Black hole bound on the number of species and quantum gravity at CERN 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 ${M}_{\mathrm{Planck}}/\sqrt{N}$. This bound suggests a novel solution to the hierarchy problem in which there are $N\ensuremath{\approx}{10}^{32}$ 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 ${\ensuremath{\Lambda}}_{G}\ensuremath{\approx}{M}_{\mathrm{Planck}}/\sqrt{N}$ and a new description is needed around this scale. In particular, black holes smaller than ${\ensuremath{\Lambda}}_{G}^{\ensuremath{-}1}$ are already no longer semiclassical. The nature of the completion is model dependent. One natural possibility is that ${\ensuremath{\Lambda}}_{G}$ 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.