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

TL;DR

This paper derives bounds on the fundamental scale of gravity in models with extra dimensions by analyzing the non-observation of vacuum decay catalyzed by micro black holes formed from ultra-high energy cosmic ray collisions.

Contribution

It provides new astrophysical bounds on the fundamental gravity scale in extra-dimensional theories based on cosmic ray data and vacuum stability considerations.

Findings

Lower bounds on E_* are close to the GZK suppression energy.

Excluded E_* range is approximately 10^{17} to 10^{18.8} eV for n=1.

Bounds rule out parameter space inaccessible to colliders and astrophysical tests.

Abstract

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 may place new bounds on the black hole formation rate and thus on the fundamental scale of gravity in these models. For theories with fundamental scale $E_{*}$ above the Higgs instability scale of the Standard Model, we find a lower bound on $E_{*}$ that is within about an order of magnitude of the energy where the cosmic ray spectrum begins to show suppression from the GZK effect. Otherwise, the abundant formation of semiclassical black holes with short lifetimes would likely initiate vacuum decay. Assuming a Higgs instability scale at the low end of the range compatible with experimental data, the excluded range is approximately $10^{17} \,\text{eV} \lesssim E_{*} \leq 10^{18.8}\,\text{eV}$ for theories with $n=1$ extra dimension, narrowing to $10^{17}\,\text{eV} \lesssim E_{*} \leq 10^{18.1}\,\text{eV}$ for $n=6$. These bounds rule out regions of parameter space that are inaccessible to collider experiments, small-scale gravity tests, or estimates of Kaluza-Klein processes in neutron stars and supernovae.