Lattice QCD at the physical point: Simulation and analysis details

TL;DR

This paper presents a detailed methodology for high-precision lattice QCD simulations at the physical point, including algorithm choices, scale setting, finite volume effects, and quark mass determinations, with extensive validation and error analysis.

Contribution

It provides a comprehensive account of simulation techniques, scale setting, and systematic error control for precise light quark mass calculations in 2+1 flavor QCD.

Findings

Precise determination of light quark masses m_{ud} and m_s.

Validation of scaling properties and finite volume effects.

Consistent results with chiral perturbation theory and dispersion theory.

Abstract

We give details of our precise determination of the light quark masses m_{ud}=(m_u+m_d)/2 and m_s in 2+1 flavor QCD, with simulated pion masses down to 120 MeV, at five lattice spacings, and in large volumes. The details concern the action and algorithm employed, the HMC force with HEX smeared clover fermions, the choice of the scale setting procedure and of the input masses. After an overview of the simulation parameters, extensive checks of algorithmic stability, autocorrelation and (practical) ergodicity are reported. To corroborate the good scaling properties of our action, explicit tests of the scaling of hadron masses in N_f=3 QCD are carried out. Details of how we control finite volume effects through dedicated finite volume scaling runs are reported. To check consistency with SU(2) Chiral Perturbation Theory the behavior of M_\pi^2/m_{ud} and F_\pi as a function of m_{ud} is investigated. Details of how we use the RI/MOM procedure with a separate continuum limit of the running of the scalar density R_S(\mu,\mu') are given. This procedure is shown to reproduce the known value of r_0m_s in quenched QCD. Input from dispersion theory is used to split our value of m_{ud} into separate values of m_u and m_d. Finally, our procedure to quantify both systematic and statistical uncertainties is discussed.