A non-universal transition to asymptotic freedom in low-energy quantum gravity

TL;DR

This paper explores a specific low-energy quantum gravity model, revealing a non-universal transition to asymptotic freedom that follows a scaling rule, with transition ranges differing between protons and electrons.

Contribution

It demonstrates that the transition to asymptotic freedom in this model is non-universal and obeys a specific scaling law based on particle type and energy.

Findings

Transition range for protons: 10^{-11} to 10^{-13} meters.

Transition range for electrons: 10^{-13} to 10^{-15} meters.

Transition obeys a scaling rule involving distance and energy.

Abstract

The model of low-energy quantum gravity by the author has the property of asymptotic freedom at very short distances. The character of transition to asymptotic freedom is studied here. It is shown that this transition is not universal, but the one obeys the scaling rule: the range of this transition in units of $r/E^{1/2}$, where $r$ is a distance between particles and $E$ is an energy of the screening particle, is the same for any micro-particle. This range for a proton is between $10^{-11} - 10^{-13}$ meter, while for an electron it is approximately between $10^{-13} - 10^{-15}$ meter.