Control of multi-particle intermediate-state effects in lattice QCD calculations of long-distance weak amplitudes

Develop and validate lattice QCD methodologies that reliably control and quantify contributions from multi-particle intermediate states in long-distance components of rare weak decay amplitudes (such as K→πℓℓ, KL→μ+μ−, and Bs→μ+μ−γ). This includes establishing a consistent finite-volume formalism and systematic-error estimates so that precise Standard Model predictions for these processes can be obtained.

Background

The precision interpretation of rare and forbidden flavour-changing processes increasingly relies on first-principles lattice QCD inputs, including long-distance contributions to weak amplitudes.

Recent advances have enabled first steps toward computing these long-distance effects, but robust treatment of multi-hadron intermediate states remains a key bottleneck for achieving controlled uncertainties.

Resolving this issue is essential for making stringent Standard Model predictions that can be confronted with the high-precision measurements expected at future e+e− facilities.

References

There remain open questions, such as controlling the contributions from multi-particle intermediate states, but we expect these to be tackled in the coming years.

— ECFA Higgs, electroweak, and top Factory Study  (2506.15390 - Abidi et al., 18 Jun 2025) in Section "Expected precision from lattice QCD", 2nd-order weak processes (Flavour Physics)

It is not clear how one should interpret these results, given that lattice QCD should yield a fairly dense spectrum which depends upon the finite spatial volume of the lattice, one which can be related to scattering amplitudes and resonances having hadronic decays.

— Exotics with gluonic excitations  (2608.16784 - Dudek, 17 Aug 2026) in Section 2, Glueballs