# $F_K/F_\pi$ from Möbius domain-wall fermions solved on gradient-flowed HISQ ensembles

We report the results of a lattice quantum chromodynamics calculation of $F_K/F_\pi$ using Möbius domain-wall fermions computed on gradient-flowed $N_f=2+1+1$ highly-improved staggered quark ensembles. The calculation is performed with five values of the pion mass ranging from $130 \lesssim m_\pi \lesssim 400$ MeV, four lattice spacings of $a\sim 0.15, 0.12, 0.09$ and $0.06$ fm and multiple values of the lattice volume. The interpolation/extrapolation to the physical pion and kaon mass point, the continuum, and infinite volume limits are performed with a variety of different extrapolation functions utilizing both the relevant mixed-action effective field theory expressions as well as discretization-enhanced continuum chiral perturbation theory formulas. We find that the $a\sim0.06$ fm ensemble is helpful, but not necessary to achieve a subpercent determination of $F_K/F_\pi$. We also include an estimate of the strong isospin breaking corrections and arrive at a final result of $F_{\hat{K}^+}/F_{\hat{\pi}^+} = 1.1942(45)$ with all sources of statistical and systematic uncertainty included. This is consistent with the Flavour Lattice Averaging Group average value, providing an important benchmark for our lattice action. Combining our result with experimental measurements of the pion and kaon leptonic decays leads to a determination of $|V_{us}|/|V_{ud}| = 0.2311(10)$.

## $V_{us}$ from the lattice [talk]

Los Alamos National Lab [invited talk] [PDF of slides]

## The nucleon mass and sigma term from lattice QCD [talk]

Chiral Dynamics 2021 bulletin [PDF of slides]

## lsqfit-gui

Graphical user interface for lsqfit using dash.

## Determining properties of hyperons [talk]

Lattice 2021 bulletin [PDF of slides]

## $V_{us}$ from semileptonic hyperon decays [poster]

Director’s review of the Nuclear Science Division [PDF of poster]

## Scale setting with $m_\Omega$

Python code for our scale setting analysis.

## Scale setting the Möbius Domain Wall Fermion on gradient-flowed HISQ action using the Omega baryon mass and the gradient-flow scales $t_0$ and $w_0$

Phys. Rev. D 103, 054511 (2021) [arXiv:2011.12166]

## Lattice calculation of $F_K/F_\pi$ from a mixed domain-wall on HISQ action [talk]

American Physical Society bulletin [PDF of slides]

## spacetime-plots

A python noteboook for plotting points and lines, expressly written for making spacetime diagrams. To get started with a tutorial, launch the binder inst...

## $F_K/F_\pi$ from MDWF on HISQ
Python code for our $F_K/F_\pi$ analysis.