Black Holes from Cosmic Rays: Probes of Extra Dimensions and New Limits on TeV-Scale Gravity

TL;DR

This paper investigates the possibility that microscopic black holes could form in ultra-high-energy collisions if gravity becomes strong at the TeV scale in models with large extra dimensions. It analyzes a geometric BH production cross section, explores theoretical uncertainties (mass ejection, angular momentum, sub-relativistic effects, and potential exponential suppression), and links BH production to observable quasi-horizontal air showers from cosmogenic neutrinos. Using AGASA data, it derives 95% CL lower bounds on the fundamental Planck scale $M_D$ for $n \ge 4$, and provides optimistic yet realistic projections for the Auger Observatory, which could discover tens of BH events or set robust limits up to $M_D \sim 3-4$ TeV. The work also demonstrates how Earth-skimming neutrino events can distinguish BH-induced signals from Standard Model expectations, offering a practical strategy to identify extra dimensions prior to collider discoveries.

Abstract

If extra spacetime dimensions and low-scale gravity exist, black holes will be produced in observable collisions of elementary particles. For the next several years, ultra-high energy cosmic rays provide the most promising window on this phenomenon. In particular, cosmic neutrinos can produce black holes deep in the Earth's atmosphere, leading to quasi-horizontal giant air showers. We determine the sensitivity of cosmic ray detectors to black hole production and compare the results to other probes of extra dimensions. With n \ge 4 extra dimensions, current bounds on deeply penetrating showers from AGASA already provide the most stringent bound on low-scale gravity, requiring a fundamental Planck scale M_D > 1.3 - 1.8 TeV. The Auger Observatory will probe M_D as large as 4 TeV and may observe on the order of a hundred black holes in 5 years. We also consider the implications of angular momentum and possible exponentially suppressed parton cross sections; including these effects, large black hole rates are still possible. Finally, we demonstrate that even if only a few black hole events are observed, a standard model interpretation may be excluded by comparison with Earth-skimming neutrino rates.

Figures (12)

• Figure 1: Cross sections $\sigma(\nu N \to {\rm BH})$ for $n=1,\ldots, 7$ from below for $M_D = 1~\text{TeV}$, $x_{\text{min}}=1$ (solid) and 3 (dashed), and parton cross sections $\pi r_s^2$ (left) and $\pi r_s^2 e^{-I_E}$ (right). The SM cross section $\sigma(\nu N \to \ell X)$ (dotted) is also shown.
• Figure 2: Cosmogenic $\nu_{\mu} + \bar{\nu}_{\mu} + \nu_e$ fluxes from Protheroe and Johnson with energy cutoff of $3 \times 10^{21}~\text{eV}$ (solid) Protheroe:1996ft, Hill and Schramm (dashed) Hill:1985mk, and previous estimate by Stecker without source evolution (dotted) Stecker:1979ah. See text for discussion.
• Figure 3: Slant depths corresponding to various zenith angles $\theta$.
• Figure 4: Ground array acceptances for quasi-horizontal air showers at the Auger Observatory (solid) and AGASA (dashed). See text for discussion.
• Figure 5: 95% CL lower bound on $M_D$ from non-observation of quasi-horizontal air showers in 1710.5 live days at AGASA for $x_{\text{min}}=1$ (solid) and 3 (dashed), assuming the cosmogenic neutrino flux of Protheroe and Johnson (lower) and Hill and Schramm (upper).