Control multi-particle intermediate-state contributions in lattice QCD calculations of second-order weak processes

Determine how to control and incorporate contributions from multi-hadron intermediate states in lattice QCD computations of long-distance second-order weak processes, including K→πℓ+ℓ−, KL→μ+μ−, and Bs→μ+μ−γ, so that precise Standard Model predictions can be provided for global flavour fits and rare-decay phenomenology.

Background

Lattice QCD enables first-principles calculations of hadronic matrix elements that enter precision flavour observables, but extending these methods to processes governed by second-order weak interactions still faces technical challenges.

In rare kaon and B-meson decays, long-distance contributions from multi-hadron intermediate states can be sizeable and must be accurately controlled to match the experimental precision anticipated at future Higgs/electroweak/top factories.

Addressing this problem will improve the reliability of theoretical inputs to global analyses of flavour observables, thereby sharpening indirect searches for physics beyond the Standard Model.

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 4.2, Expected precision from lattice QCD

However, there are still open questions on the modeling of long-distance contributions from local hadronic form factors and non-local resonance loops ($s\bar{s}$, $c\bar{c}$, $D\bar{D}$, etc.).

— Recent results in $b \rightarrow s\,\ell\ell$ transitions at LHCb  (2610.13165 - Castella, 9 Oct 2026) in Section 1, Introduction