Dynamical Twisted Mass Fermions with Light Quarks

TL;DR

This study demonstrates the viability of dynamical $N_f=2$ Wilson twisted mass fermions at maximal twist with $a\lesssim 0.1$ fm, achieving automatic $O(a)$ improvement and enabling precise determinations of the pseudoscalar sector. By measuring $mPS$ and $fPS$ over $mPS\approx$300–550 MeV and calibrating the lattice scale via $f_\pi$ and $m_\pi$, the authors fit next-to-leading-order chiral perturbation theory with finite-size corrections to extract the low-energy constants $F$, $l3bar$, and $l4bar$, finding values around $F\approx 121$ MeV, $l3bar\approx 3.65$, and $l4bar\approx 4.52$. They also quantify isospin-breaking effects, with the neutral pion lighter than the charged one by ~20% at the smallest mass, consistent with twisted-mass expectations and phase-transition scenarios. The results provide important benchmarks for the chiral effective theory in the dynamical twisted mass setup and establish a path toward controlled continuum extrapolations and precise determinations of QCD low-energy constants.

Abstract

We present results of dynamical simulations with 2 flavours of degenerate Wilson twisted mass quarks at maximal twist in the range of pseudo scalar masses from 300 to 550 MeV. The simulations are performed at one value of the lattice spacing a \lesssim 0.1 fm. In order to have O(a) improvement and aiming at small residual cutoff effects, the theory is tuned to maximal twist by requiring the vanishing of the untwisted quark mass. Precise results for the pseudo scalar decay constant and the pseudo scalar mass are confronted with chiral perturbation theory predictions and the low energy constants F, \bar{l}_3 and \bar{l}_4 are evaluated with small statistical errors.

Figures (4)

• Figure 1: (a) PCAC quark mass $am_\mathrm{PCAC}$ as function of $a\mu$ and (b) Sommer parameter $(r_0/a)$ as functions of $(a\mu)^2$. The solid line in subfigure (b) represents a linear fit in $(a\mu)^2$ to the data.
• Figure 2: In (a) we show $(am_\mathrm{PS})^2/(a\mu)$ as a function of $a\mu$. In addition we plot the $\chi$PT fit with Eq. (\ref{['eq:chirfo1']}) to the data from the lowest four $\mu$-values. In (b) we show $(am_\mathrm{PS})^2$ as a function of $a\mu$. Here we present two $\chi$PT fits with Eq. (\ref{['eq:chirfo1']}), one taking all data points and one leaving out the point at the largest value $a\mu=0.015$. In both figures (a) and (b) we show finite size corrected ($L\to\infty$) data points.
• Figure 3: We show $af_\mathrm{PS}$ as a function of $a\mu$ together with fits to $\chi$PT formula Eq. (\ref{['eq:chirfo2']}). We present two fits, one taking all data and one leaving out the point at the largest value $a\mu=0.015$. We show finite size corrected ($L\to\infty$) data points.
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