Light hadrons from Nf=2+1+1 dynamical twisted mass fermions

TL;DR

The paper investigates light hadron observables in QCD with $N_f=2+1+1$ dynamical quarks using Wilson twisted mass fermions at maximal twist, implementing a mass-split heavy doublet for strange and charm. It reports ensembles at three lattice spacings ($a\approx$ 0.06, 0.08, 0.09 fm) and outlines tuning procedures to achieve automatic $O(a)$ improvement and to match strange and charm masses to their physical values, enabling NLO $SU(2)$ chiral perturbation theory analyses of $m_{PS}$ and $f_{PS}$. The analysis yields $f_0$, $\bar{l}_3$, $\bar{l}_4$ and lattice spacings with results broadly compatible across lattice spacings, though a complete determination of the renormalization factor $Z_P$ remains to be completed. Overall, the preliminary NLO $SU(2)$ χPT fits demonstrate a consistent description of light-mlection observables and validate the multi-spacing twisted-mass approach for controlling systematic effects in the light-quark sector.

Abstract

We present results of lattice QCD simulations with mass-degenerate up and down and mass-split strange and charm (Nf=2+1+1) dynamical quarks using Wilson twisted mass fermions at maximal twist. The tuning of the strange and charm quark masses is performed at three values of the lattice spacing a~0.06 fm, a~0.08 fm and a~0.09 fm with lattice sizes ranging from L~1.9 fm to L~3.9 fm. We perform a preliminary study of SU(2) chiral perturbation theory by combining our lattice data from these three values of the lattice spacing.

Figures (3)

• Figure 1: Status of the tuning. The ratio $m_{{\rm PCAC},l}/\mu_{l}$ is plotted as a function of the mass parameter $2B_{0}\mu_{l}$. When $|m_{{\rm PCAC},l}/\mu_{l}| \lesssim 0.1$, the ensemble is adequately tuned. Orange, blue and green symbols respectively correspond to $\beta=1.90$, $\beta=1.95$ and $\beta=2.10$ ensembles respectively.
• Figure 2: $2m_K^2 -m_{\rm{PS}}^2$ and $m_D$ as a function of $m_{\rm{PS}}^2$. The physical point is shown (black star) Amsler:2008zzb. Data points have been scaled with the lattice spacing $a=0.0863(4)$ fm for $\beta=1.90$, $a=0.0779(4)$ fm for $\beta=1.95$ and $a=0.0607(2)$ fm for $\beta=2.10$, where the errors quoted on the lattice spacing are only statistical.
• Figure 3: The charged pseudoscalar mass ratio $m_{\rm{PS}}^2 /2B_0\mu_l$ and the pseudoscalar decay constant $f_{\rm{PS}}$ as a function of the mass parameter $2B_0\mu_l$, for the combined ensembles at $\beta =1.90$, $\beta =1.95$ and $\beta =2.10$. The scale is set by $a\mu_\mathrm{phys}$, the value of $a\mu_l$ at which the ratio $f_{\rm{PS}}^{[L=\infty]}/m_{\rm{PS}}^{[L=\infty]}$ assumes its physical value Amsler:2008zzb$f_\pi/m_\pi = 130.4(2)/135.0$ (black star). Open symbols refer to runs with full statistics, but not properly tuned to maximal twist within our criterion. Runs not at full statistics and those aimed at controlling the tuning of the strange and charm mass are not included in the plot.