• [1]

    G. Aad et al. (ATLAS), Phys. Lett. B 716, 1 (2012), arXiv:1207.7214[hep-ex]

  • [2]

    S. Chatrchyan et al. (CMS), Phys. Lett. B 716, 30 (2012), arXiv:1207.7235[hep-ex]

  • [3]

    W. A. Bardeen, FERMILAB-CONF-95-391-T

  • [4]

    M. Shaposhnikov and C. Wetterich, Phys. Lett. B 683, 196 (2010), arXiv:0912.0208[hep-th]

  • [5]

    C. Wetterich and M. Yamada, Phys. Lett. B 770, 268 (2017), arXiv:1612.03069[hep-th]

  • [6]

    A. Eichhorn, Y. Hamada, J. Lumma et al., Phys. Rev. D 97(8), 086004 (2018), arXiv:1712.00319[hep-th]

  • [7]

    J. M. Pawlowski, M. Reichert, C. Wetterich et al., Phys. Rev. D 99(8), 086010 (2019), arXiv:1811.11706[hep-th]

  • [8]

    C. Wetterich, arXiv: 1901.04741 [hep-th]

  • [9]

    S. Matsuzaki, H. Ohki, and K. Yamawaki, arXiv: 1608.03691 [hep-ph]

  • [10]

    K. Yamawaki, arXiv: 1803.07271 [hep-ph]

  • [11]

    R. Hempfling, Phys. Lett. B 379, 153 (1996), arXiv:hep-ph/9604278[hep-ph]

  • [12]

    K. A. Meissner and H. Nicolai, Phys. Lett. B 648, 312 (2007), arXiv:hep-th/0612165[hep-th]

  • [13]

    L. Alexander-Nunneley and A. Pilaftsis, JHEP 09, 021 (2010), arXiv:1006.5916[hep-ph]

  • [14]

    A. Farzinnia, H. J. He, and J. Ren, Phys. Lett. B 727, 141 (2013), arXiv:1308.0295[hep-ph]

  • [15]

    E. Gabrielli, M. Heikinheimo, K. Kannike et al., Phys. Rev. D 89(1), 015017 (2014), arXiv:1309.6632[hep-ph]

  • [16]

    S. R. Coleman and E. J. Weinberg, Phys. Rev. D 7, 1888 (1973)

  • [17]

    E. Gildener and S. Weinberg, Phys. Rev. D 13, 3333 (1976)

  • [18]

    F. Sannino and J. Virkajärvi, Phys. Rev. D 92(4), 045015 (2015), arXiv:1505.05872[hep-ph]

  • [19]

    S. Iso and Y. Orikasa, PTEP 2013, 023B08 (2013), arXiv:1210.2848[hep-ph]

  • [20]

    M. Hashimoto, S. Iso, and Y. Orikasa, Phys. Rev. D 89(5), 056010 (2014), arXiv:1401.5944[hep-ph]

  • [21]

    Y. Hamada, K. Tsumura, and M. Yamada, Eur. Phys. J. C 80(5), 368 (2020), arXiv:2002.03666[hep-ph]

  • [22]

    H. Ishida, S. Matsuzaki, and R. Ouyang, Chin. Phys. C 44(11), 111002 (2020), arXiv:1907.09176[hep-ph]

  • [23]

    H. Ishida and S. Matsuzaki, Phys. Lett. B 804, 135390 (2020), arXiv:1912.09740[hep-ph]

  • [24]

    H. X. Zhang, S. Matsuzaki, and H. Ishida, Phys. Lett. B 846, 138256 (2023), arXiv:2306.15471[hep-ph]

  • [25]

    T. Appelquist et al. (LSD), Phys. Rev. D 90(11), 114502 (2014), arXiv:1405.4752[hep-lat]

  • [26]

    Y. Aoki et al. (LatKMI), Phys. Rev. D 89, 111502 (2014), arXiv:1403.5000[hep-lat]

  • [27]

    A. Hasenfratz, D. Schaich, and A. Veernala, JHEP 06, 143 (2015), arXiv:1410.5886[hep-lat]

  • [28]

    Y. Aoki et al. (LatKMI), Phys. Rev. D 96(1), 014508 (2017), arXiv:1610.07011[hep-lat]

  • [29]

    T. Appelquist, R. C. Brower, G. T. Fleming et al., Phys. Rev. D 93(11), 114514 (2016), arXiv:1601.04027[hep-lat]

  • [30]

    T. Appelquist et al. (Lattice Strong Dynamics), Phys. Rev. D 99(1), 014509 (2019), arXiv:1807.08411[hep-lat]

  • [31]

    K. Miura, H. Ohki, S. Otani et al., JHEP 10, 194 (2019), arXiv:1811.05670[hep-ph]

  • [32]

    K. Yamawaki, M. Bando, and K. i. Matumoto, Phys. Rev. Lett. 56, 1335 (1986)

  • [33]

    M. Bando, K. i. Matumoto, and K. Yamawaki, Phys. Lett. B 178, 308 (1986)

  • [34]

    A. Salvio, JCAP 04, 051 (2023), arXiv:2302.10212[hep-ph]

  • [35]

    A. Salvio, JCAP 12, 046 (2023), arXiv:2307.04694[hep-ph]

  • [36]

    G. Agazie et al. (NANOGrav), Astrophys. J. Lett. 951(1), L8 (2023), arXiv:2306.16213[astro-ph.HE]

  • [37]

    H. Xu, S. Chen, Y. Guo et al., Res. Astron. Astrophys. 23(7), 075024 (2023), arXiv:2306.16216[astro-ph.HE]

  • [38]

    J. Antoniadis et al. (EPTA and InPTA:), Astron. Astrophys. 678, A50 (2023), arXiv:2306.16214[astro-ph.HE]

  • [39]

    D. J. Reardon, A. Zic, R. M. Shannon et al., Astrophys. J. Lett. 951(1), L6 (2023), arXiv:2306.16215[astro-ph.HE]

  • [40]

    P. Amaro-Seoane et al. (LISA)], arXiv: 1702.00786 [astro-ph.IM]

  • [41]

    C. Caprini, M. Chala, G. C. Dorsch et al., JCAP 03, 024 (2020), arXiv:1910.13125[astro-ph.CO]

  • [42]

    V. Corbin and N. J. Cornish, Class. Quant. Grav. 23, 2435 (2006), arXiv:gr-qc/0512039[gr-qc]

  • [43]

    G. M. Harry, P. Fritschel, D. A. Shaddock et al., Class. Quant. Grav. 23 , 4887 (2006) [Erratum: Class. Quant. Grav. 23 , 7361 (2006)]

  • [44]

    S. Kawamura, T. Nakamura, M. Ando et al., Class. Quant. Grav. 23, S125 (2006)

  • [45]

    K. Yagi and N. Seto, Phys. Rev. D 83 , 044011 (2011) [Erratum: Phys. Rev. D 95 (10), 109901 (2017)], arXiv: 1101.3940[astro-ph.CO]

  • [46]

    R. L. Workman et al. (Particle Data Group), PTEP 2022, 083C01 (2022)

  • [47]

    D. Curtin, P. Meade, and H. Ramani, Eur. Phys. J. C 78(9), 787 (2018), arXiv:1612.00466[hep-ph]

  • [48]

    E. Senaha, Symmetry 12(5), 733 (2020)

  • [49]

    E. Witten, Nucl. Phys. B 177, 477 (1981)

  • [50]

    S. Iso, P. D. Serpico, and K. Shimada, Phys. Rev. Lett. 119(14), 141301 (2017), arXiv:1704.04955[hep-ph]

  • [51]

    T. Hambye, A. Strumia, and D. Teresi, JHEP 08, 188 (2018), arXiv:1805.01473[hep-ph]

  • [52]

    L. Sagunski, P. Schicho, and D. Schmitt, Phys. Rev. D 107(12), 123512 (2023), arXiv:2303.02450[hep-ph]

  • [53]

    K. Kawana, Phys. Rev. D 105(10), 103515 (2022), arXiv:2201.00560[hep-ph]

  • [54]

    P. Athron, L. Morris, and Z. Xu, arXiv: 2309.05474 [hep-ph]

  • [55]

    P. Athron, C. Balázs, A. Fowlie et al., arXiv: 2305.02357 [hep-ph]

  • [56]

    J. Ellis, M. Lewicki, and J. M. No, JCAP 04, 003 (2019), arXiv:1809.08242[hep-ph]

  • [57]

    J. Ellis, M. Lewicki, J. M. No et al., JCAP 06, 024 (2019), arXiv:1903.09642[hep-ph]

  • [58]

    M. Kierkla, A. Karam, and B. Swiezewska, JHEP 03, 007 (2023), arXiv:2210.07075[astro-ph.CO]

  • [59]

    D. Bodeker and G. D. Moore, JCAP 05, 009 (2009), arXiv:0903.4099[hep-ph]

  • [60]

    C. Caprini, M. Hindmarsh, S. Huber et al., JCAP 04, 001 (2016), arXiv:1512.06239[astro-ph.CO]

  • [61]

    H. An, X. Tong, and S. Zhou, Phys. Rev. D 107(2), 023522 (2023), arXiv:2208.14857[hep-ph]

  • [62]

    S. J. Huber and T. Konstandin, JCAP 09, 022 (2008), arXiv:0806.1828[hep-ph]

  • [63]

    C. J. Moore, R. H. Cole, and C. P. L. Berry, Class. Quant. Grav. 32(1), 015014 (2015), arXiv:1408.0740[gr-qc]

  • [64]

    K. Schmitz, JHEP 01, 097 (2021), arXiv:2002.04615[hep-ph]

  • [65]

    S. Iso, K. Kohri, and K. Shimada, Phys. Rev. D 91(4), 044006 (2015), arXiv:1408.2339[hep-ph]

  • [66]

    G. Cacciapaglia, D. Y. Cheong, A. Deandrea et al., JCAP 10, 063 (2023), arXiv:2307.01852[hep-ph]

  • [67]

    M. Blennow, E. Fernandez-Martinez, and B. Zaldivar, JCAP 01, 003 (2014), arXiv:1309.7348[hep-ph]

  • [68]

    L. J. Hall, K. Jedamzik, J. March-Russell et al., JHEP 03, 080 (2010), arXiv:0911.1120[hep-ph]