f_K/f_pi in Full QCD with Domain Wall Valence Quarks

TL;DR

This work addresses precision determination of the ratio $f_K/f_ u$ in full QCD using a mixed-action lattice approach with domain-wall valence quarks on MILC 2+1 KS sea, enabling a robust extraction of the low-energy constant $L_5$ via continuum chiral perturbation theory. By carefully performing chiral extrapolations, testing at NLO and exploring partial NNLO scenarios, the authors obtain $f_K/f_\pi = 1.218 \pm 0.002^{+0.011}_{-0.024}$ and $L_5(f_^{phy}) = (5.65 \pm 0.02)\times 10^{-3}$, with results consistent with MILC and experiment. The analysis demonstrates that the choice of valence quarks induces only small systematic errors and validates the mixed-action framework for high-precision hadronic quantities. The study also outlines how NNLO-inspired variations contribute to the chiral-systematics, guiding future refinements with more light-mquark data and broader valence mass coverage.

Abstract

We compute the ratio of pseudoscalar decay constants f_K/f_pi using domain-wall valence quarks and rooted improved Kogut-Susskind sea quarks. By employing continuum chiral perturbation theory, we extract the Gasser-Leutwyler low-energy constant L_5, and extrapolate f_K/f_pi to the physical point. We find: f_K/f_pi = 1.218 (+- 0.002) (+0.011 -0.024) where the first error is statistical and the second error is an estimate of the systematic due to chiral extrapolation and fitting procedures. This value agrees within the uncertainties with the determination by the MILC collaboration, calculated using Kogut-Susskind valence quarks, indicating that systematic errors arising from the choice of lattice valence quark are small.

Figures (4)

• Figure 1: "Effective" $f_K/f_\pi$ determined from the smeared-smeared and smeared-point correlation functions with eq. (\ref{['eq:FpsEFF']}). The solid black lines and shaded regions are the fits (with $1\sigma$ errors) tabulated in Table \ref{['tab:LatResults']}.
• Figure 2: ${\cal F}$ vs. $m^2_{\pi}/f^2_{\pi}$ at NLO, along with the three different fits, A, B and C. The solid bars near the y-axis denote the value of $L_5$ and its uncertainty from the three fits. The point denoted by the star corresponds to the experimental value.
• Figure 3: ${\cal F}$ vs. $m^2_{\pi}/f^2_{\pi}$ at NNLO. The solid bars near the y-axis denote the value of $\tilde{L}_5={\cal F}(m_\pi =0)$ and its uncertainty from the fits. The point denoted by the star corresponds to the experimental value. The circles denote the lattice data with only the NLO chiral logs subtracted, while the squares are the lattice data with the NLO chiral logs and the NNLO $\log^2$ term subtracted.
• Figure 4: 68% confidence-level error ellipses for fits D and E described in the text.