New Standard Model constraints on the scales and dimension of spacetime

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 × 102 TeV, and is tightened to E*> 9 × 108 TeV for the typical value α = 1/2 of the fractional exponents in the spacetime measure. We also find an upper bound dH< 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.