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.
Highlights
In models with extra dimensions, the fundamental scale of gravity may be lower than the four-dimensional Planck scale, MPl
In addition to searches for microscopic black holes formed in particle collisions, experimental constraints on extra dimensions have generally come from searches for modifications of the inverse-square force law of gravity at small scales or from signatures of KaluzaKlein gravitons or other exotic particles
We have presented constraints on the fundamental scale and the size of extra dimensions in higher-dimensional theories, based on the nonobservation of vacuum decay catalyzed by microscopic black holes
Summary
In models with extra dimensions, the fundamental scale of gravity may be lower than the four-dimensional Planck scale, MPl. We are assuming that the results of [6,7,8] hold in a qualitatively similar way for theories with more than four spacetime dimensions, i.e., that black hole evaporation can seed vacuum decay This was explored in [9], where the authors construct an approximate instanton solution for a braneworld black hole in a theory with one extra dimension and estimate that their results extend to regimes where small black holes are produced in particle collisions. Assuming that the Higgs vacuum is metastable and that its decay is catalyzed by black hole evaporation, we take its persistence as evidence against black hole evaporation in our past light cone While this observation can constrain the production of low mass primordial black holes in the early Universe, we apply it here to the production of microscopic black holes in particle collisions. Appendix A considers the various criteria that must be satisfied for a reliable semiclassical analysis of black hole formation, and Appendix B discusses an analytical result for black hole formation rates that supports the numerical results used in the main text
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