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If scale invariance is a classical symmetry then both the Planck scale and the weak scale should emerge as quantum effects.
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For a review, see e.g. Y. Fuji and K. Maeda, The scalar-Tensor Gravity
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The earliest work, which we aware of, where the hierarchy problem is explicitly discussed in relation to the classical scale invariance is: W. A. Bardeen, FERMILAB-CONF-95-391-T
Cited in the paper.
J. R. Espinosa and M. Quiros, arXiv:hep-ph/0701145
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W. F. Chang, J. N. Ng and J. M. S. Wu, arXiv:hep-ph/0701254
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T. Hambye and M. H. G. Tytgat, arXiv:0707.0633 [hep-ph]
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K. A. Meissner and H. Nicolai, arXiv:0710.2840 [hep-th]
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R. Foot, A. Kobakhidze, K. L. McDonald and R. R. Volkas, Phys. Rev. D 76
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D. J. Kapner, T. S. Cook, E. G. Adelberger, J. H. Gundlach, B. R. Heckel, C. D. Hoyle and H. E. Swanson, Phys. Rev. Lett. 98
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