1) Project IB (Isospin-breaking effects)
The first step of this project was to include electromagnetic corrections in lattice calculations of the hadronic vacuum polarisation, a crucial contribution to the anomalous magnetic moment of the muon (g-2). The project delivered the first proof-of-concept calculation [1] of these effects, the first theoretical estimation of electromagnetic finite-size effects [2], and the first realistic calculation of the muon g-2 which includes these effects [3]. The project then focused on generalising the theoretical formalism for electromagnetic finite-size effects introduced in [4] to include effects from hadronic structures fully. The main aim was to compute higher-order finite-size effects for radiative corrections to leptonic decays, which was achieved in [5] and revealed a more challenging structure than previously known in the literature. In parallel, a 5-years effort led to the first lattice calculation of these corrections using physical-point lattice simulations [6]. Our result agrees with a previous determination by the RM123S Collaboration, which was extrapolated from simulations at non-physical masses.
2) Project RK (Rare kaon decays)
The first calculation of the rare kaon decay K+ to pi+l+l- was published in [7]. This work represents a substantial 5-year technical effort, and despite the investment of considerable computational resources in the calculation, it did not lead to a statistically resolved result. However, this result allowed us to understand precisely this new challenge and potentially how to resolve it, and this observation could only have been done with a realistic calculation of this grade. During the project, members of the phenomenology community and the LHCb experiment prompted us several times about a potential generalisation of our methodology to hyperons decays. Therefore, we started a theoretical project on rare Sigma decays, which was published in [8]. A numerical proof-of-concept calculation was done, which we expect will lead to a publication in the short term.
3) Project HC (Holographic cosmology)
This subproject was the highest risk component of the grant. We managed to solve critical problems, enabling the use of lattice simulation to constrain holographic cosmological models. One of the most significant issues in current work in holographic cosmology is the use of perturbation theory, which is affected by severe infrared divergence problems. We confirmed in [9] that, as conjectured in 1981 by Jackiw and Templeton, these divergences are an artefact of perturbation theory. We also solved how to renormalise the EMT in scalar theories [10], a vital issue of the lattice methodology. Research on that topic will continue, and couple to research in cosmology in the next couple of years.
4) Project G (Development of the Grid library)
Grid & Hadrons are now well-established, exascale-ready open-source lattice software. The contribution of this project was significant, as both frameworks were expanded and used to implement all work packages. The Grid software was used to procure the two phases of the £14M national supercomputer Tursa in the UK. Approximately two-thirds of the computing resources on Tursa were used to support this project. This had a considerable influence on the shaping of the service and drove innovation, for example, around optimising the energy efficiency of lattice simulations [11], leading to an estimated 100 MWh of energy saving using Tursa.
[1]:
https://doi.org/10.1007/JHEP09(2017)153(öffnet in neuem Fenster)[2]:
https://doi.org/10.1103/PhysRevD.100.014508(öffnet in neuem Fenster)[3]:
https://doi.org/10.1103/PhysRevLett.121.022003(öffnet in neuem Fenster)[4]:
https://doi.org/10.1103/PhysRevD.99.03451(öffnet in neuem Fenster)[5]:
https://doi.org/10.1103/PhysRevD.105.074509(öffnet in neuem Fenster)[6]:
https://doi.org/10.1007/JHEP02(2023)242(öffnet in neuem Fenster)[7]:
https://doi.org/10.1103/PhysRevD.107.L011503(öffnet in neuem Fenster)[8]:
https://doi.org/10.1007/JHEP04(2023)108(öffnet in neuem Fenster)[9]:
https://doi.org/10.1103/PhysRevLett.126.221601(öffnet in neuem Fenster)[10]:
https://doi.org/10.1103/PhysRevD.103.114501(öffnet in neuem Fenster)[11]:https://zenodo.org/records/7057319
