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Convergence of the chiral expansion in two-flavor lattice QCD

J. Noaki, S. Aoki, T. W. Chiu, H. Fukaya, S. Hashimoto, T. H. Hsieh, T. Kaneko, H. Matsufuru, T. Onogi, E. Shintani, N. Yamada

TL;DR

It is found that the chiral expansion is well saturated at the next-to-leading order for pions lighter than approximately 450 MeV, and better convergence behavior is found for a resummed expansion parameter xi.

Abstract

We test the convergence property of the chiral perturbation theory (ChPT) using a lattice QCD calculation of pion mass and decay constant with two dynamical quark flavors. The lattice calculation is performed using the overlap fermion formulation, which realizes exact chiral symmetry at finite lattice spacing. By comparing various expansion prescriptions, we find that the chiral expansion is well saturated at the next-to-leading order (NLO) for pions lighter than $\sim$450 MeV. Better convergence behavior is found in particular for a resummed expansion parameter $ξ$, with which the lattice data in the pion mass region 290$\sim$750 MeV can be fitted well with the next-to-next-to-leading order (NNLO) formulae. We obtain the results in two-flavor QCD for the low energy constants $\bar{l}_3$ and $\bar{l}_4$ as well as the pion decay constant, the chiral condensate, and the average up and down quark mass.

Convergence of the chiral expansion in two-flavor lattice QCD

TL;DR

It is found that the chiral expansion is well saturated at the next-to-leading order for pions lighter than approximately 450 MeV, and better convergence behavior is found for a resummed expansion parameter xi.

Abstract

We test the convergence property of the chiral perturbation theory (ChPT) using a lattice QCD calculation of pion mass and decay constant with two dynamical quark flavors. The lattice calculation is performed using the overlap fermion formulation, which realizes exact chiral symmetry at finite lattice spacing. By comparing various expansion prescriptions, we find that the chiral expansion is well saturated at the next-to-leading order (NLO) for pions lighter than 450 MeV. Better convergence behavior is found in particular for a resummed expansion parameter , with which the lattice data in the pion mass region 290750 MeV can be fitted well with the next-to-next-to-leading order (NNLO) formulae. We obtain the results in two-flavor QCD for the low energy constants and as well as the pion decay constant, the chiral condensate, and the average up and down quark mass.

Paper Structure

This paper contains 2 equations, 3 figures.

Figures (3)

  • Figure 1: Comparison of the chiral fits including the NLO terms for $m_\pi^2/m_q$ (top) and $f_\pi$ (bottom). Fit curves to three lightest data points obtained with different choices of the expansion parameter ($x$, $\hat{x}$, and $\xi$) are shown as a function of $m_\pi^2$.
  • Figure 2: NNLO chiral fits using all the data points for $m_\pi^2/m_q$ (top) and $f_\pi$ (bottom). Data are normalized by the value in the chiral limit. Solid curves show the NNLO fit, and the truncated expansions at NLO are shown by dashed curves.
  • Figure 3: Comparison of the ChPT parameters obtained from the NLO fit and NNLO fit. Red circles, blue squares and green diamonds are corresponding to the results of the fit using the lightest 4, 5 and all 6 data points. Error bars indicate statistical error. Pluses and star represent reference points.