REVIEW
2+1 flavor domain wall QCD on a (2 fm)^3 lattice: light meson spectroscopy with Ls = 16
High Energy Physics - Lattice · Submitted 17 Jan 2007 · 30 references
Pith's verdict: A solid, honest first 2+1-flavor domain wall ensemble paper; the physics numbers rest on a linear chiral fit that the data cannot test, and the authors say so.
T0 · AI review
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Referee report
The paper
The paper claims
The first 2+1-flavor domain wall lattice simulation gives $f_�� = 127(4)$ MeV, $f_K = 157(5)$ MeV and $f_K/f_�� = 1.24(2)$, matching experiment with statistical errors only.
The reading
What carries the argument
The load-bearing object is the residual mass $m_{res}$, which for domain wall fermions enters as a simple additive renormalization: the chiral limit sits at $m_f + m_{res} = 0$ rather than $m_f = 0$. That single replacement is what lets the authors extrapolate meson masses and decay constants with a straight line in $(m + m_{res})$ and treat the leftover chiral symmetry breaking as a small, quantified perturbation rather than an unknown. The second piece of machinery is the rational hybrid Monte Carlo with a partial-fraction split of the fermion force into light and heavy poles, evaluated on three Sexton-Weingarten timescales; the reworked variant evaluates each determinant ratio with a single pseudo-fermion field and preconditions the light quark by the strange quark, which allows a coarser integration step at higher acceptance.
Extended reading notes
Core claim
With the fifth dimension held at $L_s = 16$, the residual chiral symmetry breaking in these ensembles amounts to an additive mass shift $m_{res} = 0.00308(4)$, roughly a third of the lightest simulated quark mass. Using three light sea masses ($0.85 m_s$, $0.59 m_s$, $0.33 m_s$) plus a strange sea mass near the physical $m_s$, and fitting linearly in $(m + m_{res})$, the collaboration extracts $f_�� = 127(4)$ MeV, $f_K = 157(5)$ MeV and $f_K/f_�� = 1.24(2)$. Two independent routes to the decay constant agree: one from local axial-vector correlators normalized by $Z_A = 0.7162(2)$, the other from Coulomb-gauge wall sources normalized numerically by the ratio $N_W$. The same data give a lattice scale $a^{-1} = 1.62(4)$ GeV, consistent across three methods (the $��$ mass, $r_0$ from the static potential, and the method of lattice planes), and bare quark masses $��m = 0.00162(8)$ and $m_s = 0.0390(21)$ in lattice units.
Load-bearing premise
The physical values of $f_��$, $f_K$ and the quark masses rest on a straight-line extrapolation in $(m + m_{res})$, justified only because the simulated pion masses (roughly 400 to 627 MeV) are too heavy for next-to-leading-order chiral perturbation theory to fit; if the true dependence carries curvature or chiral logs between the simulated points and the physical point, the quoted numbers shift by an amount the paper does not bound.
Editorial extensions
If this is right
- Because the two independent determinations of $f_P$ — the point-source route through $Z_A$ and the wall-source route through $N_W$ — agree within errors, the collaboration has an internal cross-check that can be carried over to other quantities computed on the same ensembles.
- The measured $m_{res} = 0.00308(4)$ at $L_s = 16$ sets a concrete budget for residual chiral symmetry breaking at this lattice spacing, replacing the looser $L_s = 8$ situation from earlier work.
- The reworked algorithm delivers more than a factor of two in speed and visibly better topological-charge tunneling, which is what makes the announced larger-volume runs at lighter quark masses affordable.
- Three mutually consistent scale determinations ($1.61(3)$, $1.63(5)$ and $1.62(5)$ GeV) give a stable conversion between lattice and physical units for the derived quark masses and decay constants.
Reading between the lines
- The physical light point, expressed as $m + m_{res} = 0.00162$, lies below $m_{res}$ itself, so the linear fit is genuinely a short extrapolation in the shifted variable rather than a long one in the bare mass; the announced $(3~fm)^3$ run at lighter masses will show directly whether curvature appears over that interval and how much it moves $f_��$.
- The authors report that separate next-to-leading-order chiral fits to masses and to decay constants each work while a simultaneous fit fails badly; that failure is itself information about where the chiral expansion breaks, and a joint fit that succeeds at lighter masses would be a sharper test than either fit alone.
- The long-range autocorrelations seen in the original algorithm but not in the reworked one suggest that part of the error inflation (the factor of 1.5 applied to the largest statistical error) reflects sampling rather than physics, and could shrink with better topological mobility rather than more statistics.
- Finite-volume effects at $(2~fm)^3$ are assumed negligible for pseudoscalars down to $m_P/m_V \approx 0.5$; comparing the same observables across the two planned volumes would convert that assumption into a measured systematic.
Original abstract
We present results for light meson masses and pseudoscalar decay constants from the first of a series of lattice calculations with 2+1 dynamical flavors of domain wall fermions and the Iwasaki gauge action. The work reported here was done at a fixed lattice spacing of about 0.12 fm on a 16^3\times32 lattice, which amounts to a spatial volume of (2 fm)^3 in physical units. The number of sites in the fifth dimension is 16, which gives m_{res} = 0.00308(4) in these simulations. Three values of input light sea quark masses, m_l^{sea} \approx 0.85 m_s, 0.59 m_s and 0.33 m_s were used to allow for extrapolations to the physical light quark limit, whilst the heavier sea quark mass was fixed to approximately the physical strange quark mass m_s. The exact rational hybrid Monte Carlo algorithm was used to evaluate the fractional powers of the fermion determinants in the ensemble generation. We have found that f_\pi = 127(4) MeV, f_K = 157(5) MeV and f_K/f_\pi = 1.24(2), where the errors are statistical only, which are in good agreement with the experimental values.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
We present results for light meson masses and pseudoscalar decay constants from the first of a series of lattice calculations with 2+1 dynamical flavors of domain wall fermions and the Iwasaki gauge action. The work reported here was done at a fixed lattice spacing of about 0.12 fm on a 16^3\times32 lattice, which amounts to a spatial volume of (2 fm)^3 in physical units. The number of sites in the fifth dimension is 16, which gives m_{res} = 0.00308(4) in these simulations. Three values of input light sea quark masses, m_l^{sea} \approx 0.85 m_s, 0.59 m_s and 0.33 m_s were used to allow for extrapolations to the physical light quark limit, whilst the heavier sea quark mass was fixed to approximately the physical strange quark mass m_s. The exact rational hybrid Monte Carlo algorithm was used to evaluate the fractional powers of the fermion determinants in the ensemble generation. We have found that f_\pi = 127(4) MeV, f_K = 157(5) MeV and f_K/f_\pi = 1.24(2), where the errors are statistical only, which are in good agreement with the experimental values.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We present results for light meson masses and pseudoscalar decay constants from the first of a series of lattice calculations with 2+1 dynamical flavors of domain wall fermions and the Iwasaki gauge action. | contribution 1.00 | 0.96 | 0.15 | asserted 0.99 |
| s1 | The work reported here was done at a fixed lattice spacing of about 0.12 fm on a 16^3\times32 lattice, which amounts to a spatial volume of (2 fm)^3 in physical units. | method 0.99 | 0.92 | 0.03 | asserted 0.99 |
| s2 | The number of sites in the fifth dimension is 16, which gives m_{res} = 0.00308(4) in these simulations. | method 0.93 | 0.93 | 0.03 | asserted 1.00 |
| s3 | Three values of input light sea quark masses, m_l^{sea} \approx 0.85 m_s, 0.59 m_s and 0.33 m_s were used to allow for extrapolations to the physical light quark limit, whilst the heavier sea quark mass was fixed to approximately the physical strange quark mass m_s. | method 0.99 | 0.93 | 0.03 | asserted 0.99 |
| s4 | The exact rational hybrid Monte Carlo algorithm was used to evaluate the fractional powers of the fermion determinants in the ensemble generation. | method 1.00 | 0.80 | 0.02 | asserted 1.00 |
| s5 | We have found that f_\pi = 127(4) MeV, f_K = 157(5) MeV and f_K/f_\pi = 1.24(2), where the errors are statistical only, which are in good agreement with the experimental values. | result 1.00 | 0.97 | 0.62 | asserted 1.00 |
What was examined, and what was not
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Figures
Showing 10 of the paper's 14 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:hep-lat/0701013 by the authors.
References
How the literature uses it
52 arXiv papers cite this in 77 sentences
Papers citing it · 38 sentences without a confident label
Uses its method or tool 10 papers
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These include: a) the use of domain wall fermions with good chiral symmetry [ref] , b) the implementation of domain wall fermions in dynamical simulations with 2 + 1 flavours of light quarks [ref] , and c) the use of SU(2) ChPT for chiral extrapolations of 2+1 flavour simulations, first exploited by the RBC-UKQCD collaborations [ref] .
Continuum Limit of $B_K$ from 2+1 Flavor Domain Wall QCD · Conclusions · 0.86
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From the amplitudes $N_O_1O_2^s_1s_2$, we construct $f_π$ following Ref [ref] , [equation] where $Z_A$ is the renormalization constant of the local axial current $A_μ$, calculated in Ref. [ref] .
Light Quark Mass Reweighting · Pion Mass and Decay Constant · 1.00
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The trick of combining periodic and anti-periodic boundary conditions for valence quarks [ref] is used in these measurements.
Finite-size scaling tests for SU(3) lattice gauge theory with color sextet fermions · Numerical techniques and background · 1.00
Uses its data or values 17 papers
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We apply reweighting to $2+1$ flavor dynamical DWF and Iwasaki gluon configurations generated by the RBC-UKQCD collaborations [ref] .
Full QED+QCD Low-Energy Constants through Reweighting · Introduction · 0.96
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Using the data from Ref. [ref] , we extrapolated to stronger coupling in order to estimate the bare input parameters: the gauge coupling, input light quark mass, and input strange quark mass ($β$, $m_l$, $m_s$), appropriate for the region of the finite-temperature transition at $N_t=8$.
The finite temperature QCD using 2+1 flavors of domain wall fermions at N_t = 8 · Simulation Details · 0.97
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In the numerical evaluation we then use $⟨q̅ q⟩= - (272(5) )^3$ [ref] , and $f_ρ^T/f_ρ= 0.68(2)$ [ref] , as obtained in lattice QCD, together with $f_ρ^exp≃208$ MeV and $m_ρ=0.77$ GeV [ref] .] yields $χ_ℓ^(2 GeV)= 1.9(1) ^-2$, in good agreement with the QCDSR result, $χ_ℓ^(2 GeV)= 2.1(2) ^-2$ [ref] , but both being considerably different from the values advocated in Refs. [ref] .
Lattice QCD determination of the normalization of the leading-twist photon distribution amplitude and susceptibility of the quark condensate · Introduction · 0.97
Compares with it 2 papers
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We performed [ref] lattice simulations of the domain wall fermion which preserves the chiral symmetry in the zero - mass limit using the full QCD gauge configurations of the RBC/UKQCD collaboration of $16^3×32×16$ lattice [ref] and compared with results of staggered fermion of the MILC collaboration [ref] .
The self-dual gauge fields and the domain wall fermion zero modes · Introduction · 0.85
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Our measured values are roughly consistent with those found by the RBC and UKQCD collaborations [ref] .
Electromagnetic mass splittings of the low lying hadrons and quark masses from 2+1 flavor lattice QCD+QED · Electromagnetic effects in $m_res$ · 0.98
Cites it as background 7 papers
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The RBC and UKQCD collaborations have recently started large-scale lattice QCD calculations [ref] with dynamical domain wall fermions and renormalization-group-improved gauge actions.
The bottomonium spectrum from lattice QCD with 2+1 flavors of domain wall fermions · Introduction · 0.90
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RIKEN-BNL-Columbia (RBC) and UKQCD collaborations have been jointly generating dynamical 2+1-flavor domain-wall fermions (DWF) numerical lattice-QCD ensembles for over a decade now [ref] .
Nucleon isovector form factors from physical-mass 2+1-flavor dynamical domain-wall QCD · Introduction · 0.96
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For the Iwasaki gauge action, the residual chiral symmetry breaking has been extensively studied by the RBC-UKQCD collaboration for $β≥2.13$ and $L_s=16$ [ref] .
The finite temperature QCD using 2+1 flavors of domain wall fermions at N_t = 8 · Residual Mass · 0.96
Discussion
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