Challenges in high-precision determinations of CKM matrix elements using lattice QCD

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The current precision on determining CKM matrix elements is below a per cent in several cases, and tensions between results are present, for example, in the Vus/Vud plane. Investigating that problem is essential for searching for new physics through weak decays. At this level of precision, a crucial ingredient is the determination of radiative corrections to pseudoscalar meson weak decays. Those have been computed mainly through effective field theories, which can have uncontrolled uncertainties. It is, therefore, important for lattice QCD+QED simulations to provide accurate predictions from first principles.

In this talk, I will present various results, mainly from the UKQCD collaboration, illustrating several challenges faced when performing such calculations. The first calculation at physical quark masses of radiative corrections to kaon and pion was published in [1] after the pioneering work from [2]. A feature of [1] is an uncomfortably sizeable systematic error due to theoretical uncertainties on higher-order finite-size corrections. I will present our result and detail this issue based on the formalism established in [3]. I will conclude with future possible directions to address this problem.

[1]: https://doi.org/10.1007/JHEP02(2023)242

[2]: https://doi.org/10.1103/PhysRevD.100.034514

[3]: https://doi.org/10.1103/PhysRevD.105.074509 .

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