Abstract
Similar puzzles are also encountered within the Standard Model of particle physics, for example the Higgs Hierarchy problem of why the Higgs mass is so small relative to the Planck scale. These hierarchies are puzzling as they do not seem to be protected without the help of new physics, such as supersymmetry.
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Notes
- 1.
Without loss of generality we assume for now that \(\mathrm {h}\) and \({\uppi }\) are diagonalized.
- 2.
We are omitting here the part containing the helicity-1 interactions, which can uniquely be restored due to diff invariance of the helicity-2+helicity-1 system, and the \(\mathrm {U}(1)\) invariance of the helicity-1+helicity-0 system.
- 3.
In this analysis, the graviton mass \(\mathrm{m}\) is completely absorbed into \(\Lambda _3\), and nothing special happens at the scale \(\mathrm{m}\) as far as the strong coupling is concerned.
- 4.
Of course, as noted above, one should be cautious about the meaning of “graviton mass”, if \(\mathrm {c}_1\ne \mathrm {c}_2\) in (5.12), which one should anticipate to hold in the quantum theory. However, such a detuning of the Fierz-Pauli structure, as is well-known, does not spoil consistency of the effective theory if \(\mathrm {c}_{1,2}\ll 1\), which is true for the theory at hand.
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Heisenberg, L. (2015). Quantum Corrections: Natural Versus Non-natural. In: Theoretical and Observational Consistency of Massive Gravity. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-18935-2_5
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