Quarks are the fundamental particles that make up most of ordinary matter, such as protons and neutrons in atomic nuclei. They are bound together by the strong nuclear force, mediated by the exchange of gluons, as described by the theory of strong interactions, Quantum Chromodynamics (QCD). They come in different *flavours* and are found to change into one another. The study of such flavour-changing transitions could well be the arena in which the first hints of physics beyond the Standard Model are discovered. Increased experimental precision and novel theory calculations are required to better understand them. In this context we note our last year’s Dirac Science Highlight on hadronic K→ππ decays which has in the meantime appeared in Physical Review Letter, where it was highlighted as Editor’s Suggestion.

Within the RBC/UKQCD collaboration with researchers from the UK and USA, we are studying flavour-changing processes that are found extremely rarely in nature and dominated by so-called *long-distance effects*. Over the past years our collaboration has developed novel theoretical and numerical tools and is now in a strong and unique position to compute the underlying physics.The particular class of processes we are focussing on at the moment are the rare kaon decays K → πl+l− and K → πνν ̄. These Flavour Changing Neutral Current (FCNC) decays are in parallel being studied experimentally at NA62 (CERN) and KOTO (J-PARC). Our calculations rely crucially on the cancellation of power divergences through the GIM mechanism for which inclusion of charm valence quarks on fine lattices is crucial. Because of its longstanding experience in kaon physics and the use of chiral fermions, RBC/UKQCD has a significant advantage to carry out these calculations in a timely fashion that coincides with the NA62 timeline. By repeating our exploratory studies on the most advanced data set generated with the help of DiRAC resources we will make predictions for this decay, which complement NA62’s experimental program.

The problem to be solved is to evaluate quantum field theory correlation functions defined by path integrals, from which particle masses, decay rates and other physical quantities can subsequently be determined. By discretising a finite volume of space time, the path integral becomes an extremely high- but finite-dimensional ordinary integral. A transformation to Euclidean space allows us to treat the action term in the integral as a probability weight and the integral can then be evaluated by importance sampling. Lattice QCD simulations naturally fall into two steps: The first step is to use a Markov chain Monte Carlo to generate an ensemble of field configurations. In the second step correlation functions are evaluated using the previously generated ensemble as input.

Working with a fine enough lattice spacing on a large enough volume and with light quarks at or near their physical mass poses a computational challenge which needs a large-scale HPC facility at the petaflops scale if simulations are to be completed on a competitive time scale. The DiRAC Extreme Scaling Service is ideally suited for this task.

Due to the strong suppression in the Standard Model these processes are highly sensitive to new physics and could very well allow to find first signs of it.

DiRAC resources are now enabling a detailed study which will allow direct comparison to experiment. RBC/UKQCD’s calculation to date is the only one of its kind and therefore highly anticipated.

**Bibliography:**

- “Lattice QCD study of the rare kaon decay K+→π+ννˉ at a near-physical pion mass”, Christ et al., Phys.Rev.D 100 (2019) 11, 114506, arXiv:1910.10644
- “K+→π+ννˉ decay amplitude from lattice QCD”, Bai et al., Phys.Rev.D 98 (2018) 7, 074509, arXiv:1806.11520
- “Exploratory Lattice QCD Study of the Rare Kaon Decay K+→π+ννˉ”, Bai et al., Phys.Rev.Lett. 118 (2017) 25, 252001, arXiv:1701.02858
- “First exploratory calculation of the long-distance contributions to the rare kaon decays K→πℓ+ℓ−“, Christ et al. , Phys. Rev. D94 (2016) 11, 114516 arXiv:1608.07585
- “Prospects for a lattice computation of rare kaon decay amplitudes II K→πννˉK→πννˉ decays:, Christ et al., Phys.Rev.D 93 (2016) 11, 114517, arXiv:1605.04442
- “Prospects for a lattice computation of rare kaon decay amplitudes: K→πℓ+ℓ−decays”, Christ et al., Phys.Rev.D 92 (2015) 9, 094512, arXiv:1507.03094
- “Standard Model Prediction for Direct CP Violation in K→ππ Decay, Bai et al. Phys. Rev. Lett. 115, 212001