Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

High-quality composite Pati-Salam axion

Tony Gherghetta1,*, Hitoshi Murayama2,3,4,†, and Pablo Quílez5,‡

  • *Contact author: tgher@umn.edu
  • †Contact author: hitoshi@berkeley.edu, hitoshi.murayama@ipmu.jp
  • ‡Contact author: pquilez@ucsd.edu

Phys. Rev. D 112, 095036 – Published 24 November, 2025

DOI: https://doi.org/10.1103/f1dg-n9h7

Abstract

We present a composite QCD axion model where the Peccei-Quinn symmetry emerges as a high-quality, accidental symmetry. The axion potential is only modified by eight-fermion, dimension-12 operators, which if present at the Planck scale, allow for axion dark matter from misalignment while solving the strong CP problem. The model is an SU(Nc) gauge theory with ten flavors where the Pati-Salam unified subgroup SO(6)×SO(4)⊂SU(10)L and Sp(10)⊂SU(10)R are weakly gauged. The dynamics breaks SU(10)L×SU(10)R→SU(10)V and the weakly gauged groups to U(3)×U(2)⊃SU(3)c×SU(2)L×U(1)Y, with the QCD axion identified as one of the Nambu-Goldstone bosons. This axion has a relatively large coupling to photons while a residual θ¯eff may be just below the current limit on the neutron electric dipole moment. If the dimension-12 operators are present near the grand unified theory scale, they can cause domain wall networks to decay, allowing for axion dark matter even for the postinflationary scenario.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (85)

  1. R. D. Peccei and H. R. Quinn, CP conservation in the presence of instantons, Phys. Rev. Lett. 38, 1440 (1977).
  2. S. Weinberg, A new light boson?, Phys. Rev. Lett. 40, 223 (1978).
  3. F. Wilczek, Problem of strong P and T invariance in the presence of instantons, Phys. Rev. Lett. 40, 279 (1978).
  4. H. M. Georgi, L. J. Hall, and M. B. Wise, Grand unified models with an automatic Peccei-Quinn symmetry, Nucl. Phys. B192, 409 (1981).
  5. M. Kamionkowski and J. March-Russell, Planck scale physics and the Peccei-Quinn mechanism, Phys. Lett. B 282, 137 (1992).
  6. R. Holman, S. D. H. Hsu, T. W. Kephart, E. W. Kolb, R. Watkins, and L. M. Widrow, Solutions to the strong CP problem in a world with gravity, Phys. Lett. B 282, 132 (1992).
  7. R. Kallosh, A. D. Linde, D. A. Linde, and L. Susskind, Gravity and global symmetries, Phys. Rev. D 52, 912 (1995).
  8. S. M. Barr and D. Seckel, Planck scale corrections to axion models, Phys. Rev. D 46, 539 (1992).
  9. S. Ghigna, M. Lusignoli, and M. Roncadelli, Instability of the invisible axion, Phys. Lett. B 283, 278 (1992).
  10. R. Alonso and A. Urbano, Wormholes and masses for Goldstone bosons, J. High Energy Phys. 02 (2019) 136.
  11. J. Alvey and M. Escudero, The axion quality problem: Global symmetry breaking and wormholes, J. High Energy Phys. 01 (2021) 032; 11 (2023) 223(E).
  12. D. Harlow and H. Ooguri, Symmetries in quantum field theory and quantum gravity, Commun. Math. Phys. 383, 1669 (2021).
  13. P. Svrček and E. Witten, Axions in string theory, J. High Energy Phys. 06 (2006) 051.
  14. A. Arvanitaki, S. Dimopoulos, S. Dubovsky, N. Kaloper, and J. March-Russell, String axiverse, Phys. Rev. D 81, 123530 (2010).
  15. B. Gavela, P. Quílez, and M. Ramos, The QCD axion sum rule, J. High Energy Phys. 04 (2024) 056.
  16. J. E. Kim, A composite invisible axion, Phys. Rev. D 31, 1733 (1985).
  17. K. Choi and J. E. Kim, Dynamical axion, Phys. Rev. D 32, 1828 (1985).
  18. L. Randall, Composite axion models and Planck scale physics, Phys. Lett. B 284, 77 (1992).
  19. M. Redi and R. Sato, Composite accidental axions, J. High Energy Phys. 05 (2016) 104.
  20. B. Lillard and T. M. P. Tait, A high quality composite axion, J. High Energy Phys. 11 (2018) 199.
  21. M. B. Gavela, M. Ibe, P. Quílez, and T. T. Yanagida, Automatic Peccei–Quinn symmetry, Eur. Phys. J. C 79, 542 (2019).
  22. M. Ardu, L. Di Luzio, G. Landini, A. Strumia, D. Teresi, and J.-W. Wang, Axion quality from the (anti)symmetric of SU(N), J. High Energy Phys. 11 (2020) 090.
  23. R. Contino, A. Podo, and F. Revello, Chiral models of composite axions and accidental Peccei-Quinn symmetry, J. High Energy Phys. 04 (2022) 180.
  24. P. Cox, T. Gherghetta, and M. D. Nguyen, A holographic perspective on the axion quality problem, J. High Energy Phys. 01 (2020) 188.
  25. P. Cox, T. Gherghetta, and A. Paul, A common origin for the QCD axion and sterile neutrinos from SU(5) strong dynamics, J. High Energy Phys. 12 (2023) 180.
  26. M. B. Wise, H. Georgi, and S. L. Glashow, SU(5) and the invisible axion, Phys. Rev. Lett. 47, 402 (1981).
  27. L. Di Luzio, A. Ringwald, and C. Tamarit, Axion mass prediction from minimal grand unification, Phys. Rev. D 98, 095011 (2018).
  28. A. Ernst, A. Ringwald, and C. Tamarit, Axion predictions in SO(10)×U(1)PQ models, J. High Energy Phys. 02 (2018) 103.
  29. P. Fileviez Pérez, C. Murgui, and A. D. Plascencia, The QCD axion and unification, J. High Energy Phys. 11 (2019) 093.
  30. P. Fileviez Pérez, C. Murgui, and A. D. Plascencia, Axion dark matter, proton decay and unification, J. High Energy Phys. 01 (2020) 091.
  31. P. Agrawal, M. Nee, and M. Reig, Axion couplings in grand unified theories, J. High Energy Phys. 10 (2022) 141.
  32. L. Di Luzio, Accidental SO(10) axion from gauged flavour, J. High Energy Phys. 11 (2020) 074.
  33. L. Di Luzio, Pati-Salam axion, J. High Energy Phys. 07 (2020) 071.
  34. L. Vecchi, Axion quality straight from the GUT, Eur. Phys. J. C 81, 938 (2021).
  35. L. Di Luzio, G. Landini, F. Mescia, and V. Susič, High-quality Peccei-Quinn symmetry from the interplay of vertical and horizontal gauge symmetries, arXiv:2503.16648.
  36. J. Preskill, M. B. Wise, and F. Wilczek, Cosmology of the invisible axion, Phys. Lett. 120B, 127 (1983).
  37. L. F. Abbott and P. Sikivie, A cosmological bound on the invisible axion, Phys. Lett. 120B, 133 (1983).
  38. M. Dine and W. Fischler, The not so harmless axion, Phys. Lett. 120B, 137 (1983).
  39. J. Hisano, Proton decay in SUSY GUTs, Prog. Theor. Exp. Phys. 2022, 12B104 (2022).
  40. M. B. Smy (Hyper-Kamiokande Collaboration), Hyper-Kamiokande, Phys. Sci. Forum 8, 41 (2023).
  41. R. S. Bedi, T. Gherghetta, and M. Pospelov, Enhanced EDMs from small instantons, Phys. Rev. D 106, 015030 (2022).
  42. M. Dine and N. Seiberg, String theory and the strong CP problem, Nucl. Phys. B273, 109 (1986).
  43. C. Csáki, R. T. D’Agnolo, E. Kuflik, and M. Ruhdorfer, Instanton NDA and applications to axion models, J. High Energy Phys. 04 (2024) 074.
  44. M. Kawasaki, K. Saikawa, and T. Sekiguchi, Axion dark matter from topological defects, Phys. Rev. D 91, 065014 (2015).
  45. P. Langacker and S.-Y. Pi, Magnetic monopoles in grand unified theories, Phys. Rev. Lett. 45, 1 (1980).
  46. B. Grinstein, X. Lu, C. Miró, and P. Quílez, Accidental symmetries, Hilbert series, and friends, J. High Energy Phys. 03 (2025) 172.
  47. K. Springmann, M. Stadlbauer, S. Stelzl, and A. Weiler, A universal bound on QCD axions from supernovae, Phys. Rev. D 112, 075009 (2025).
  48. P. Carenza, T. Fischer, M. Giannotti, G. Guo, G. Martínez-Pinedo, and A. Mirizzi, Improved axion emissivity from a supernova via nucleon-nucleon bremsstrahlung, J. Cosmol. Astropart. Phys. 10 (2019) 016; 05 (2020) E01.
  49. D. F. G. Fiorillo, Á. Gil Muyor, H.-T. Janka, G. G. Raffelt, and E. Vitagliano, Axion-photon conversion in transient compact stars: Systematics, constraints, and opportunities, arXiv:2509.13322.
  50. E. Witten, An SU(2) anomaly, Phys. Lett. 117B, 324 (1982).
  51. J. E. Kim, Weak interaction singlet and strong CP invariance, Phys. Rev. Lett. 43, 103 (1979).
  52. M. A. Shifman, A. I. Vainshtein, and V. I. Zakharov, Can confinement ensure natural CP invariance of strong interactions?, Nucl. Phys. B166, 493 (1980).
  53. A. R. Zhitnitsky, On possible suppression of the axion hadron interactions. (In Russian), Yad. Fiz. 31, 497 (1980) [Sov. J. Nucl. Phys. 31, 260 (1980)].
  54. D. Kondo, H. Murayama, B. Noether, and D. R. Varier, Broken conformal window, J. High Energy Phys. 04 (2025) 152.
  55. C. Vafa and E. Witten, Restrictions on symmetry breaking in vector-like gauge theories, Nucl. Phys. B234, 173 (1984).
  56. W. A. Bardeen, J. Bijnens, and J. M. Gerard, Hadronic matrix elements and the π+π0 mass difference, Phys. Rev. Lett. 62, 1343 (1989).
  57. A. Manohar and H. Georgi, Chiral quarks and the nonrelativistic quark model, Nucl. Phys. B234, 189 (1984).
  58. A. G. Cohen, D. B. Kaplan, and A. E. Nelson, Counting 4π’s in strongly coupled supersymmetry, Phys. Lett. B 412, 301 (1997).
  59. B. M. Gavela, E. E. Jenkins, A. V. Manohar, and L. Merlo, Analysis of general power counting rules in effective field theory, Eur. Phys. J. C 76, 485 (2016).
  60. V. A. Rubakov, Grand unification and heavy axion, JETP Lett. 65, 621 (1997).
  61. T. Gherghetta, N. Nagata, and M. Shifman, A visible QCD axion from an enlarged color group, Phys. Rev. D 93, 115010 (2016).
  62. P. Agrawal and K. Howe, Factoring the strong CP problem, J. High Energy Phys. 12 (2018) 029.
  63. M. K. Gaillard, M. B. Gavela, R. Houtz, P. Quílez, and R. Del Rey, Color unified dynamical axion, Eur. Phys. J. C 78, 972 (2018).
  64. J. Fuentes-Martín, M. Reig, and A. Vicente, Strong CP problem with low-energy emergent QCD: The 4321 case, Phys. Rev. D 100, 115028 (2019).
  65. R. Matsumiya et al. (TUCAN Collaboration), The precision nEDM measurement with UltraCold neutrons at TRIUMF, J. Phys. Soc. Jpn. Conf. Proc. 37, 020701 (2022).
  66. S. N. Balashov, K. Green, M. G. D. van der Grinten, P. G. Harris, H. Kraus, J. M. Pendlebury, D. B. Shiers, M. A. H. Tucker, and D. L. Wark, A proposal for a cryogenic experiment to measure the neutron electric dipole moment (nEDM), arXiv:0709.2428.
  67. R. K. Ellis et al., Physics briefing book: Input for the European strategy for particle physics update 2020, arXiv:1910.11775.
  68. J. Alexander et al., The storage ring proton EDM experiment, arXiv:2205.00830.
  69. G. Grilli di Cortona, E. Hardy, J. Pardo Vega, and G. Villadoro, The QCD axion, precisely, J. High Energy Phys. 01 (2016) 034.
  70. L. Di Luzio, F. Mescia, and E. Nardi, Redefining the axion window, Phys. Rev. Lett. 118, 031801 (2017).
  71. L. Di Luzio, F. Mescia, and E. Nardi, Window for preferred axion models, Phys. Rev. D 96, 075003 (2017).
  72. V. Plakkot and S. Hoof, Anomaly ratio distributions of hadronic axion models with multiple heavy quarks, Phys. Rev. D 104, 075017 (2021).
  73. A. Cheek, J. K. Osiński, and L. Roszkowski, Extending preferred axion models via heavy-quark induced early matter domination, J. Cosmol. Astropart. Phys. 03 (2024) 061.
  74. L. Di Luzio, S. Hoof, C. Marinissen, and V. Plakkot, Catalogues of cosmologically self-consistent hadronic QCD axion models, J. Cosmol. Astropart. Phys. 04 (2025) 072.
  75. F. del Aguila and L. E. Ibáñez, Higgs bosons in SO(10) and partial unification, Nucl. Phys. B177, 60 (1981).
  76. S. Dimopoulos and H. M. Georgi, Extended survival hypothesis and fermion masses, Phys. Lett. 140B, 67 (1984).
  77. A. Djouadi, R. Fonseca, R. Ouyang, and M. Raidal, Non-supersymmetric SO(10) models with Gauge and Yukawa coupling unification, Eur. Phys. J. C 83, 529 (2023).
  78. W. Buchmüller, P. Di Bari, and M. Plümacher, Leptogenesis for pedestrians, Ann. Phys. (Amsterdam) 315, 305 (2005).
  79. K. S. Babu and R. N. Mohapatra, Predictive neutrino spectrum in minimal SO(10) grand unification, Phys. Rev. Lett. 70, 2845 (1993).
  80. B. Bajc, A. Melfo, G. Senjanovic, and F. Vissani, Yukawa sector in non-supersymmetric renormalizable SO(10), Phys. Rev. D 73, 055001 (2006).
  81. T. Ohlsson and M. Pernow, Fits to non-supersymmetric SO(10) models with type I and II seesaw mechanisms using renormalization group evolution, J. High Energy Phys. 06 (2019) 085.
  82. Q. Lu, M. Reece, and Z. Sun, The quality/cosmology tension for a post-inflation QCD axion, J. High Energy Phys. 07 (2024) 227.
  83. G. Lazarides and Q. Shafi, Axion models with no domain wall problem, Phys. Lett. 115B, 21 (1982).
  84. M. Gorghetto, E. Hardy, and G. Villadoro, More axions from strings, SciPost Phys. 10, 050 (2021).
  85. C. O’Hare, cajohare/axionlimits: Axionlimits, 10.5281/zenodo.3932430 (2020).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation