[Paper Review] Light meson spectrum with $N_f=2$ dynamical overlap fermions

J. Noaki, Sinya Aoki+7 more|ArXiv.org|Oct 4, 2007

Quantum Chromodynamics and Particle Interactions9 references4 citations

TL;DR

This study presents a lattice QCD simulation of the light meson spectrum using $N_f=2$ dynamical overlap fermions on a $16^3 \times 32$ lattice with exact chiral symmetry. By employing low-mode averaging and finite-size effect corrections, the authors perform chiral extrapolations using NLO and NNLO chiral perturbation theory, finding consistent results with phenomenological values and confirming the necessity of NNLO corrections up to strange quark masses.

ABSTRACT

We present numerical simulation of QCD with two dynamical quark flavors described by the overlap fermion action on a $16^3 imes 32 imes (0.12 { m fm})^4$ lattice. We calculate pseudo-scalar masses and decay constants and investigate their chiral properties. We test the consistency of our data with the two-loop chiral perturbation theory predictions, which should also be valid at finite lattice spacings because of the exact chiral symmetry, including the finite size effects.

Motivation & Objective

• To investigate the light meson spectrum in $N_f=2$ dynamical QCD using overlap fermions with exact chiral symmetry.
• To test the consistency of numerical results with two-loop chiral perturbation theory (ChPT) at finite lattice spacing.
• To correct for finite-size effects (FSE) in the pion mass and decay constant using analytic NNLO ChPT results from Colangelo et al.
• To perform chiral extrapolation of $m_\pi^2/m_q$ and $f_\pi$ using NLO and NNLO ChPT formulae, assessing the validity of low-energy effective field theory in the $m_q \sim m_s$ region.

Proposed method

• Numerical simulations are performed using the overlap fermion action and Iwasaki gauge action on a $16^3 \times 32$ lattice with $a = 0.1184(12)(11)$ fm.
• Low-lying eigenmodes of the overlap Dirac operator are computed and stored to decompose the quark propagator into low- and high-mode contributions.
• Low-mode-averaging is applied to meson correlation functions to improve statistical precision, especially in the pion channel.
• Finite-size corrections are estimated using NNLO ChPT results for $m_\pi$ and $f_\pi$ from Colangelo et al., incorporating LECs $\bar{l}_{1,2,3,4}^\text{phys}$.
• Chiral fits are performed using NLO, NNLO, and modified NNLO' formulae for $m_\pi^2/m_q$ and $f_\pi$, with $\xi = m_\pi^2 / (4\pi f)^2$ as the expansion parameter.
• The renormalized quark mass is obtained via non-perturbative $Z_m^{\overline{\text{MS}}}(2\,\text{GeV}) = 0.742(12)$ in the RI/MOM scheme.

Experimental results

Research questions

• RQ1 Does the use of overlap fermions allow consistent application of continuum ChPT at finite lattice spacing, even with finite volume effects?
• RQ2 Are NLO ChPT formulae sufficient to describe the $m_\pi^2/m_q$ and $f_\pi$ data up to strange quark masses, or are NNLO corrections necessary?
• RQ3 How significant are finite-size effects in the $m_\pi L < 3.0$ regime, and can they be reliably corrected using analytic ChPT?
• RQ4 Do the extracted low-energy constants $\bar{l}_3^\text{phys}$ and $\bar{l}_4^\text{phys}$ agree with phenomenological estimates?
• RQ5 Is the modified NNLO' fit, which approximates $\xi^2 \ln \xi \approx -2.5 \xi^2$, a reliable alternative to full NNLO fits in the $\xi \lesssim 0.1$ region?

Key findings

• The chiral extrapolation of $m_\pi^2/m_q$ and $f_\pi$ shows that NLO fits are inconsistent with the data, indicating the necessity of NNLO corrections.
• The NNLO and NNLO' fits yield consistent results for $f$, $\Sigma^{1/3}$, $\bar{l}_3^\text{phys}$, and $\bar{l}_4^\text{phys}$, with $\Sigma^{1/3} = 0.251(7)(11)$ GeV in agreement with previous $\epsilon$-regime results.
• The extracted $f = 86.7(1.2)$ MeV is consistent with the phenomenological value of $130$ MeV when normalized accordingly, and $\Sigma^{1/3} = 0.251(7)(11)$ GeV is consistent with the $\epsilon$-regime result.
• The value of $\bar{l}_3^\text{phys} = -0.4 \pm 0.6$ is consistent with the phenomenological estimate, while $\bar{l}_4^\text{phys} = 4.3 \pm 0.1$ is in good agreement with the NNLO fit.
• The finite-size corrections are significant for $m_\pi L < 3.0$, and the use of analytic NNLO ChPT results from Colangelo et al. effectively removes these effects from the data.
• The low-mode-averaging technique improves statistical precision, as shown by the effective mass plot, enabling more reliable extraction of $f_\pi$ from simultaneous fits to smeared-local and local-local correlators.