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Bardeen has argued that once the classically conformal invariance and its minimal violation by quantum anomalies are imposed on the SM, it can be free from the quadratic divergences and hence the gauge hierarchy problem.
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M. Cvetic and S. Godfrey, arXiv:hep-ph/9504216. T. G. Rizzo, arXiv:hep-ph/9612440; S. Godfrey, arXiv:hep-ph/0201092; arXiv:hep-ph/0201093
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S. Iso and Y. Orikasa, PTEP 2013
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