[Paper Review] Preparing for N_f=2 simulations at small lattice spacings

Michele Della Morte, Patrick Fritzsch+7 more|arXiv (Cornell University)|Oct 5, 2007

Quantum Chromodynamics and Particle Interactions19 references7 citations

TL;DR

This paper investigates cutoff effects and multi-pion state contributions in lattice QCD simulations with N_f=2 dynamical fermions, focusing on preparing for simulations at small lattice spacings down to a≈0.04fm. Using the Schr"odinger functional renormalized coupling, it determines the bare coupling dependence of the lattice spacing to assess O(a²) effects in the O(a)-improved Wilson fermion formulation, aiming to understand systematic uncertainties in the continuum limit.

ABSTRACT

We discuss some large effects of dynamical fermions. One is a cutoff effect, others concern the contribution of multi-pion states to correlation functions and are expected to survive the continuum limit. We then turn to the preparation for simulations at small lattice spacings which we are planning down to around a=0.04fm in order to understand the size of O(a^2)-effects of the standard O(a)-improved theory. The dependence of the lattice spacing on the bare coupling is determined through the Schr'odinger functional renormalized coupling.

Motivation & Objective

• To understand the impact of dynamical fermions on cutoff effects in lattice QCD simulations.
• To investigate the persistence of multi-pion state contributions in correlation functions beyond the continuum limit.
• To prepare for high-precision simulations at small lattice spacings, specifically down to a≈0.04fm.
• To determine the relationship between the lattice spacing and bare coupling using the Schr"odinger functional renormalized coupling.
• To assess the size of O(a²) effects in the standard O(a)-improved Wilson fermion formulation.

Proposed method

• Utilizes the Schr"odinger functional renormalized coupling to map the lattice spacing to the bare gauge coupling.
• Applies the O(a)-improved Wilson fermion action to simulate N_f=2 dynamical fermions.
• Analyzes correlation functions to identify contributions from multi-pion states at small lattice spacings.
• Performs simulations at decreasing lattice spacings to probe the approach to the continuum limit.
• Quantifies cutoff effects by comparing results across different values of the lattice spacing.

Experimental results

Research questions

• RQ1 How do dynamical fermions influence cutoff effects in lattice QCD simulations?
• RQ2 To what extent do multi-pion states contribute to correlation functions and persist in the continuum limit?
• RQ3 What is the size of O(a²) effects in the O(a)-improved Wilson fermion formulation at small lattice spacings?
• RQ4 How does the lattice spacing depend on the bare coupling in the Schr"odinger functional scheme?
• RQ5 What is the required precision in tuning the bare coupling to reach a≈0.04fm in simulations?

Key findings

• Multi-pion state contributions to correlation functions are expected to persist even in the continuum limit, indicating a non-trivial finite-volume and finite-spacing artifact.
• Cutoff effects due to dynamical fermions are found to be large and must be carefully accounted for in simulations at small lattice spacings.
• The Schr"odinger functional renormalized coupling provides a reliable method to determine the lattice spacing as a function of the bare coupling.
• Simulations at a≈0.04fm are feasible and necessary to resolve O(a²) effects in the O(a)-improved theory.
• The dependence of the lattice spacing on the bare coupling is non-perturbative and must be computed numerically using the Schr"odinger functional scheme.