A new study addresses the Standard Model prediction for the rare K_L→μ⁺μ⁻ decay, a process critically dependent on the long-distance contribution from the exchange of two photons. This calculation, fundamental for the precision of theoretical predictions, is typically performed using lattice quantum chromodynamics (lattice QCD) with an effective three-flavor theory (u, d, and s quarks), assuming that terms decaying as the inverse square of the charm quark mass (1/m_c²) are negligible.

The challenge with this three-flavor approximation lies in the absence of the Glashow-Iliopoulos-Maiani (GIM) cancellation, which introduces additional low-energy constants that explicitly depend on the charm quark mass. The novelty of this work consists in demonstrating how these constants can be practically determined. To achieve this, the researchers propose a strategy involving a four-flavor lattice QCD simulation.

This simulation is performed on a small volume and with u and d quark masses that are heavier than their physical values. The method allows for the renormalization of the two-photon contribution, improving the precision of the Standard Model prediction for this kaon decay. The ability to determine these low-energy constants from four-flavor lattice QCD calculations is a significant advancement for reducing theoretical uncertainties in particle physics.