Black Hole Bound on the Number of Species and Quantum Gravity at 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_{Planck}/\sqrt{N}. This bound suggests a novel solution to the hierarchy problem in which there are N \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 \Lambda_G \approx M_{Planck}/\sqrt{N} and a new description is needed around this scale. In particular black-holes smaller than \Lambda_G^{-1} are already no longer semi-classical. The nature of the completion is model dependent. One natural possibility is that \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.

• The paper establishes that black hole evaporation constraints impose an upper mass bound Λ ≤ M_P/√N, ensuring consistency in theories with many particle species.
• The paper shows that in large-N scenarios the effective quantum gravity scale is reduced to Λ_G, potentially making quantum gravitational effects observable at the LHC.
• The authors argue that these findings offer a fresh perspective on the hierarchy problem and extra-dimensional models, suggesting new experimental avenues.

Black Hole Bound on the Number of Species and Quantum Gravity at the LHC

The paper authored by Gia Dvali and Michele Redi explores the implications of having a large number of particle species in relation to black hole physics and quantum gravity phenomena, especially at the Large Hadron Collider (LHC). It proposes that for theories with $N$ species, black hole physics imposes an upper bound on the mass of these species: $\Lambda \leq \frac{M_{Planck}}{\sqrt{N}}$. This relationship offers a novel perspective on the hierarchy problem by suggesting that $N \approx 10^{32}$ gravitationally coupled species provide a stable hierarchy through a natural cutoff scale $\Lambda_G \approx \frac{M_{Planck}}{\sqrt{N}}$.

Key Findings and Arguments

1. Black Hole Bound: The paper posits that with a large number of species $N$, the Planck mass $M_P$ must necessarily be related to the masses of these species to prevent inconsistencies in black hole evaporation processes. Specifically, for the Planck mass squared, the estimate becomes $M_P^2 \geq N \Lambda^2$.
2. Quantum Gravity Scale: The authors argue that the effective gravitational cutoff is inherently reduced to $\Lambda_G$ for scenarios with large $N$. They provide various arguments, including perturbative and non-perturbative ones, outlining that new gravitational dynamics appear below the scale $\Lambda_G$, beyond which the semi-classical treatment of black holes is invalid.
3. Implications for the LHC: If $\Lambda_G$ corresponds to the weak scale, quantum gravity effects might be observed at the LHC through the production of micro black holes. The paper challenges the conventional intuition, indicating that these black holes largely retain memory of the species of origin, predominantly decaying into Standard Model particles, thus exhibiting a species hierarchy in their interactions.
4. Entropy and Temperature Constraints: By considering entropy bounds, the existence of a maximal temperature was derived, effectively limiting the thermal distribution for species below the full quantum gravity scale.

Implications for Future Research

The findings presented indicate potential avenues in exploring the impacts of a large number of species on gravitational physics. It presents a compelling alternative interpretation of existing extra-dimensional theories, such as the ADD model, as a case of large $N$ species frameworks. The implications are broad, not only providing insights into the hierarchy problem but also suggesting unforeseen experimental signatures for ongoing particle physics experiments like those at the LHC.

Speculations on AI and Beyond

While this paper focuses narrowly on particle physics and gravity, its methodology and implications could interface with future artificial intelligence research in discovering patterns or new physics frameworks. The cross-disciplinary application lies in computational approaches to model complex systems with numerous interactive components, akin to the numerous species considered in this theory.

Ultimately, the authors suggest that these large $N$ theories may necessitate rethinking fundamental assumptions about particle interactions in high-energy physics, potentially shaping the future trajectory of both theoretical and experimental physics. The adaptability of the concept across domains illustrates the transformative potential in understanding intricate systems, whether in quantum mechanics, cosmology, or artificial intelligence.