### Abstract

We provide the perturbative and non-perturbative arguments showing that theories with large number of species of the quantum fields, imply an inevitable hierarchy between the masses of the species and the Planck scale, shedding a different light on the hierarchy problem. In particular, using the black hole physics, we prove that any consistent theory that includes N Z_{2}-conserved species of the quantum fields of mass Λ, must have a value of the Planck mass, which in large N limit is given byM^{2}_{P}^{>}_{~} NΛ^{2}. An useful byproduct of this proof is that any exactly conserved quantum charge, not associated with a long-range classical field, must be defined maximum modulo N, with N ς (M_{P}/m)^{2}, where m is the mass of the unit charge. For example, a continuous global U(1) 'baryon number' symmetry, must be explicitly broken by gravity, at least down to a Z_{N} subgroup, with N< (M_{P}/m_{b})^{2}, where mb is the baryon mass. The same constraint applies to any discrete gauge symmetry, as well as to other quantum-mechanically-detectable black hole charges that are associated with the massive quantum hair of the black hole.We show that the gravitationally-coupled N-species sector that solves the gauge hirearchy problem, should be probed by LHC.

Original language | English (US) |
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Pages (from-to) | 528-536 |

Number of pages | 9 |

Journal | Fortschritte der Physik |

Volume | 58 |

Issue number | 6 |

DOIs | |

State | Published - Jun 1 2010 |

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### Keywords

- Black holes
- Hierarchy problem

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Fortschritte der Physik*,

*58*(6), 528-536. https://doi.org/10.1002/prop.201000009