Phenomenology of scale-dependent space-time dimension

TL;DR

This paper investigates how experimental data from B-oscillations and muon g-2 measurements constrain the idea that space-time dimension varies with scale, finding that current data cannot exclude a range of dimensions between 2 and 5 at certain energies.

Contribution

It introduces a phenomenological framework for a scale-dependent space-time dimension and analyzes experimental constraints on this concept using existing particle physics data.

Findings

Sensitivity to dimension variations is lost around 350 GeV.

Any dimension between 2 and 5 at this scale is compatible with current data.

Current experiments do not exclude scale-dependent space-time dimensions.

Abstract

Loop-mediated processes characterized by dynamical scale M indirectly measure space-time dimension d at this scale. Assuming the latter to be scale-dependent d=d(L) and taking as examples B-oscillations and muon (g-2) experimental results we address the question about constraints put by this data on 4-d(L). It is shown that sensitivity is lost for 1/L around 350 GeV, and any value of d(L) between 2 and 5 at this scale is compatible with the data.