Bounds on extra dimensions from micro black holes in the context of the metastable Higgs vacuum

Katherine J. Mack, Robert McNees

Published 2018-09-13Version 1

We estimate the rate at which collisions between ultra-high energy cosmic rays can form small black holes in models with extra dimensions. If recent conjectures about false vacuum decay catalyzed by black hole evaporation apply, the lack of vacuum decay events in our past light cone places tight bounds on the black hole formation rate and thus on the fundamental scale of gravity in these models. Conservatively, we find that the lower bound on the fundamental scale $E_{*}$ must be within about an order of magnitude of the energy where the cosmic ray spectrum begins to show suppression from the GZK effect, in order to avoid the abundant formation of semiclassical black holes with short lifetimes. Our bound, which assumes a Higgs vacuum instability scale at the low end of the range compatible with experimental data, ranges from $E_{*} \geq 10^{18.8}\,\text{eV}$ for $n=1$ extra dimension down to $E_{*} \geq 10^{18.1}\,\text{eV}$ for $n=6$. These bounds are many orders of magnitude higher than the previous most stringent bounds, which derive from collider experiments or from estimates of Kaluza-Klein processes in neutron stars and supernovae.