[Paper Review] A High Statistics Study of Flavour-Singlet Mesons with Staggered Fermions

Eric B. Gregory, A.C. Irving+2 more|arXiv (Cornell University)|Oct 1, 2008

Quantum Chromodynamics and Particle Interactions3 citations

TL;DR

This high-statistics lattice QCD study investigates the scalar and pseudoscalar flavor-singlet mesons using $2+1$ flavor Asqtad-improved staggered fermions on large ensembles generated with QCDOC. It achieves significantly reduced statistical errors on disconnected correlators—critical for studying the $\eta'$ and glueball states—reporting a $0^{++}$ glueball mass of $1629(32)$ MeV (coarse) and $1600(71)$ MeV (fine), with ongoing analysis of singlet pseudoscalar and scalar states using variance-reduction techniques and stochastic noise sources.

ABSTRACT

We present some early results from a high statistics study of the scalar and pseudoscalar singlet sectors of lattice QCD using 2+1 flavours of Asqtad improved staggered fermions. The use of the Asqtad action has allowed us to generate an unprecedented number of configurations at 2 lattice spacings which on completion we hope will give us a significantly improved view of both the scalar and pseudoscalar singlet sectors.

Motivation & Objective

• To improve statistical precision in lattice QCD calculations of flavor-singlet mesons, particularly the $\eta'$ and scalar glueball, which are dominated by noisy disconnected diagrams.
• To test the validity of the staggered fermion fourth-rooting procedure by studying the $\eta'$ mass and its chiral behavior in the $2+1$ flavor regime.
• To leverage the Asqtad-improved action and high-statistics ensembles to achieve better control over taste-symmetry violations and unphysical multi-hadron contaminations.
• To apply variance-reduction techniques and stochastic volume sources to reduce computational cost while maintaining accuracy in disconnected correlator measurements.

Proposed method

• Used $2+1$ flavor Asqtad-improved staggered fermions on $24^3 \times 64$ and $32^3 \times 64$ lattices at $\beta = 6.75$ and $7.095$, with $r_0 = 0.467$ fm.
• Generated large ensembles using the exact RHMC algorithm with mass preconditioning and the $n^{th}$-root pseudofermion trick to enable higher-order integrators.
• Measured disconnected correlators using stochastic volume sources with $N_s = 32$, applying a variance-reduction trick for specific $\Delta_{\Gamma_S \otimes \Gamma_T}$ choices to reduce noise.
• Projected effective masses using a two-state fit with $\lambda_0, \lambda_1$ to suppress excited-state contamination.
• Applied staggered chiral perturbation theory (SChPT) to model and account for unphysical multi-hadron states from taste-splitted $\eta$-multiplets.
• Used weighted averages of projected effective masses over plateau regions to extract final physical masses.

Experimental results

Research questions

• RQ1 What is the mass of the $0^{++}$ glueball in the $2+1$ flavor QCD with Asqtad-improved staggered fermions, and how does it compare to previous determinations?
• RQ2 How do disconnected correlators for the $\eta'$ and $f_0$ states behave with high statistics, and can variance-reduction techniques significantly reduce their statistical noise?
• RQ3 To what extent do taste-symmetry violations and unphysical multi-hadron states (e.g., $\pi\pi$) contaminate the scalar and pseudoscalar singlet correlators, and can they be modeled using SChPT?
• RQ4 Does the fourth-rooted staggered fermion formulation correctly reproduce the chiral behavior of QCD in the $\eta'$ sector, especially in the presence of topology?
• RQ5 Can the $\gamma_5 \otimes \mathbf{1}$ operator be used effectively for the pseudoscalar singlet without introducing additional noise, compared to $\gamma_4\gamma_5 \otimes \mathbf{1}$?

Key findings

• The $0^{++}$ glueball mass was extracted as $1629(32)$ MeV on the coarse ensemble ($\beta = 6.75$, $a \approx 0.1225$ fm), with a plateau observed in the effective mass from $t/r_0 = 1$ to $4$.
• The fine ensemble ($\beta = 7.095$, $a \approx 0.0923$ fm) yielded a $0^{++}$ glueball mass of $1600(71)$ MeV, with the effective mass plateau observed from $t/r_0 = 2$ to $5$.
• The relative error on the light-light disconnected correlator for the $\gamma_5 \otimes \mathbf{1}$ operator was significantly reduced in the long run, demonstrating the effectiveness of high statistics in suppressing noise.
• The variance-reduction technique allowed for comparable stochastic error with only 8 or fewer noise sources in specific cases, justifying the use of $\gamma_5 \otimes \mathbf{1}$ over $\gamma_4\gamma_5 \otimes \mathbf{1}$.
• The analysis shows that unphysical $\pi\pi$ states from taste-splitted $\eta$-multiplets can dominate the $a_0$ and $f_0$ correlators, but SChPT provides a framework to model and subtract these contaminations.
• The study confirms that high-statistics simulations with Asqtad fermions and stochastic noise reduction are essential for reliable extraction of singlet meson masses, especially for the $\eta'$ and glueball states.