[Paper Review] Chiral Limit and Light Quark Masses in 2+1 Flavor Domain Wall QCD

UKQCD Collaboration, Min Ren Lin+1 more|arXiv (Cornell University)|Oct 2, 2007

Quantum Chromodynamics and Particle Interactions15 references4 citations

TL;DR

This paper presents a precision determination of light and strange quark masses and pion/kaon decay constants using 2+1 flavor domain wall fermion lattice QCD simulations at a lattice spacing of ~0.1 fm. By applying SU(2)×SU(2) and SU(3)×SU(3) chiral perturbation theory to data with pion masses as light as 250 MeV, the authors extract physical quark masses and $|V_{us}|$ with controlled extrapolation errors, finding $m_l = 3.72(16)$ MeV and $m_s = 107.3(4.5)$ MeV in the $\overline{\text{MS}}$ scheme at 2 GeV using non-perturbative RI/MOM renormalization.

ABSTRACT

We present results for meson masses and decay constants measured on 24^3x64 lattices using the domain wall fermion formulation with an extension of the fifth dimension of L_s=16 for N_f=2+1 dynamical quark flavors. The lightest dynamical meson mass in our set-up is around 331 MeV, while partially quenched mesons reach masses as low as 250 MeV. The applicability of SU(3)xSU(3) and SU(2)xSU(2) (partially quenched) chiral perturbation theory will be compared and we quote values for the low-energy constants from both approaches. We will extract the average light quark and strange quark masses and use a non-perturbative renormalization technique (RI/MOM) to quote their physical values. The pion and kaon decay constants are determined at those values from our chiral fits and their ratio is used to obtain the CKM-matrix element |V_us|. The results presented here include statistical errors only.

Motivation & Objective

• To determine the physical light and strange quark masses from lattice QCD simulations with controlled chiral extrapolation errors.
• To assess the applicability of SU(2)×SU(2) and SU(3)×SU(3) chiral perturbation theory in the regime of light pion masses (~250 MeV).
• To extract the CKM matrix element $|V_{us}|$ from the ratio of kaon to pion decay constants using physical quark masses.
• To apply non-perturbative RI/MOM renormalization to convert bare lattice quark masses to the $\overline{\text{MS}}$ scheme at 2 GeV.
• To compare the reliability of two-flavor vs. three-flavor chiral fits in the context of domain wall fermions with small residual mass.

Proposed method

• Simulations were performed on $24^3 \times 64$ lattices with $N_f = 2+1$ dynamical domain wall fermions and $L_s = 16$ in the fifth dimension, using $\beta = 2.13$ and tuned strange quark mass ($am_s = 0.04$).
• Four light sea quark masses ($am_l = 0.005, 0.01, 0.02, 0.03$) and valence quark masses down to $am = 0.001$ were used to enable chiral extrapolations and partially quenched analyses.
• Pseudoscalar meson masses and decay constants were extracted from correlators using wall sources and wall/local sinks, with statistical errors only reported.
• SU(2)×SU(2) and SU(3)×SU(3) chiral perturbation theory were applied to fit the data, with the latter used to extract low-energy constants and the former used for reliable pion and kaon sector extrapolations.
• Non-perturbative RI/MOM scheme was used to compute the quark mass renormalization factor $Z_m^{\overline{\text{MS}}}(2\,\text{GeV}) = 1.656(48)(11)$, enabling conversion of bare lattice masses to physical $\overline{\text{MS}}$ values.
• The physical quark masses were obtained via $m_x = Z_m^{\overline{\text{MS}}}(2\,\text{GeV}) \cdot (1/a) \cdot am_x^{\text{phys}}$, with $a \approx 0.1$ fm.

Experimental results

Research questions

• RQ1 Does SU(2)×SU(2) chiral perturbation theory provide a more reliable extrapolation for pion masses below 300 MeV than SU(3)×SU(3) in domain wall fermion simulations?
• RQ2 What is the physical value of the average light quark mass ($m_l$) and strange quark mass ($m_s$) in the $\overline{\text{MS}}$ scheme at 2 GeV, with controlled systematic errors?
• RQ3 To what extent does the inclusion of partially quenched strange quarks affect the reliability of kaon mass and decay constant extrapolations in the absence of a second dynamical strange quark mass point?
• RQ4 How do the results for $f_\pi$ and $f_K$ at physical quark masses compare with experimental values, and what is the resulting value of $|V_{us}|$?
• RQ5 What is the size of the residual mass effect on the quark mass renormalization and its impact on the final physical quark mass values?

Key findings

• The physical average light quark mass was determined to be $m_l = 3.72(16)$ MeV in the $\overline{\text{MS}}$ scheme at 2 GeV, with statistical errors only.
• The strange quark mass was found to be $m_s = 107.3(4.5)$ MeV in the $\overline{\text{MS}}$ scheme at 2 GeV, yielding a ratio $m_l : m_s = 1 : 28.8(4)$.
• The pion and kaon decay constants were extrapolated to physical quark masses using chiral fits, enabling a determination of $|V_{us}|$ from the ratio $f_K / f_\pi$.
• The use of SU(2)×SU(2) chiral perturbation theory for the pion sector provided a more reliable fit than SU(3)×SU(3) at the lightest pion masses studied (~250 MeV).
• The non-perturbative RI/MOM renormalization technique yielded $Z_m^{\overline{\text{MS}}}(2\,\text{GeV}) = 1.656(48)(11)$, with the second error estimating residual chiral symmetry breaking effects.
• The results suggest that chiral perturbation theory at NLO is applicable in the pion mass range down to ~250 MeV when using two-flavor chiral fits, improving extrapolation control.