Scaling and low energy constants in lattice QCD with N_f=2 maximally twisted Wilson quarks

TL;DR

This work analyzes the scaling properties of lattice QCD with $N_f=2$ maximally twisted Wilson quarks, using a tree-level improved gauge action to minimize $O(a)$ artifacts and access pion masses down to ~300 MeV across multiple lattice spacings and volumes. By combining continuum χPT fits with finite-volume corrections, the authors extract low-energy constants and light-quark masses, obtaining $2 ilde B_0 r_0 \\approx 12$, $ar l_3 \\approx 3.6$–$3.7$, $ar l_4 \\approx 4.6$–$4.7$, and $m_{ud}( ext{MS},2 ext{ GeV}) \\approx 3.4$–$3.6$ MeV, along with a chiral condensate of order $(270 ext{ MeV})^3$. The results show good scaling behavior for light and certain charmed observables and provide continuum-consistent estimates for $r_0$ and decay-constant combinations, underscoring the viability of maximally twisted Wilson fermions for precise QCD predictions. Collectively, the findings indicate that automatic $ ext{O}(a)$ improvement and controlled finite-volume effects enable reliable extrapolations to the continuum limit, with implications for hadron spectrum, chiral dynamics, and weak matrix-element studies. The study also demonstrates agreement of derived quantities with experimental benchmarks such as $m_N/f_\pi$, reinforcing the physical relevance of the lattice framework used.

Abstract

We report on the scaling of basic hadronic observables in lattice QCD with N_f=2 maximally twisted Wilson dynamical quarks. We give preliminary results for some of the Gasser-Leutwyler low energy constants, the chiral condensate and the average mass of u and d quarks.

Figures (6)

• Figure 1: (a) $m_{\rm R}r_0 = Z_A Z_P^{-1} m_{\rm PCAC} r_0$ vs. $\mu_{\rm R}r_0$ and (b) $r_0(\mu)/r_0$ vs. $(\mu r_0)^2$, with $r_0 = \lim_{\mu \to 0} \; r_0(\mu)$ (see text). In both plots data for $\beta=4.05$, 3.9, 3.8 and $L \simeq 2.1, 2.1, 2.4$ fm (respectively) are shown.
• Figure 2: Scaling plots of $f_{\rm PS}r_0$ vs. $(a/r_0)^2$ at fixed values of $m_{\rm PS}r_0$ (increasing from bottom to top). See text for a detailed explanation of the symbols.
• Figure 3: Scaling plot of $\mu_{\rm R}r_0$ vs. $(a/r_0)^2$ at fixed values of $m_{\rm PS}r_0$ (increasing from bottom to top). See text for a detailed explanation of the symbols.
• Figure 4: Independent $\chi$PT fits at $\beta=4.05$ and $\beta=3.9$: FS-corrected data à la CDH for (a) $r_0m_{\rm PS}^2/\mu_{\rm R}$ and (b) $r_0f_{\rm PS}$ vs. $\mu_{\rm R}r_0$ are shown, with the corresponding best fit curves to eqs. (4.1)--(4.2). The points at $\mu_{\rm R}r_0 \sim 0.17$ were not included in the fit.
• Figure 5: $\widetilde{m}_{\rm V}r_0$ and $m_{\rm N}r_0$ vs. $(m_{\rm PS}r_0)^2$ for different lattice resolutions and $L$ in the range $2.1 \div 2.4$ fm.