Muon $g!-!2$ experiment at Fermilab

From the abstract of The Status and Prospects of the Muon g−2 Experiment at Fermilab:

There stands a greater than 3 standard deviations discrepancy between the Brookhaven measurement of $a_μ$ and the theoretical value predicted using the Standard Model. The Fermilab experiment seeks to either resolve or confirm this discrepancy, which is suggestive of new physics interactions.

If the discrepancy remains or grows bigger, it will indicate that the standard model is not enough to explain the data. Then the field is open for extensions, or deterministic models to supply a mathematical model for the discrepancy.

Already the preon model was proposed when the present discrepancy was found, in 2001:

We make a fresh evaluation of contributions to (g-2) of the muon in the framework of a preonic model with coloured vectorlike leptons and heavy coloured Z bosons and discuss their implications in the light of the recent Brookhaven measurement. It is shown that the observed deviation can be explained within this framework with masses and couplings consistent with all constraints: