Lattice QCD at the physical point: simulation and analysis details

• Published in: The journal of high energy physics Vol. 2011; no. 8
• Main Authors: Dürr, S., Fodor, Z., Hoelbling, C., Katz, S. D., Krieg, S., Kurth, T., Lellouch, L., Lippert, T., Szabó, K. K., Vulvert, G.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01-08-2011; Springer Nature B.V; Springer Verlag (Germany)
• Subjects: Algorithms; Chiral dynamics; Classical and Quantum Gravitation; Computer simulation; Elementary Particles; Fermions; Flavor (particle physics); High energy physics; High Energy Physics - Lattice; High Energy Physics - Phenomenology; Mud; Perturbation theory; Physics; Physics and Astronomy; Pions; Quantum chromodynamics; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Relativity Theory; Scaling; String Theory; Lattice QCD; Lattice Gauge Field Theories
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP08(2011)148

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
π
2
/m
ud
and
F
π
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
(
μ
,
μ
′) are given. This procedure is shown to reproduce the known value of
r
0
m
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.