Dynamical Twisted Mass Fermions with Light Quarks: Simulation and Analysis Details

TL;DR

This study presents a comprehensive technical treatment of dynamical twisted mass fermions with two light degenerate quarks at maximal twist, emphasizing automatic $O(a)$ improvement and precise meson observables. It details the simulation setup, including tuning to maximal twist via the PCAC condition, stochastic time-slice sources and the one-end trick for efficient charged- and neutral-meson correlators, and a rigorous error analysis with the $\Gamma$-method. The work reports high-precision results for charged and neutral pseudoscalar masses, decay constants, PCAC mass, and $Z_V$, and exploits finite-size corrected chiral perturbation theory to extract low-energy constants $B_0$, $F$, $\Lambda_3$, and $\Lambda_4$. It also analyzes the static potential to determine the scale $r_0/a$ and discusses systematic uncertainties, including NNLO effects in finite-volume corrections. Overall, the paper provides a detailed methodological blueprint for ETMC-style simulations and a baseline of precise results to test continuum and chiral-limit extrapolations.

Abstract

In a recent paper [hep-lat/0701012] we presented precise lattice QCD results of our European Twisted Mass Collaboration (ETMC). They were obtained by employing two mass-degenerate flavours of twisted mass fermions at maximal twist. In the present paper we give details on our simulations and the computation of physical observables. In particular, we discuss the problem of tuning to maximal twist, the techniques we have used to compute correlators and error estimates. In addition, we provide more information on the algorithm used, the autocorrelation times and scale determination, the evaluation of disconnected contributions and the description of our data by means of chiral perturbation theory formulae.

Figures (10)

• Figure 1: The Monte Carlo history of the ratio of correlators defining the PCAC quark mass estimator described in the text on the configurations of the ensemble $B_1$. The configuration number corresponds to the number of trajectories divided by two.
• Figure 2: The autocorrelation function (see eq. (\ref{['eq:est_gamma']})) from the data presented in fig. \ref{['fig_algo_mpcac']}. The vertical line shows the window $W$ from eq. (\ref{['eq:est_tau_int']}) used to evaluate the integrated autocorrelation function.
• Figure 3: Effective masses for the ground state energy of the Wilson loop at quark-antiquark separation $r/a = 4$, for ensembles $B_1$ to $B_5$.
• Figure 4: Mass dependence of $r_0/a$. The shaded area shows the error band of the quadratic fit (full line) to the data (circles). The additional plus symbols are further determinations of $r_0/a$ corresponding to different values of the fit parameters to the ansatz (\ref{['eq:correlation_fit_ansatz']}). The spread provides an indication of the systematic error due to interpolation (see text) in $r_0/a$.
• Figure 5: Effective mass for the pseudoscalar channel from $B_1$ lattice data. The effective masses obtained using 3 different interpolating operators as described in the text are shown.