New Standard Model constraints on the scales and dimension of spacetime

TL;DR

This paper derives new constraints on multi-fractional spacetime theories using particle lifetime data, setting upper bounds on energy scales and spacetime dimensions, thus informing quantum gravity models.

Contribution

It provides the first comprehensive bounds on the scales and dimensions of multi-fractional theories with weighted and q-derivatives using experimental data.

Findings

Energy scale $E_*>3 imes 10^2$ TeV for weighted derivatives

Tightened bound $E_*>9 imes 10^8$ TeV for $eta=1/2$

Upper bound $d_H<2.9$ on Hausdorff dimension

Abstract

Using known estimates for the kaon--antikaon transitions, the mean lifetime of the muon and the mean lifetime of the tau, we place new and stronger constraints on the scales of the multi-fractional theories with weighted and $q$-derivatives. These scenarios reproduce a quantum-gravity regime where fields live on a continuous spacetime with a scale-dependent Hausdorff dimension. In the case with weighted derivatives, constraints from the muon lifetime are various orders of magnitude stronger than those from the tau lifetime and the kaon--antikaon transitions. The characteristic energy scale of the theory cannot be greater than $E_*>3\times 10^2\,{\rm TeV}$, and is tightened to $E_*>9\times 10^{8}\,{\rm TeV}$ for the typical value $\alpha=1/2$ of the fractional exponents in the spacetime measure. We also find an upper bound $d_{\rm H}<2.9$ on the spacetime Hausdorff dimension in the ultraviolet. In the case with $q$-derivatives, the strongest bound comes from the tau lifetime, but it is about 10 orders of magnitude weaker than for the theory with weighted derivatives.