Transplanckian Collisions at the LHC and Beyond

TL;DR

The paper analyzes transplanckian gravitational scattering in brane-world scenarios with extra dimensions, formulating a model-independent elastic scattering description via the eikonal approximation. It derives the forward eikonal amplitude, characterizes cross sections, and interprets the scattering in distinct classical and quantum regimes, while discussing corrections and potential quantum-gravity or string effects. The authors then explore LHC phenomenology, predicting diffractive di-jet signatures and contrasting them with black-hole production, and extend the discussion to future colliders to outline reach and precision tests. Overall, the work provides a framework to test higher-dimensional gravity at colliders and outlines practical strategies and limitations for distinguishing gravitational signals from Standard Model processes.

Abstract

Elastic collisions in the transplanckian region, where the center-of-mass energy is much larger than the fundamental gravity mass scale, can be described by linearized general relativity and known quantum-mechanical effects as long as the momentum transfer of the process is sufficiently small. For larger momentum transfer, non-linear gravitational effects become important and, although a computation is lacking, black-hole formation is expected to dominate the dynamics. We discuss how elastic transplanckian collisions can be used at high-energy colliders to study, in a quantitative and model-independent way, theories in which gravity propagates in flat extra dimensions. At LHC energies, however, incalculable quantum-gravity contributions may significantly affect the experimental signal.

Figures (9)

• Figure 1: The dominant Feynman diagrams contributing to elastic scattering of $\Phi$ particles in the eikonal approximation at tree $(a)$ and one-loop $(b)$ level. Wavy lines represent the exchange of $D$-dimensional gravitons, and the dashed line represents the cut from the physical-region singularity.
• Figure 2: Plots of the function $F_n(y)$ versus $y$ for $n$ between 2 and 6. The dashed line is the real part, the dash-dotted line is the imaginary part, and the solid line is the absolute value of the function. The bottom right panel plots the relative error of $|F_6(y)|$ compared to the asymptotic expressions, see Eqs. (\ref{['singg']}) and (\ref{['statp']}), as $y\rightarrow 0$ (dashed line) and $y\rightarrow\infty$ (solid line).
• Figure 3: Ladder and cross-ladder Feynman diagrams contributing to elastic scattering of $\Phi$ particles. The dashed lines represent the exchange of brane excitations.
• Figure 4: The di-jet differential cross section $d\sigma_{jj}/d|\Delta\eta |$ from eikonal gravity for $n=6$, $M_{jj}>9\hbox{\rm,TeV}$, when both jets have $|\eta | <5$ and $p_T>100\hbox{\rm,GeV}$, and for $M_D=1.5\hbox{\rm,TeV}$ and $3\hbox{\rm,TeV}$. The dashed line is the expected rate from QCD.
• Figure 5: The di-jet differential cross section $d\sigma_{jj}/d|\Delta\eta |$ from eikonal gravity for $M_D=1.5\hbox{\rm,TeV}$ and $n=6$ (solid line), $n=4$ (dotted line), and $n=2$ (dashed line). We require $M_{jj}>9\hbox{\rm,TeV}$ and that both jets have $|\eta | <5$ and $p_T>100\hbox{\rm,GeV}$.