Numerical simulations with two flavours of twisted-mass Wilson quarks and DBW2 gauge action

TL;DR

This study investigates discretisation errors in two-flavour lattice QCD using Wilson twisted-mass fermions with the DBW2 gauge action, comparing two lattice spacings to assess scaling towards the continuum. It determines twist angles and renormalisation factors (Z_V, Z_A, Z_P/Z_S) from TMQCD data and tests next-to-leading order lattice chiral perturbation theory (tmWChPT) including O(a) effects against the numerical results. The DBW2 action is shown to weaken the problematic first-order phase transition near zero quark mass, enabling simulations at lighter quark masses and showing reasonable scaling and qualitative ChPT consistency, though precise extraction of low-energy constants remains challenging at these spacings. These findings lay groundwork for future high-precision studies at smaller lattice spacings and with lighter quarks.

Abstract

Discretisation errors in two-flavour lattice QCD with Wilson-quarks and DBW2 gauge action are investigated by comparing numerical simulation data at two values of the bare gauge coupling. Both non-zero and zero twisted mass values are considered. The results, including also data from simulations using the Wilson plaquette gauge action, are compared to next-to-leading order chiral perturbation theory formulas.

Figures (18)

• Figure 1: The squared pion to $\rho$-meson mass ratio $(m_\pi/m_\rho)^2$ versus $(r_0 m_\pi)^2$. Only simulation points with positive quark mass are considered. The physical point is shown by an asterisk. The straight line connecting the origin with it is the continuum expectation for small quark masses where both quantities are approximately proportional to the quark mass.
• Figure 2: Determination of $\tan\omega_V$ and $\tan\omega_A$ as in Eqs. (\ref{['eq22']}), (\ref{['eq23']}) for the point ($a^\prime$). The lines represent the fitted values.
• Figure 3: Determination of $\mu_{\kappa cr}$ at $\beta=0.67$, $a\mu=0.01$ by parity-restoration and by extrapolating the untwisted PCAC quark mass $m_\chi^{\rm PCAC}$ to zero.
• Figure 4: Determination of $\mu_{\kappa cr}$ at $\beta=0.74$, $a\mu=0.0075$ by parity-restoration and by extrapolating the untwisted PCAC quark mass $m_\chi^{\rm PCAC}$ to zero.
• Figure 5: Full twist extrapolation of $Z_V^{(1)}$ at $\beta=0.67$, $a\mu=0.01$.