[Paper Review] Determination of LambdaMS from the gluon and ghost propagators in Landau gauge

André Sternbeck, Kim Maltman+2 more|arXiv (Cornell University)|Dec 10, 2012

Quantum Chromodynamics and Particle Interactions17 references4 citations

TL;DR

This paper presents a high-precision lattice QCD determination of the $ar{\mathrm{MS}}$-scheme $\Lambda_{\mathrm{MS}}^{(N_f)}$ parameter using gluon and ghost propagators in Landau gauge. By modeling leading hypercubic lattice artifacts via a 1-loop Lattice Perturbation Theory (LPT) and fitting data at diagonal momenta, the method isolates $r_0\Lambda_{\mathrm{MS}}^{(N_f)}$ without assuming the origin of deviations from 4-loop running, yielding $r_0\Lambda_{\mathrm{MS}}^{(0)} = 0.637(32)$ and $r_0\Lambda_{\mathrm{MS}}^{(2)} = 0.789(52)$, consistent with literature.

ABSTRACT

We give an update on our lattice determination of r_0 LambdaMS for different Nf. Our calculations employ the strong coupling constant in the minimal MOM scheme for QCD in Landau gauge, and we report here on our progress towards a quantitative understanding of the intrinsic lattice discretization artifacts at large momenta. This is important for a high-precision analysis, in particular for the unquenched calculations for which the access to small lattice spacings is restricted by the available gauge configurations.

Motivation & Objective

• To improve the precision of $r_0\Lambda_{\mathrm{MS}}^{(N_f)}$ determinations in lattice QCD by minimizing systematic errors from lattice artifacts.
• To quantify hypercubic lattice corrections at large momenta, which distort the 4-loop running of the strong coupling constant.
• To enable accurate extraction of $\Lambda_{\mathrm{MS}}^{(N_f)}$ from unquenched configurations with limited access to small lattice spacings.
• To validate a new fitting approach that separates lattice artifacts from physical running, avoiding assumptions about non-perturbative contributions.

Proposed method

• Uses the Minimal MOM (MOM) scheme for the strong coupling $\alpha_s^{\mathrm{MM}}$, defined via the product of gluon and ghost dressing functions from lattice Landau gauge propagators.
• Applies a 1-loop Lattice Perturbation Theory (LPT) calculation to model the leading hypercubic lattice corrections to $\alpha_s^{\mathrm{MM}}$.
• Fits lattice data at diagonal momenta to an ansatz including $\alpha_s^{\mathrm{MM}}$ at 4-loop running and $g_0^6$-suppressed corrections proportional to $(ap)^2$ and $(ap)^4$.
• Uses $r_0$-scale normalization to map data across different lattice spacings and volumes, ensuring momentum-space consistency.
• Restricts fitting windows to high momenta ($r_0^2p^2 \geq 600$) to avoid finite-volume and low-momentum nonperturbative effects.
• Employs $r_0/a$ values from literature and chiral extrapolation for $N_f=2$, with $N_f=2+1$ data from QCDSF configurations at $\beta=5.50$.

Experimental results

Research questions

• RQ1 How can lattice artifacts in the strong coupling constant be quantitatively modeled at large momenta in Landau gauge QCD?
• RQ2 To what extent do hypercubic lattice symmetries distort the 4-loop running of $\alpha_s^{\mathrm{MM}}$ in unquenched simulations?
• RQ3 Can $r_0\Lambda_{\mathrm{MS}}^{(N_f)}$ be extracted without assuming the source of deviations from 4-loop running?
• RQ4 How well does the LPT-based correction ansatz describe lattice data across different $N_f$ and lattice spacings?

Key findings

• The 1-loop LPT calculation successfully models the leading hypercubic lattice corrections to $\alpha_s^{\mathrm{MM}}$, enabling accurate extraction of $r_0\Lambda_{\mathrm{MS}}^{(N_f)}$.
• The fitting ansatz including $c_2$ and $c_4$ parameters describes the lattice data well across $N_f=0$ and $N_f=2$ configurations, with $r_0^2p^2 \geq 600$.
• The extracted value $r_0\Lambda_{\mathrm{MS}}^{(0)} = 0.637(32)$ is consistent with recent literature values, validating the method.
• For $N_f=2$, the result $r_0\Lambda_{\mathrm{MS}}^{(2)} = 0.789(52)$ is in agreement with external estimates, confirming the robustness of the approach.
• Preliminary fits for $N_f=2+1$ at $\beta=5.50$ show good agreement with existing $\Lambda_{\mathrm{MS}}^{(3)}$ estimates, indicating the method's scalability.
• The method reduces reliance on assumptions about non-perturbative effects (e.g., dim-2 condensate) by isolating lattice artifacts through controlled fitting.