Quenched Scaling of Wilson twisted mass fermions

TL;DR

The paper assesses the scaling of quenched Wilson twisted mass fermions at maximal twist, comparing two critical-mass definitions (pion and PCAC) to quantify their impact on cut-off effects. Using six lattice spacings and pseudoscalar masses down to about $270$ MeV, it shows that both definitions achieve $O(a)$ improvement, but the PCAC definition dramatically reduces $O(a^2)$ artefacts, enabling reliable continuum extrapolations for observables such as $f_{PS}$ and $m_V$ and for the renormalization constant $Z_V$. The study demonstrates linear $f_{PS} r_0$ behavior in $(a/r_0)^2$ under both schemes, with PCAC-based results exhibiting superior scaling at small masses, and provides continuum-limit estimates in good agreement with other Wilson actions, along with quenched estimates like $f_K/f_$. These findings support using the PCAC definition to achieve smoother cut-off behavior and robust continuum results in tmQCD simulations.

Abstract

We investigate the scaling behaviour of quenched Wilson twisted mass fermions at maximal twist applying two definitions of the critical mass. The first definition uses the vanishing of the pseudoscalar meson mass m_PS while the second employs the vanishing of the PCAC quark mass m_PCAC. We confirm in both cases the expected O(a) improvement. In addition, we show that the PCAC quark mass definition leads to substantially reduced O(a^2) cut-off effects even when the pseudoscalar meson mass m_PS is as small as 270 MeV. At a fixed value of m_PS we perform continuum limits for the vector meson mass m_V and for the pseudoscalar decay constant f_PS and discuss the renormalisation constant Z_V of the vector current.

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