FLAG: Lattice QCD Tests of the Standard Model and Foretaste for Beyond

TL;DR

This paper reviews lattice QCD results related to meson physics, providing key form factors and decay constants that inform CKM matrix elements and tests of the Standard Model, with implications for physics beyond it.

Contribution

It compiles and discusses recent FLAG lattice results on meson decay constants and form factors, highlighting their impact on CKM matrix elements and beyond Standard Model physics.

Findings

Precise values for $f_K$, $f_$, and their ratio.

Updated CKM matrix element estimates from lattice data.

Insights into $B_K$ parameters and beyond Standard Model implications.

Abstract

After a short presentation of the FLAG collaboration, we review lattice results related to pion, $K$-, $D$- and $B$-meson physics with the aim of making them easily accessible to the particle-physics community. Only a selection of FLAG averages or estimates is presented. For light flavours, we present results on the form factor $f_+(0)$, arising in semileptonic $K \rightarrow \pi$ transition at zero momentum transfer, as well as the decay-constants $f_K,f_\pi$ and their ratio. The consequences of these results for the CKM matrix elements $|V_{us}|$ and $|V_{ud}|$ are discussed. For heavy flavours we focus on $D$- and $B$-meson decay constants and form factors, as well as the CKM matrix elements $|V_{cs}|$, $|V_{cd}|$ and $|V_{ub}|$. In addition we briefly cover the recent advances stemming from the calculation the $B_K$-parameters and touch upon related current results relevant to the Physics beyond the Standard Model, which will be the subject of the next FLAG edition.