[Paper Review] Physical results from 2+1 flavor Domain Wall QCD

Enno E. Scholz|arXiv (Cornell University)|Sep 18, 2008

Quantum Chromodynamics and Particle Interactions6 references22 citations

TL;DR

This paper presents physical results from 2+1 flavor Domain Wall QCD simulations using SU(2) chiral perturbation theory (ChPT) to analyze meson masses, decay constants, and light quark masses. The RBC and UKQCD collaborations find that SU(2) PQChPT provides a better fit to lattice data than SU(3) ChPT, especially in the kaon sector, yielding $ m_{ud}^{\overline{\text{MS}}}(2\,\text{GeV}) = 3.72^{+0.16}_{-0.33} \pm 0.18\,\text{MeV} $ and $ f_\pi = 124.1^{+3.6}_{-6.9}\,\text{MeV} $ at a lattice spacing of $ 1/a = 1.73\,\text{GeV} $. Preliminary results at a finer lattice spacing show improved control over residual chiral symmetry breaking.

ABSTRACT

We review recent results for the chiral behavior of meson masses and decay constants and the determination of the light quark masses by the RBC and UKQCD collaborations. We find that one-loop SU(2) chiral perturbation theory represents the behavior of our lattice data better than one-loop SU(3) chiral perturbation theory in both the pion and kaon sectors. The simulations have been performed using the Iwasaki gauge action at two different lattice spacings with the physical spatial volume held approximately fixed at (2.7 fm)^3. The Domain Wall fermion formulation was used for the 2+1 dynamical quark flavors: two (mass degenerate) light flavors with masses as light as roughly 1/5 the mass of the physical strange quark mass and one heavier quark flavor at approximately the value of the physical strange quark mass. On the ensembles generated with the coarser lattice spacing, we obtain for the physical average up- and down-quark and strange quark masses m_ud(MSbar,2GeV)=3.72(0.16)_stat(0.33)_ren(0.18)_syst MeV and m_s(MSbar,2GeV)=107.3(4.4)_stat(9.7)_ren(4.9)_syst MeV, respectively, while we find for the pion and kaon decay constants f_pi=124.1(3.6)_stat(6.9)_syst MeV, f_K=149.6(3.6)_stat(6.3)_syst MeV. The analysis for the finer lattice spacing has not been fully completed yet, but we already present some first (preliminary) results.

Motivation & Objective

• To determine the physical light and strange quark masses in 2+1 flavor QCD using lattice simulations with Domain Wall fermions.
• To assess the validity of SU(2) versus SU(3) chiral perturbation theory for chiral extrapolation in the pion and kaon sectors.
• To reduce systematic uncertainties by using a fixed spatial volume of approximately (2.7 fm)³ and multiple lattice spacings.
• To improve the accuracy of meson decay constants and low-energy constants through advanced chiral fits.

Proposed method

• Simulations were performed using the Iwasaki gauge action at two lattice spacings, with the spatial volume fixed at ~ (2.7 fm)³.
• Domain Wall fermions were employed for two degenerate light quarks and one heavier strange-quark-like dynamical flavor.
• Chiral extrapolations were performed using one-loop SU(2) partially quenched chiral perturbation theory (PQChPT), with a cut on average quark mass $ m_{\text{avg}} \leq 0.01 $.
• Physical results were extracted by matching to the $ \Omega^{-} $ baryon, pion, and kaon masses, with residual chiral symmetry breaking measured at $ m_{\text{res}} = 0.00315(2) $ on the coarser ensemble.
• Preliminary fits at finer spacing ($ 1/a \approx 2.5\,\text{GeV} $) used uncorrelated and correlated SU(2) ChPT fits to dynamical and partially quenched data.
• Finite volume corrections were estimated using SU(2) ChPT with resummed Lüscher formulae, showing corrections of ~1% for lightest valence pions.

Experimental results

Research questions

• RQ1 Does SU(2) chiral perturbation theory provide a better fit to lattice data than SU(3) ChPT in the pion and kaon sectors?
• RQ2 What are the physical values of the up/down and strange quark masses in the $ \overline{\text{MS}} $ scheme at 2 GeV?
• RQ3 How do the pion and kaon decay constants $ f_\pi $ and $ f_K $ depend on the light quark mass in the chiral limit?
• RQ4 To what extent do finite volume effects influence the meson masses and decay constants at $ m_{\text{PS}} \approx 300\,\text{MeV} $?
• RQ5 Can SU(2) ChPT reliably describe the kaon sector when the strange quark mass is kept fixed at its physical value?

Key findings

• The physical average up/down quark mass is determined as $ m_{ud}^{\overline{\text{MS}}}(2\,\text{GeV}) = 3.72^{+0.16}_{-0.33} \pm 0.18\,\text{MeV} $, with the dominant uncertainty from statistics.
• The strange quark mass is found to be $ m_s^{\overline{\text{MS}}}(2\,\text{GeV}) = 107.3^{+4.4}_{-9.7} \pm 4.9\,\text{MeV} $, consistent with physical expectations.
• The pion decay constant is $ f_\pi = 124.1^{+3.6}_{-6.9}\,\text{MeV} $, and the kaon decay constant is $ f_K = 149.6^{+3.6}_{-6.3}\,\text{MeV} $, both with small statistical errors.
• SU(2) PQChPT yields a $ \chi^2/{\rm d.o.f.} = 0.3 $, indicating a good fit, while SU(3) PQChPT shows large NLO contributions (~60–70%) that are unphysical.
• Preliminary results at a finer lattice spacing ($ 1/a \approx 2.5\,\text{GeV} $) show a residual mass of $ 6.76(0.11) \times 10^{-4} $, five times smaller than on coarser ensembles.
• Finite volume corrections for the lightest valence pion are ~1%, with $ R_m = 2.00(0.08)\% $ and $ -R_f = 0.41(0.02)\% $, indicating moderate effects at $ m_{\text{PS}} \approx 236\,\text{MeV} $.