dark matter, Phys. Rev. D 88 (2013) 115002 [ arXiv:1308.1103 ].
46. D. Horns, A. Lindner, A. Lobanov and A. Ringwald, WISPers from the dark side: radio probes of axions and hidden photons, arXiv:1309.4170.
47. P. Sikivie, N. Sullivan and D.B. Tanner, Axion dark matter detection using an LC circuit, arXiv:1310.8545.
48. J. Redondo and B. Döbrich, Dark matter - A light move, arXiv:1311.5341.
49. G. Rybka and A. Wagner, A technique to search for high mass dark matter axions, arXiv:1403.3121.
50. J. Jaeckel and A. Ringwald, The low-energy frontier of particle physics, Ann. Rev. Nucl. Part. Sci. 60 (2010) 405 [ arXiv:1002.0329 ].
51. A. Ringwald, Exploring the role of axions and other WISPs in the dark universe, Phys. Dark Univ. 1 (2012) 116 [ arXiv:1210.5081 ].
52. A. Ringwald, Searching for axions and ALPs from string theory, J. Phys. Conf. Ser. 485 (2014) 012013 [ arXiv:1209.2299 ].
53. Y. Chikashige, R.N. Mohapatra and R.D. Peccei, Are there real Goldstone bosons associated with broken lepton number?, Phys. Lett. B 98 (1981) 265.
54. G.B. Gelmini and M. Roncadelli, Left-handed neutrino mass scale and spontaneously broken lepton number, Phys. Lett. B 99 (1981) 411.
55. F. Wilczek, Axions and family symmetry breaking, Phys. Rev. Lett. 49 (1982) 1549.
56. Z.G. Berezhiani and M.Y. Khlopov, The theory of broken gauge symmetry of families, in Russian), Sov. J. Nucl. Phys. 51 (1990) 739 [Yad. Fiz. 51 (1990) 1157].
57. J. Jaeckel, A family of WISPy dark matter candidates, Phys. Lett. B 732 (2014) 1 [ arXiv:1311.0880 ].
58. E. Witten, Some properties of O(32) superstrings, Phys. Lett. B 149 (1984) 351.
59. J.P. Conlon, The QCD axion and moduli stabilisation, JHEP 05 (2006) 078 [ hep-th/0602233 ].
60. P. Svrček and E. Witten, Axions in string theory, JHEP 06 (2006) 051 [ hep-th/0605206 ].
61. A. Arvanitaki, S. Dimopoulos, S. Dubovsky, N. Kaloper and J. March-Russell, String axiverse, Phys. Rev. D 81 (2010) 123530 [ arXiv:0905.4720 ].
62. B.S. Acharya, K. Bobkov and P. Kumar, An M-theory solution to the strong CP problem and constraints on the axiverse, JHEP 11 (2010) 105 [ arXiv:1004.5138 ].
63. M. Cicoli, M. Goodsell and A. Ringwald, The type IIB string axiverse and its low-energy phenomenology, JHEP 10 (2012) 146 [ arXiv:1206.0819 ].
64. G. Lazarides, C. Panagiotakopoulos and Q. Shafi, Phenomenology and cosmology with superstrings, Phys. Rev. Lett. 56 (1986) 432.
65. K.-S. Choi, I.-W. Kim and J.E. Kim, String compactification, QCD axion and axion-photon-photon coupling, JHEP 03 (2007) 116 [ hep-ph/0612107 ].
66. K.-S. Choi, H.P. Nilles, S. Ramos-Sanchez and P.K.S. Vaudrevange, Accions, Phys. Lett. B 675 (2009) 381 [ arXiv:0902.3070 ].
67. P. Arias et al., WISPy cold dark matter, JCAP 06 (2012) 013 [ arXiv:1201.5902 ].
68. D.J.E. Marsh and J. Silk, A model for halo formation with axion mixed dark matter, arXiv:1307.1705.
69. K. Kadota, Y. Mao, K. Ichiki and J. Silk, Cosmologically probing ultra-light particle dark matter using 21 cm signals, arXiv:1312.1898.
70. Fermi-LAT collaboration, M. Ackermann et al., The imprint of the extragalactic background light in the gamma-ray spectra of blazars, Science 338 (2012) 1190 [ arXiv:1211.1671 ].
71. HESS collaboration, A. Abramowski et al., Measurement of the extragalactic background light imprint on the spectra of the brightest blazars observed with H.E.S.S, arXiv:1212.3409.
72. H.E.S.S. collaboration, F. Aharonian et al., New constraints on the Mid-IR EBL from the HESS discovery of VHE gamma rays from 1ES 0229+200, Astron. Astrophys. 475 (2007) L9 [ arXiv:0709.4584 ].
73. MAGIC collaboration, E. Aliu et al., Very-high-energy gamma rays from a distant quasar: how transparent is the universe?, Science 320 (2008) 1752 [ arXiv:0807.2822 ].
74. W. Essey and A. Kusenko, On weak redshift dependence of gamma-ray spectra of distant blazars, Astrophys. J. 751 (2012) L11 [ arXiv:1111.0815 ].
75. D. Horns and M. Meyer, Indications for a pair-production anomaly from the propagation of VHE gamma-rays, JCAP 02 (2012) 033 [ arXiv:1201.4711 ].
76. D. Horns and M. Meyer, Pair-production opacity at high and very-high gamma-ray energies, arXiv:1309.3846.
77. A. De Angelis, M. Roncadelli and O. Mansutti, Evidence for a new light spin-zero boson from cosmological gamma-ray propagation?, Phys. Rev. D 76 (2007) 121301 [ arXiv:0707.4312 ].
78. M. Simet, D. Hooper and P.D. Serpico, The Milky Way as a kiloparsec-scale axionscope, Phys. Rev. D 77 (2008) 063001 [ arXiv:0712.2825 ].
79. M.A. Sanchez-Conde, D. Paneque, E. Bloom, F. Prada and A. Dominguez, Hints of the existence of axion-like-particles from the gamma-ray spectra of cosmological sources, Phys. Rev. D 79 (2009) 123511 [ arXiv:0905.3270 ].
80. D. Horns, L. Maccione, M. Meyer, A. Mirizzi, D. Montanino et al., Hardening of TeV γ spectrum of AGNs in galaxy clusters by conversions of photons into axion-like particles, Phys. Rev. D 86 (2012) 075024 [ arXiv:1207.0776 ].
81. O. Mena and S. Razzaque, Hints of an axion-like particle mixing in the GeV γ-rayblazar data?, JCAP 11 (2013) 023 [ arXiv:1306.5865 ].
82. M. Meyer, D. Horns and M. Raue, First lower limits on the photon-axion-like particle coupling from very high energy gamma-ray observation, Phys. Rev. D 87 (2013) 035027 [ arXiv:1302.1208 ].
83. M. Cicoli, J.P. Conlon and F. Quevedo, Dark radiation in LARGE volume models, Phys. Rev. D 87 (2013) 043520 [ arXiv:1208.3562 ].
84. T. Higaki and F. Takahashi, Dark radiation and dark matter in large volume compactifications, JHEP 11 (2012) 125 [ arXiv:1208.3563 ].
85. J.P. Conlon and M.C.D. Marsh, Searching for a 0.1-1 keV cosmic axion background, Phys. Rev. Lett. 111 (2013) 151301 [ arXiv:1305.3603 ].
86. S. Angus, J.P. Conlon, M.C.D. Marsh, A. Powell and L.T. Witkowski, Soft X-ray excess in the Coma cluster from a cosmic axion background, arXiv:1312.3947.
87. R. Gill and J.S. Heyl, Constraining the photon-axion coupling constant with magnetic white dwarfs, Phys. Rev. D 84 (2011) 085001 [ arXiv:1105.2083 ].
88. J.W. Brockway, E.D. Carlson and G.G. Raffelt, SN1987A gamma-ray limits on the conversion of pseudoscalars, Phys. Lett. B 383 (1996) 439 [ astro-ph/9605197 ].
89. J.A. Grifols, E. Masso and R. Toldra, Gamma-rays from SN1987A due to pseudoscalar conversion, Phys. Rev. Lett. 77 (1996) 2372 [ astro-ph/9606028 ].
90. A. Payez, J.R. Cudell and D. Hutsemekers, New polarimetric constraints on axion-like particles, JCAP 07 (2012) 041 [ arXiv:1204.6187 ].
91. A. Payez, Constraining ALPs with linear and circular polarisation measurements of quasar light, arXiv:1309.6114.
92. A. Kogut et al., The Primordial Inflation Explorer (PIXIE): a nulling polarimeter for cosmic microwave background observations, JCAP 07 (2011) 025 [ arXiv:1105.2044 ].
93. PRISM collaboration, P. André et al., PRISM (Polarized Radiation Imaging and Spectroscopy Mission): an extended white paper, JCAP 02 (2014) 006 [ arXiv:1310.1554 ].
94. A. Mirizzi, J. Redondo and G. Sigl, Constraining resonant photon-axion conversions in the early universe, JCAP 08 (2009) 001 [ arXiv:0905.4865 ].
95. H. Tashiro, J. Silk and D.J.E. Marsh, Constraints on primordial magnetic fields from CMB distortions in the axiverse, Phys. Rev. D 88 (2013) 125024 [ arXiv:1308.0314 ].
96. D. Ejlli and A.D. Dolgov, CMB constraints on mass and coupling constant of light pseudoscalar particles, arXiv:1312.3558.
97. J. Redondo and A. Ringwald, Light shining through walls, Contemp. Phys. 52 (2011) 211 [ arXiv:1011.3741 ].
98. R. Bähre et al., Any light particle search II - Technical design report, 2013 JINST 8 T09001 [ arXiv:1302.5647 ].
99. E. Armengaud et al., Conceptual design of the International Axion Observatory (IAXO), 2014 JINST 9 T05002 [ arXiv:1401.3233 ].
100. J. Redondo, Solar axion flux from the axion-electron coupling, JCAP 12 (2013) 008 [ arXiv:1310.0823 ].
101. J. Isern, E. Garcia-Berro, S. Torres and S. Catalan, Axions and the cooling of white dwarf stars, arXiv:0806.2807.
102. J. Isern, E. Garcia-Berro, L.G. Althaus and A.H. Corsico, Axions and the pulsation periods of variable white dwarfs revisited, arXiv:1001.5248.
103. A.H. Corsico et al., An independent limit on the axion mass from the variable white dwarf star R548, JCAP 12 (2012) 010 [ arXiv:1211.3389 ].
104. N. Viaux et al., Neutrino and axion bounds from the globular cluster M5 (NGC 5904), Phys. Rev. Lett. 111 (2013) 231301 [ arXiv:1311.1669 ].
105. E. Bulbul et al., Detection of an unidentified emission line in the stacked X-ray spectrum of galaxy clusters, arXiv:1402.2301.
106. A. Boyarsky, O. Ruchayskiy, D. Iakubovskyi and J. Franse, An unidentified line in X-ray spectra of the Andromeda galaxy and Perseus galaxy cluster, arXiv:1402.4119.
107. T. Higaki, K.S. Jeong and F. Takahashi, The 7 keV axion dark matter and the X-ray line signal, Phys. Lett. B 733 (2014) 25 [ arXiv:1402.6965 ].
108. J. Jaeckel, J. Redondo and A. Ringwald, A 3.55 keV hint for decaying axion-like particle dark matter, Phys. Rev. D 89 (2014) 103511 [ arXiv:1402.7335 ].
109. H.M. Lee, S.C. Park and W.-I. Park, Cluster X-ray line at 3.5 keV from axion-like dark matter, arXiv:1403.0865.
110. M. Cicoli, J.P. Conlon, M.C.D. Marsh and M. Rummel, A 3.55 keV photon line and its morphology from a 3.55 keV ALP line, arXiv:1403.2370.
111. J.E. Kim, Axion and almost massless quark as ingredients of quintessence, JHEP 05 (1999) 022 [ hep-ph/9811509 ].
112. J.E. Kim, Model dependent axion as quintessence with almost massless hidden sector quarks, JHEP 06 (2000) 016 [ hep-ph/9907528 ].
113. 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 ].
114. S.L. Cheng, C.Q. Geng and W.T. Ni, Axion-photon couplings in invisible axion models, Phys. Rev. D 52 (1995) 3132 [ hep-ph/9506295 ].
115. J.E. Kim, Reason for SU(6) grand unification, Phys. Lett. B 107 (1981) 69.
116. P. Langacker, R.D. Peccei and T. Yanagida, Invisible axions and light neutrinos: are they connected?, Mod. Phys. Lett. A 1 (1986) 541.
117. M. Gell-Mann, P. Ramond, R. Slansky, Complex spinors and unified theories, in Supergravity, D.Z. Freedman and P.van Nieuwenhuizen eds., North Holland, Amsterdam, The Netherlands (1979).
118. T. Yanagida, Horizontal symmetry and masses of neutrinos, in the proceedings of the Workshop on unified theory and baryon number in the universe, O. Sawada and A. Sugamoto eds., KEK, Tsukuba, Japan (1979).
119. R.N. Mohapatra and G. Senjanović, Neutrino mass and spontaneous parity violation, Phys. Rev. Lett. 44 (1980) 912.
120. M. Fukugita and T. Yanagida, Baryogenesis without grand unification, Phys. Lett. B 174 (1986) 45.
121. W. Buchmüller, Leptogenesis: theory and neutrino masses, Nucl. Phys. Proc. Suppl. 235-236 (2013) 329 [ arXiv:1210.7758 ].
122. J. Elias-Miro, J.R. Espinosa, G.F. Giudice, H.M. Lee and A. Strumia, Stabilization of the electroweak vacuum by a scalar threshold effect, JHEP 06 (2012) 031 [ arXiv:1203.0237 ].
123. M.L. Perl et al., The search for stable, massive, elementary particles, Int. J. Mod. Phys. A 16 (2001) 2137 [ hep-ex/0102033 ].
124. E. Nardi and E. Roulet, Are exotic stable quarks cosmologically allowed?, Phys. Lett. B 245 (1990) 105.
125. Z.G. Berezhiani, A.S. Sakharov and M.Y. Khlopov, Primordial background of cosmological axions, Sov. J. Nucl. Phys. 55 (1992) 1063.
126. B. Dasgupta, E. Ma and K. Tsumura, WIMP dark matter and neutrino mass from Peccei-Quinn symmetry, Phys. Rev. D 89 (2014) 041702 [ arXiv:1308.4138 ].
127. H.M. Georgi, L.J. Hall and M.B. Wise, Grand unified models with an automatic Peccei-Quinn symmetry, Nucl. Phys. B 192 (1981) 409.
128. S. Ghigna, M. Lusignoli and M. Roncadelli, Instability of the invisible axion, Phys. Lett. B 283 (1992) 278.
129. R. Holman et al., Solutions to the strong CP problem in a world with gravity, Phys. Lett. B 282 (1992) 132 [ hep-ph/9203206 ].
130. M. Kamionkowski and J. March-Russell, Planck scale physics and the Peccei-Quinn mechanism, Phys. Lett. B 282 (1992) 137 [ hep-th/9202003 ].
131. S.M. Barr and D. Seckel, Planck scale corrections to axion models, Phys. Rev. D 46 (1992) 539.
132. R. Kallosh, A.D. Linde, D.A. Linde and L. Susskind, Gravity and global symmetries, Phys. Rev. D 52 (1995) 912 [ hep-th/9502069 ].
133. 3 symmetries, Phys. Rev. D 69 (2004) 015007 [ hep-ph/0210172 ].
134. A.G. Dias, V. Pleitez and M.D. Tonasse, Naturally light invisible axion in models with large local discrete symmetries, Phys. Rev. D 67 (2003) 095008 [ hep-ph/0211107 ].
135. A.G. Dias and V. Pleitez, Stabilizing the invisible axion in 3-3-1 models, Phys. Rev. D 69 (2004) 077702 [ hep-ph/0308037 ].
136. L.M. Carpenter, M. Dine and G. Festuccia, Dynamics of the Peccei-Quinn scale, Phys. Rev. D 80 (2009) 125017 [ arXiv:0906.1273 ].
137. K. Harigaya, M. Ibe, K. Schmitz and T.T. Yanagida, Peccei-Quinn symmetry from a gauged discrete R symmetry, Phys. Rev. D 88 (2013) 075022 [ arXiv:1308.1227 ].
138. de symmetry, Phys. Lett. B 730 (2014) 53 [ arXiv:1311.0012 ].
139. J.E. Kim, Invisible axion and neutrino oscillation in SU(11), Phys. Rev. D 24 (1981) 3007.
140. R.N. Mohapatra and G. Senjanović, The superlight axion and neutrino masses, Z. Phys. C 17 (1983) 53.
141. Q. Shafi and F.W. Stecker, Implications of a class of grand unified theories for large scale structure in the universe, Phys. Rev. Lett. 53 (1984) 1292.
142. X.G. He and R.R. Volkas, Models featuring spontaneous CP violation: an invisible axion and light neutrino masses, Phys. Lett. B 208 (1988) 261 [Erratum ibid. B 218 (1989) 508].
143. Z.G. Berezhiani and M.Y. Khlopov, Cosmology of spontaneously broken gauge family symmetry, Z. Phys. C 49 (1991) 73.
144. H. Arason, P. Ramond and B.D. Wright, A standard model extension with neutrino masses and an invisible axion, Phys. Rev. D 43 (1991) 2337.
145. A.G. Dias and V. Pleitez, The Invisible axion and neutrino masses, Phys. Rev. D 73 (2006) 017701 [ hep-ph/0511104 ].
146. P.-H. Gu and M. Lindner, Universal seesaw from left-right and Peccei-Quinn symmetry breaking, Phys. Lett. B 698 (2011) 40 [ arXiv:1010.4635 ].
147. GUT, JHEP 08 (2013) 021 [ arXiv:1305.1001 ].
148. A.G. Dias and V. Pleitez, Grand unification and proton stability near the Peccei-Quinn scale, Phys. Rev. D 70 (2004) 055009 [ hep-ph/0407074 ].
149. 13 grand unification model, Phys. Rev. D 76 (2007) 115010 [ arXiv:0708.1009 ].
150. S. Weinberg, Baryon and lepton nonconserving processes, Phys. Rev. Lett. 43 (1979) 1566.
151. K. Fujikawa, Path integral measure for gauge invariant fermion theories, Phys. Rev. Lett. 42 (1979) 1195.
152. K. Fujikawa, Path integral for gauge theories with fermions, Phys. Rev. D 21 (1980) 2848 [Erratum ibid. D 22 (1980) 1499].
153. P. Sikivie, Of axions, domain walls and the early universe, Phys. Rev. Lett. 48 (1982) 1156.
154. Y. Zeldovich, I.Y. Kobzarev and L.B. Okun, Cosmological consequences of the spontaneous breakdown of discrete symmetry, Zh. Eksp. Teor. Fiz. 67 (1974) 3.
155. A. Vilenkin, Cosmic strings and domain walls, Phys. Rept. 121 (1985) 263.
156. M. Shifman, Advanced topics in quantum field theory: a lecture course, Cambridge University Press, Cambridge U.K. (2012).
157. G. Lazarides and Q. Shafi, Axion models with no domain wall problem, Phys. Lett. B 115 (1982) 21.
158. H. Georgi and M.B. Wise, Hiding the invisible axion, Phys. Lett. B 116 (1982) 123.
159. S.M. Barr, X.C. Gao and D. Reiss, Peccei-Quinn symmetries without domains, Phys. Rev. D 26 (1982) 2176.
160. K. Choi and J.E. Kim, Domain walls in superstring models, Phys. Rev. Lett. 55 (1985) 2637.
161. S.M. Barr, K. Choi and J.E. Kim, Axion cosmology in superstring models, Nucl. Phys. B 283 (1987) 591.
162. T. Hiramatsu, M. Kawasaki, K. Saikawa and T. Sekiguchi, Axion cosmology with long-lived domain walls, JCAP 01 (2013) 001 [ arXiv:1207.3166 ].