Spectrum of quenched twisted mass lattice QCD at maximal twist

TL;DR

Twisted mass lattice QCD at maximal twist ($\omega=\pi/2$) aims to remove linear lattice artifacts and avoid exceptional configurations in quenched simulations. The authors compare two practical definitions of maximal twist—the Wilson $\kappa_{cW}$ criterion and a parity-conservation criterion—by computing the hadron spectrum at two lattice spacings and several $\mu$ values, examining $m_\pi^2$ against $a\mu$ and the pion decay constant $f_\pi$. They find that the parity-conservation definition better achieves $\omega=\pi/2$, yielding smaller curvature in $m_\pi^2$ and a more realistic $f_\pi$, while most other masses show mild $a$-dependence. Flavor breaking, probed via the $\Delta(1232)$ multiplet, persists at finite $a$ but decreases toward the continuum, consistent with suppression of flavor-violating effects at maximal twist.

Abstract

Hadron masses are computed from quenched twisted mass lattice QCD for a degenerate doublet of up and down quarks with the twist angle set to pi/2, since this maximally twisted theory is expected to be free of linear discretization errors. Two separate definitions of the twist angle are used, and the hadron masses for these two cases are compared. The flavor breaking, that can arise due to twisting, is discussed in the context of mass splittings within the Delta(1232) multiplet.

Figures (16)

• Figure 1: Pseudoscalar meson mass squared as a function of the twisted mass parameter. The standard mass parameter was held fixed to the value obtained from the Wilson $\kappa_{cW}$ definition of maximal twist, Eq. (\ref{['kappacWdef']}). Data labelled by "$\chi$LF" are taken from Ref. GoingChiral.
• Figure 2: Vector meson mass as a function of the pseudoscalar meson mass squared. The standard mass parameter was held fixed to the value obtained from the Wilson $\kappa_{cW}$ definition of maximal twist, Eq. (\ref{['kappacWdef']}). Data labelled by "$\chi$LF" are taken from Ref. GoingChiral.
• Figure 3: Spin 1/2 baryon masses (both parities) as functions of the pseudoscalar meson mass squared. The standard mass parameter was held fixed to the value obtained from the Wilson $\kappa_{cW}$ definition of maximal twist, Eq. (\ref{['kappacWdef']}). Data labelled by "$\chi$LF" are taken from Ref. GoingChiral.
• Figure 4: Spin 3/2 baryon masses (both parities) as functions of the pseudoscalar meson mass squared. These data are averages of the $\Delta^{++}$ and $\Delta^-$ masses. The standard mass parameter was held fixed to the value obtained from the Wilson $\kappa_{cW}$ definition of maximal twist, Eq. (\ref{['kappacWdef']}). Data labelled by "$\chi$LF" are taken from Ref. GoingChiral.
• Figure 5: Vector meson and $(1/2)^+$ baryon masses as functions of lattice spacing squared. Axes are in units of $r_0=0.5$ fm. The calculation was done using the Wilson $\kappa_{cW}$ definition of maximal twist, Eq. (\ref{['kappacWdef']}).