[Paper Review] Scaling study for 2 HEX smeared fermions: hadron and quark masses

Thorsten Kurth, Stephan Dürr+8 more|arXiv (Cornell University)|Nov 8, 2010

Quantum Chromodynamics and Particle Interactions8 references8 citations

TL;DR

This study investigates the scaling behavior of the 2 HEX smeared fermion action in lattice QCD simulations with Nf=3 dynamical quarks. Using hadron and quark mass observables, it demonstrates a broad scaling window up to ~0.15 fm with only ~2% scaling corrections, confirming compatibility with previous results and validating the action’s suitability for large-scale unquenched phenomenological studies.

ABSTRACT

The goal of this study is to investigate the scaling behaviour of our 2 HEX action. For this purpose, we compute the $N_f=3$ spectrum and compare the results to our 6 EXP action. We find a large scaling window up to $\sim 0.15\,\mathrm{fm}$ along with small scaling corrections at the 2%-level and full compatibility with our previous study. As a second important observable to be tested for scaling, we chose the non-perturbatively renormalized quenched strange quark mass. Here we find a fairly flat scaling with a broad scaling range up to $\simeq 0.15\,\mathrm{fm}$ and perfect agreement with the literature.

Motivation & Objective

• To assess the scaling behavior of the 2 HEX smeared fermion action in Nf=3 lattice QCD simulations.
• To compare the hadron spectrum computed with the 2 HEX action to results from the 6 EXP action to validate consistency.
• To test the scaling of the non-perturbatively renormalized quenched strange quark mass across lattice spacings.
• To evaluate the continuum extrapolation of quark masses using both O(αa) and O(a²) scaling assumptions.
• To confirm the reliability of the 2 HEX action for future large-scale unquenched lattice QCD studies.

Proposed method

• Employed a tree-level improved Symanzik gauge action with c1 = -1/12 and c0 = 5/3 for the gauge sector.
• Applied a tree-level improved clover fermion action with cSW = 1, coupled to gauge links smeared via a hybrid HYP-EXP procedure using weights (α1, α2, α3) = (0.95, 0.76, 0.38).
• Used correlated cosh or sinh fits to hadronic correlation functions to extract masses, avoiding excited state contamination.
• Computed the PCAC quark mass via plateau fitting of the axial current-to-pion correlator ratio.
• Applied non-perturbative RI method with trace subtraction to compute renormalization constants for quark masses.
• Performed continuum extrapolation using both O(αa) and O(a²) scaling assumptions, with systematic error estimation via fit range and scale variation.

Experimental results

Research questions

• RQ1 Does the 2 HEX smeared fermion action exhibit a broad scaling window for hadron masses in Nf=3 simulations?
• RQ2 How do scaling corrections for hadron masses compare between the 2 HEX and 6 EXP actions?
• RQ3 To what extent does the non-perturbatively renormalized quenched strange quark mass scale consistently across lattice spacings?
• RQ4 Which scaling assumption—O(αa) or O(a²)—better describes the continuum limit of the quark mass?
• RQ5 Can the 2 HEX action be reliably used in large-scale unquenched lattice QCD simulations based on scaling and condition number analysis?

Key findings

• The 2 HEX action exhibits a broad scaling window for hadron masses extending up to ~0.15 fm with maximum scaling corrections of ~2%.
• Hadron mass continuum extrapolations favor O(a²) scaling, though O(αa) scaling is also compatible and used for systematic error estimation.
• The non-perturbatively renormalized quenched strange quark mass shows flat scaling up to ~0.15 fm, with excellent agreement with the literature.
• The continuum limit of the ratio ZS(3.5 GeV)/ZS(2.1 GeV) is flat, supporting reliable matching to perturbation theory.
• The combined result for the MS-bar strange quark mass is msMS(2 GeV) = 101.4(1.5)(1.1) MeV, with systematic uncertainties not including assumptions on ms/mud and r0.
• The 2 HEX action significantly reduces the condition number of the Wilson-Dirac operator at small quark masses, enhancing numerical stability for large-scale simulations.