New discoveries in particle physics can be made in different ways. One can let particles collide at higher and higher energies and look for direct evidence of new particles and interactions, or search instead for tiny but measurable discrepancies between experimental measurements and theoretical predictions, at the so-called *precision frontier*. This project is pushing the latter by studying with high precision the decays of mesons like pions and kaons, which are the lightest particles made of two quarks and gluons, into leptons. This is a process where the fundamental weak interaction allows the annihilation of the two constituent quarks and the consequent emission of an electron-neutrino or muon-neutrino pair (the muon being a heavier copy of the electron).

The decay of these particles is dominated by the effect of the strong interactions, also called QCD, inside the meson, but the newly aimed-for precision makes it necessary to take into account also other subleading effects. This is the case of those from QED interactions, which result in the exchange of photons between any of the charged elementary particles involved in the process – see e.g. Figure 1, where the decay of a charged pion into muon and neutrino is depicted.

One way to compute QCD-governed processes at the conditions of our current universe is to simulate them on a finitely sized four-dimensional grid or *lattice*, corresponding to a discretised and finite version of space and time. In our calculation we have been able to simulate particles with masses that match the values as found in nature. This is generally very challenging, and it has been possible thanks to recent algorithmic developments and the DiRAC high-performance computing resources. Photons, however, are massless particles and make the calculation more difficult: since they can travel large distances before interacting with other particles, simulating QED interactions in a finite box will result in sizeable *finite-volume effects*. The DiRAC Extreme Scaling facilities allow us to simulate QCD+QED on very large grids, but even with this cutting-edge technology the finite-volume effects are still large and have to be studied carefully. In our finite-volume simulation we are able to compute with very high precision the rate of the decay of the light mesons into muon-neutrino pairs including QED corrections, but when comparing with experimental results – which are performed in our vastly larger universe – the final precision of our results is dominated by these finite size effects. This is illustrated in Figure 2, where we show our result for the QED correction to the ratio of the kaon and the pion decay rates, called *δR _{Kπ}*. The point on the right is the one we obtain at the volume of our simulation through an extensive data analysis, while the point on the left shows how much larger our uncertainty gets when we try to extrapolate our result to the “infinite” volume limit. This is due to our limited knowledge of how this quantity varies when changing the size of the box. In red, green, and blue we show some scaling trajectories on which our determination of

*δR*could lie on, although with our current study we cannot discriminate between them. This means dedicated simulations on multiple and larger boxes are required to reduce the uncertainty on our infinite volume estimate.

_{Kπ}Once we will reduce such a large uncertainty with further simulations on DiRAC resources, the precision of our simulations will become comparable to that of experimental measurements, and we will be able to test the validity of our current theory of particles and interactions with unprecedented accuracy.