Scaling test for Wilson twisted mass QCD

TL;DR

The paper tests whether Wilson twisted mass QCD at twist angle ω=π/2 yields automatic $O(a)$ improvement without Clover terms in a quenched setting. By performing a scaling study of the vector meson mass $m_V$ and the pseudoscalar decay constant $F_{PS}$ at fixed $r_0 m_{PS}$ across several β values and comparing with standard Wilson and non-perturbatively improved Wilson, the authors assess lattice-spacing effects. They find that tmQCD exhibits scaling consistent with $O(a)$-improvement (i.e., small linear in a) and behaves similarly to the $O(a)$-improved Wilson results, with even smaller higher-order $a$ effects than expected. The study suggests practical advantages for dynamical simulations, including reduced eigenvalue problems and avoidance of problematic phase transitions, making Wilson tmQCD a promising path toward the physical point.

Abstract

We present a first scaling test of twisted mass QCD with pure Wilson quarks for a twisting angle of pi/2. We have computed the vector meson mass and the pseudoscalar decay constant for different values of beta at fixed value of r_0 m_PS. The results obtained in the quenched approximation are compared with data for pure Wilson and non-perturbatively O(a) improved Wilson computations. We show that our results from Wilson twisted mass QCD show clearly reduced lattice spacing errors, consistent with O(a) improvement and without the need of any improvement terms added. These results thus provide numerical evidence of the prediction in ref. [1].

Figures (3)

• Figure 1: Monte Carlo time evolution of the eleven smallest eigenvalues $\lambda$ of $(D_W+m_0)^\dagger (D_W+m_0)$, normalised by the largest eigenvalue, at $\mu_q=0$ and $m_q=\pm 0.02725$ on a $12^3\times 24$ lattice ($\kappa_{c}=0.161662(17), \beta=5.85$).
• Figure 2: Scaling behaviour of the vector meson mass as a function of the lattice spacing squared for fixed pion mass, $r_0 m_{\rm PS}= 1.79$. Open circles denote Wilson tmQCD, while filled circles are from non-perturbatively improved Wilson fermions Garden:1999fg. The Wilson data without improvement (open squares) are collected from several sources in the literature. Note that the filled circles are slightly displaced for better visibility.
• Figure 3: Scaling behaviour of the pion decay constant $F_{\rm PS}$ as a function of the lattice spacing for fixed pion mass, $r_0m_{\rm PS}= 1.79$. Open circles denote Wilson tmQCD, while filled circles are from non-perturbatively improved Wilson fermions Garden:1999fg, for which only the three data points with smallest values of $(a/r_0)^2$ are included in the fit. Note that the points corresponding to the continuum extrapolation $F_{\rm\ PS}^\mathrm{cont}$ are slightly displaced for better visibility.