New Standard Model constraints on the scales and dimension of spacetime

Understand

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.