[Paper Review] Exploring the chiral regime with dynamical overlap fermions

Hideo Matsufuru|arXiv (Cornell University)|Oct 23, 2007

Quantum Chromodynamics and Particle Interactions28 references4 citations

TL;DR

This paper presents large-scale dynamical lattice QCD simulations using overlap fermions with exact chiral symmetry on a 16³×32 lattice at a ≈ 0.12 fm spacing, covering the p- and ε-regimes for Nf=2 and Nf=2+1 flavors. By employing a topology-fixing term to suppress near-zero modes of the Wilson-Dirac operator, the simulations achieve stable molecular dynamics without discontinuity issues, enabling precision chiral extrapolation of pion mass and decay constant that agree with phenomenological ChPT predictions at NNLO level.

ABSTRACT

I report the status of the dynamical overlap fermion project by the JLQCD and TWQCD collaborations. So far, the simulations have been completed with two flavors of overlap sea quarks in a wide range of sea quark mass corresponding the $p$-regime and the $ε$-regime on a $16^3 imes 32$ lattice at $a=$0.12 fm. More recently, runs with 2+1 flavors of sea quarks have also started. This talk mainly discusses the physics results on the $N_f=2$ lattice after describing the lattice formulation and algorithms.

Motivation & Objective

• To explore the chiral regime of QCD with exact chiral symmetry using dynamical overlap fermions.
• To enable precision calculations of hadronic matrix elements with controlled chiral extrapolation.
• To reduce numerical cost and stabilize HMC updates by suppressing near-zero modes of H_W via a topology-fixing term.
• To validate the reliability of fixed-topology simulations for extracting low-energy constants in chiral perturbation theory.
• To provide high-precision data on mπ²/mq and fπ for comparison with phenomenological ChPT fits.

Proposed method

• Use of the overlap fermion action, defined via the sign function of the hermitian Wilson-Dirac operator H_W, to realize exact chiral symmetry on the lattice.
• Implementation of a topology-fixing term involving an extra Wilson fermion and twisted mass ghost to suppress near-zero eigenvalues of H_W and fix topological charge.
• Adoption of the HMC algorithm with the topology-fixing term to avoid discontinuities at λ=0, enabling stable molecular dynamics.
• Use of Iwasaki gauge action with a topology-fixing term to suppress near-zero modes and stabilize simulations.
• Simulations performed on 16³×32 lattices at a ≈ 0.12 fm spacing with Nf=2 and Nf=2+1 dynamical overlap fermions.
• Application of chiral perturbation theory (ChPT) fits at NLO and NNLO to extrapolate mπ²/mq and fπ to the physical point, with a simplified NNLO' approximation for numerical stability.

Experimental results

Research questions

• RQ1 Can dynamical overlap fermion simulations with exact chiral symmetry be performed stably in the chiral regime using a fixed-topology approach?
• RQ2 To what extent do finite-size effects and topology-fixing influence the chiral extrapolation of mπ and fπ?
• RQ3 Do the results for mπ²/mq and fπ at small quark masses agree with NNLO ChPT predictions and phenomenological values?
• RQ4 How do the NLO and NNLO ChPT fits compare in describing the data, and does the failure of NLO indicate the need for higher-order corrections?
• RQ5 Can fixed-topology simulations provide a reliable framework for precision computation of low-energy constants in QCD?

Key findings

• The fixed-topology simulation with the topology-fixing term successfully suppresses near-zero modes of H_W, eliminating discontinuities and enabling stable HMC updates.
• The pion mass and decay constant, after finite-size effect corrections, show consistent chiral extrapolation results across NLO, NNLO, and NNLO' fits.
• The NLO fit results are inconsistent with both the NNLO fits and phenomenological estimates, indicating that higher-order ChPT corrections are necessary.
• The NNLO and NNLO' fits yield results for f, Σ, l̄₃^phys, and l̄₄^phys that are consistent with each other and with phenomenological values.
• The chiral extrapolation of mπ²/mq and fπ shows that finite-size effects and fixed-topology corrections nearly cancel, supporting the reliability of the method.
• The simulations demonstrate that dynamical overlap fermions with fixed topology provide a viable and precise framework for studying chiral dynamics and computing matrix elements in the chiral regime.