[Paper Review] Collider Signatures in the Planck Regime

Sabine Hossenfelder, Marcus Bleicher+4 more|arXiv (Cornell University)|May 30, 2003

International Science and Diplomacy25 citations

TL;DR

This paper proposes that in string-theory-motivated models with extra dimensions, the fundamental Planck scale is lowered to ~1 TeV, making Planck-scale physics accessible to future colliders. Due to a generalized uncertainty principle, physics at distances below 1/M_Planck is fundamentally unresolvable, implying that Planckian effects may represent the final discovery frontier at colliders. The study calculates modified $e^+e^- \to f^+f^-$ cross-sections as a signature of this scenario.

ABSTRACT

String theory suggests the existence of a minimum length scale. An exciting quantum mechanical implication of this feature is a modification of the uncertainty principle. In contrast to the conventional approach, this generalised uncertainty principle does not allow to resolve space time distances below the Planck length. In models with extra dimensions, which are also motivated by string theory, the Planck scale can be lowered to values accessible by future colliders, i.e. $M_f\\approx$ 1 TeV. It is demonstrated that in this novel scenario, short distance physics below $1/M_f$ is completely cloaked by the uncertainty principle. Therefore, Planckian effects could be the final physics discovery at future colliders. As an application, we calculate the modifications to the $e^+e^ -> f^+f^-$ cross-sections.

Motivation & Objective

• To investigate the implications of a lowered Planck scale (~1 TeV) in models with extra dimensions, motivated by string theory.
• To explore how the generalized uncertainty principle (GUP) limits the resolution of spacetime distances below the Planck length.
• To determine whether Planck-scale physics could be the final discovery at future colliders due to the GUP's fundamental cloak on short-distance physics.
• To calculate observable modifications in $e^+e^- \to f^+f^-$ cross-sections arising from this scenario.

Proposed method

• Adopt a generalized uncertainty principle (GUP) that prevents resolution of distances below the Planck length.
• Assume a low-scale Planck scale ($M_f \approx 1$ TeV) via extra dimensions, as motivated by string theory.
• Model the effective quantum gravity corrections to $e^+e^- \to f^+f^-$ processes using the GUP framework.
• Compute the modified cross-sections by incorporating the GUP-induced momentum-space modifications.
• Use the GUP to constrain the accessible energy scale, showing that physics below $1/M_f$ is fundamentally unobservable.
• Apply the framework to derive phenomenologically testable predictions for future collider experiments.

Experimental results

Research questions

• RQ1 How do generalized uncertainty principles modify $e^+e^- \to f^+f^-$ cross-sections in models with a low Planck scale?
• RQ2 To what extent does the GUP prevent the resolution of physics at distances below the Planck length?
• RQ3 Can Planck-scale physics be the final discovery at future colliders due to the GUP's fundamental limitations?
• RQ4 What are the observable signatures of a lowered Planck scale ($\sim$1 TeV) in collider experiments?
• RQ5 How do extra dimensions in string-theory-motivated models affect the interplay between quantum gravity and collider phenomenology?

Key findings

• The generalized uncertainty principle prevents the resolution of spacetime distances below the Planck length, effectively cloaking physics at scales $< 1/M_f$.
• In models with extra dimensions, the Planck scale can be lowered to ~1 TeV, making Planck-scale physics potentially accessible to future colliders.
• Due to the GUP, physics at distances below $1/M_f$ is fundamentally unobservable, suggesting that Planckian effects may be the final discovery frontier at colliders.
• The $e^+e^- \to f^+f^-$ cross-sections are modified due to the GUP, providing a potential experimental signature for this scenario.
• The modifications to the cross-sections arise from momentum-space deformations induced by the GUP, offering a testable prediction for future collider data.