Gradient flow scale-setting with $N_f=2+1+1$ Wilson-clover twisted-mass fermions

TL;DR

This paper determines key gradient flow scales in isosymmetric QCD using $N_f=2+1+1$ Wilson-clover twisted-mass fermions, providing precise lattice scale settings and decay constant ratios relevant for particle physics.

Contribution

It introduces a new determination of gradient flow scales in $N_f=2+1+1$ QCD with physical point configurations, improving lattice scale accuracy.

Findings

Measured $w_0$, $ oot t_0$, and $t_0/w_0$ with high precision.

Provided a new value for the ratio $f_K/f_$ in isosymmetric QCD.

Set the lattice scale using the PDG pion decay constant.

Abstract

We present a determination of the gradient flow scales $w_0$, $\sqrt{t_0}$ and $t_0/w_0$ in isosymmetric QCD, making use of the gauge ensembles produced by the Extended Twisted Mass Collaboration (ETMC) with $N_f=2+1+1$ flavours of Wilson-clover twisted-mass quarks including configurations close to the physical point for all dynamical flavours. The simulations are carried out at three values of the lattice spacing and the scale is set through the PDG value of the pion decay constant, yielding $w_0=0.17383(63)$ fm, $\sqrt{t_0}=0.14436(61)$ fm and $t_0/w_0=0.11969(62)$ fm. Finally, fixing the kaon mass to its isosymmetric value, we determine the ratio of the kaon and pion leptonic decay constants to be $f_K/f_{\pi}=1.1995(44)$.