Going chiral: overlap versus twisted mass fermions

TL;DR

The paper directly compares overlap fermions, which preserve exact lattice chiral symmetry, with Wilson twisted mass fermions at full twist in quenched QCD at a fixed lattice spacing $a\approx0.123$ fm, to chart their approach to the chiral limit. Using Ward identities, meson masses, decay constants, and renormalization factors, the study shows both formulations can reach $M_ ext{\pi}\sim250$ MeV, with overlap offering a cleaner chiral behavior and twisted mass exhibiting larger renormalization factors and lattice artefacts at low masses. Renormalization analysis reveals $Z_m^{\rm RGI,ov}$ around unity and $Z_\mu^{\rm RGI,tm}$ around $2.2$–$2.6$, while $Z_A^{\rm ov}$ is determined as $1.448(4)$ in the chiral limit and $Z_V^{\rm tm}$ remains unreliable in that limit due to artefacts. The results highlight the trade-offs between computational cost, chiral symmetry realization, and renormalization behavior, informing future dynamical simulations and scaling studies.

Abstract

We compare the behavior of overlap fermions, which are chirally invariant, and of Wilson twisted mass fermions at full twist in the approach to the chiral limit. Our quenched simulations reveal that with both formulations of lattice fermions pion masses of O(250 MeV) can be reached in practical applications. Our comparison is done at a fixed value of the lattice spacing a=0.123 fm. A number of quantities are measured such as hadron masses, pseudoscalar decay constants and quark masses obtained from Ward identities. We also determine the axial vector renormalization constants in the case of overlap fermions.

Figures (5)

• Figure 1: Comparison of quenched results for the pion mass squared as a function of the bare quark mass for three lattice fermions: standard $\mathcal{O}(a)$ improved Wilson fermions HJLW01HJLWproc, twisted mass fermions and overlap fermions. The bare quark mass corresponds to $m_\mathrm{ov}$ in the overlap and to $\mu$ in the twisted mass case.
• Figure 2: Twisted mass fermions: linear and quadratic fit of the squared pion masses as function of the bare quark mass.
• Figure 3: Comparison of results for the vector meson mass as a function of the pion mass squared for overlap and twisted mass fermions. The chiral extrapolation in the overlap case is done with a linear fit in $M_\pi^2$.
• Figure 4: Effective mass plateaux for the vector meson mass at $\mu a=0.005$ and at $\mu a=0.06$. Notice the different scale on the $y$ axis.
• Figure :