[Paper Review] Pseudoscalar meson physics with four dynamical quarks

A. Bazavov, C. Bérnard+23 more|arXiv (Cornell University)|Oct 31, 2012

Quantum Chromodynamics and Particle Interactions11 references4 citations

TL;DR

This paper presents preliminary lattice QCD calculations of charm meson decay constants using four dynamical quarks with the HISQ action, employing a self-consistent scale setting via $f_\pi$ to reduce systematic errors. The key results are $f_D = 209.2(3.0)(3.6)$ MeV, $f_{D_s} = 246.4(0.5)(3.6)$ MeV, and $f_{D_s}/f_D = 1.175(16)(11)$, with uncertainties dominated by statistical and scale-setting effects.

ABSTRACT

We present preliminary results for light, strange and charmed pseudoscalar meson physics from simulations using four flavors of dynamical quarks with the highly improved staggered quark (HISQ) action. These simulations include lattice spacings ranging from 0.15 to 0.06 fm, and sea-quark masses both above and at their physical value. The major results are charm meson decay constants f_D, f_{D_s} and f_{D_s}/f_D and ratios of quark masses. This talk will focus on our procedures for finding the decay constants on each ensemble, the continuum extrapolation, and estimates of systematic error.

Motivation & Objective

• To compute precise values of charm meson decay constants $f_D$ and $f_{D_s}$ using lattice QCD with four dynamical quarks.
• To determine the ratio of quark masses $m_c/m_s$ and $m_u/m_d$ using fully dynamical charm and strange quarks.
• To reduce systematic errors in lattice scale setting by using $f_\pi$ as the physical input instead of auxiliary quantities like $r_0$ or $r_1$.
• To control finite-volume and electromagnetic/isospin-breaking effects through chiral perturbation theory and tuned mass adjustments.
• To enable improved precision by future use of staggered chiral perturbation theory and additional ensembles with physical sea-quark masses.

Proposed method

• Simulate QCD with four dynamical quarks (up, down, strange, charm) using the highly improved staggered quark (HISQ) action and one-loop Symanzik gauge action.
• Use $f_\pi$ from the same correlators as $f_D$ and $f_{D_s}$ to set the lattice spacing, minimizing scale-setting error and enabling a self-contained analysis.
• Perform two-stage analysis: first extract meson masses and amplitudes from two-point correlators with varying valence quark masses; second, interpolate to tuned valence masses at each ensemble.
• Apply finite-volume corrections using one-loop chiral perturbation theory and adjust for electromagnetic and isospin-breaking effects via Dashen's theorem violation parameter $\Delta_{\text{EM}} = 0.65(26)$.
• Estimate systematic errors by varying scale-setting procedures (e.g., using $f_{p4s}$ or $r_1$) and fitting $a^2$-dependence in continuum extrapolation.
• Use jackknife resampling to estimate statistical errors throughout the entire analysis chain, including tuning and extrapolation steps.

Experimental results

Research questions

• RQ1 What are the values of the charm meson decay constants $f_D$ and $f_{D_s}$ in the continuum limit with four dynamical quarks?
• RQ2 How do electromagnetic and isospin-breaking effects influence the kaon and pion mass differences, and how can they be corrected in lattice simulations?
• RQ3 To what extent do finite-volume effects distort the measured decay constants, and how can they be corrected using chiral perturbation theory?
• RQ4 How do different scale-setting procedures ($f_\pi$, $f_{p4s}$, $r_1$) affect the final results and their systematic uncertainties?
• RQ5 Can the use of staggered chiral perturbation theory improve the control of unphysical valence-quark mass extrapolations in future analyses?

Key findings

• The charm meson decay constant is determined as $f_D = 209.2(3.0)(3.6)$ MeV, with statistical and total systematic errors reported.
• The $D_s$ meson decay constant is found to be $f_{D_s} = 246.4(0.5)(3.6)$ MeV, with a small statistical error and comparable systematic uncertainty.
• The ratio $f_{D_s}/f_D = 1.175(16)(11)$ is consistent with other lattice and experimental determinations, with uncertainties dominated by statistical and scale-setting effects.
• The ratio of quark masses is $m_c/m_s = 11.63(4)(9)$, with the first error from statistics and the second from systematic variations.
• The up-down quark mass ratio is $m_u/m_d = 0.505(9)(33)$, with the larger systematic error arising from electromagnetic and isospin-breaking effects.
• The largest systematic error source is scale setting, contributing 2.0 MeV to $f_D$ and 1.3 MeV to $f_{D_s}$, followed by $a^2$-fit form uncertainty at 2.9 and 3.3 MeV respectively.