[Paper Review] Light hadron spectrum and quark masses in 2+1 flavor QCD

Cp-Pacs, Jlqcd Collaborations+17 more|arXiv (Cornell University)|Sep 26, 2005

Particle physics theoretical and experimental studies3 references3 citations

TL;DR

This paper presents a 2+1 flavor lattice QCD simulation using the non-perturbatively O(a)-improved Wilson quark action and Iwasaki gauge action to compute the light hadron spectrum and quark masses. The continuum limit extrapolation of meson masses and quark masses yields $ m_{ud}^{\overline{MS}}(2~\text{GeV}) = 3.34(23)~\text{MeV} $ and $ m_s^{\overline{MS}}(2~\text{GeV}) = 86.7(5.9)~\text{MeV} $, in good agreement with experiment and consistent with previous Nf=2 results.

ABSTRACT

CP-PACS and JLQCD collaborations are carrying out a joint project of the 2+1 flavor full QCD simulation. Gauge configurations are generated for the non-perturbatively $O(a)$-improved Wilson quark action and the Iwasaki gauge action using PHMC algorithm at three lattice spacings, $a\sim 0.076$, 0.010 and 0.122 fm, with a fixed physical volume $(2.0 fm)^3$. We present analysis for the light meson spectrum and quark masses in the continuum limit, which are determined using data obtained from the simulations at the two coarser lattices. Our simulations reproduce experimental values of meson masses. The ud and strange quark masses turn out to be $m_{ud}^{\bar{MS}}(μ=2 GeV)=3.34(23) MeV$ and $m_s^{\bar{MS}}(μ=2 GeV)=86.7(5.9) MeV$. We also show preliminary results at our finest lattice spacing for which simulations are still being continued.

Motivation & Objective

• To compute the light hadron spectrum and quark masses in 2+1 flavor QCD with dynamical up, down, and strange quarks.
• To reduce systematic errors in lattice QCD by including dynamical quarks beyond the quenched and Nf=2 approximations.
• To achieve continuum limit results using non-perturbatively O(a)-improved actions and multiple lattice spacings.
• To compare results from different quark mass definitions (VWI and AWI) and assess scaling violations.

Proposed method

• Simulations use the Iwasaki gauge action and non-perturbatively O(a)-improved Wilson quark action with clover improvement.
• Gauge configurations are generated via the Polynomial Hybrid Monte Carlo (PHMC) algorithm at three lattice spacings: a ≈ 0.076, 0.099, and 0.122 fm, with fixed physical volume (2.0 fm)³.
• Meson masses are extracted from time-correlators of pseudoscalar, vector, and axial-vector currents using smeared sources and point sinks.
• Quark masses are determined using both vector and axial-vector Ward identity definitions, with continuum extrapolation via quadratic fits.
• Renormalization is performed using tadpole-improved one-loop perturbation theory for Z-factors and four-loop running to μ=2 GeV.
• Statistical errors are estimated via the binned jackknife method with 100-trajectory bins.

Experimental results

Research questions

• RQ1 What is the light hadron spectrum in 2+1 flavor QCD in the continuum limit, and how does it compare to experiment?
• RQ2 How do the up and strange quark masses in the $ \overline{MS} $ scheme at μ=2 GeV compare to experimental values?
• RQ3 Which quark mass definition (VWI or AWI) yields smaller scaling violations and more reliable continuum extrapolation?
• RQ4 How do the results from 2+1 flavor QCD compare to those from quenched and Nf=2 QCD simulations?
• RQ5 What is the impact of finite lattice spacing on the quark mass determination, and how can it be corrected?

Key findings

• The light hadron spectrum in the continuum limit agrees well with experimental values, confirming the reliability of the 2+1 flavor simulation.
• The up and down quark mass in the $ \overline{MS} $ scheme at μ=2 GeV is determined to be $ 3.34(23)~\text{MeV} $.
• The strange quark mass in the $ \overline{MS} $ scheme at μ=2 GeV is determined to be $ 86.7(5.9)~\text{MeV} $.
• The AWI quark mass definition exhibits smaller scaling violations than the VWI definition, leading to a more reliable continuum extrapolation.
• The continuum limit results for quark masses in 2+1 flavor QCD are consistent with those from Nf=2 QCD, with no significant deviations within errors.
• Preliminary results at the finest lattice spacing (a ≈ 0.076 fm) show consistency with the continuum extrapolation, though statistics remain limited.