Black Hole Bound on the Number of Species and Quantum Gravity at LHC

Abstract

In theories with a large number N of particle species, black hole physics imposes an upper bound on the mass of the species equal to M_{Planck}/\sqrt{N}. This bound suggests a novel solution to the hierarchy problem in which there are N \approx 10^{32} gravitationally coupled species, for example 10^{32} copies of the Standard Model. The black hole bound forces them to be at the weak scale, hence providing a stable hierarchy. We present various arguments, that in such theories the effective gravitational cutoff is reduced to Λ_G \approx M_{Planck}/\sqrt{N} and a new description is needed around this scale. In particular black-holes smaller than Λ_G^{-1} are already no longer semi-classical. The nature of the completion is model dependent. One natural possibility is that Λ_G is the quantum gravity scale. We provide evidence that within this type of scenarios, contrary to the standard intuition, micro black holes have a (slowly-fading) memory of the species of origin. Consequently the black holes produced at LHC, will predominantly decay into the Standard Model particles, and negligibly into the other species.

15 pages, 2 figures