At the heart of this puzzle lies light-by-light scattering, a quantum process where particles of light, or photons, briefly transform into other particles. Ordinarily, light waves pass through each other without any trouble. But when quantum mechanics is involved, something strange happens: photons can interact through the creation of virtual particles that pop in and out of existence. These fleeting particles, though invisible, leave a measurable imprint on other particles.

One of those affected is the muon, a heavier cousin of the electron. How the muon “wobbles” in a magnetic field—its so-called anomalous magnetic moment—depends in part on these tiny interactions. The muon's magnetic behavior, often described using the formula aμ = (g–2)μ / 2, has been the subject of years of high-precision experiments and theory. Even the tiniest deviation between the theoretical prediction and experimental result can hint at unknown physics.

That’s why the upcoming results from the Fermilab experiment are so important. Scientists there are about to cut the experimental uncertainty in half, narrowing it from 22×10⁻¹¹ to roughly 11×10⁻¹¹. But with increased precision comes pressure. Theory must now meet that same level of detail, and one of the biggest obstacles is the hadronic light-by-light (HLbL) scattering contribution. It’s a notoriously tricky piece to calculate, involving strong nuclear forces and a tangle of particle interactions.