High Energy Physics - Lattice · arXiv:1006.1164 v2 · submitted 7 Jun 2010
Non-perturbative renormalization of quark mass in Nf=2+1 QCD with the Schroedinger functional scheme
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“The regularization independent step scaling function of the quark mass for the Nf=2+1 QCD is obtained in the continuum limit.”
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Abstract
We present an evaluation of the quark mass renormalization factor for Nf=2+1 QCD. The Schroedinger functional scheme is employed as the intermediate scheme to carry out non-perturbative running from the low energy region, where renormalization of bare mass is performed on the lattice, to deep in the high energy perturbative region, where the conversion to the renormalization group invariant mass or the MS-bar scheme is safely carried out. For numerical simulations we adopted the Iwasaki gauge action and non-perturbatively improved Wilson fermion action with the clover term. Seven renormalization scales are used to cover from low to high energy regions and three lattice spacings to take the continuum limit at each scale. The regularization independent step scaling function of the quark mass for the Nf=2+1 QCD is obtained in the continuum limit. Renormalization factors for the pseudo scalar density and the axial vector current are also evaluated for the same action and the bare couplings as two recent large scale Nf=2+1 simulations; previous work of the CP-PACS/JLQCD collaboration, which covered the up-down quark mass range heavier than mπ ∼ 500 MeV and that of PACS-CS collaboration for much lighter quark masses down to mπ = 155 MeV. The quark mass renormalization factor is used to renormalize bare PCAC masses in these simulations.
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How the main claim is stated: asserted 1.00
What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.11 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.33 · compares with prior results 0.54 · mentions code or data availability 0.02
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This table labels the abstract only (arXiv listing abstract v2). The number is the probability the classifier gave the label.
| Sentence | Role | The authors' own work | States the main conclusion | Strength |
|---|---|---|---|---|
| We present an evaluation of the quark mass renormalization factor for Nf=2+1 QCD. | contribution 1.00 | 0.96 | 0.17 | asserted 0.99 |
| The Schroedinger functional scheme is employed as the intermediate scheme to carry out non-perturbative running from the low energy region, where renormalization of bare mass is performed on the lattice, to deep in the high energy perturbative region, where the conversion to the renormalization group invariant mass or the MS-bar scheme is safely carried out. | method 0.99 | 0.72 | 0.09 | asserted 1.00 |
| For numerical simulations we adopted the Iwasaki gauge action and non-perturbatively improved Wilson fermion action with the clover term. | method 1.00 | 0.87 | 0.02 | asserted 1.00 |
| Seven renormalization scales are used to cover from low to high energy regions and three lattice spacings to take the continuum limit at each scale. | method 1.00 | 0.92 | 0.03 | asserted 0.99 |
| The regularization independent step scaling function of the quark mass for the Nf=2+1 QCD is obtained in the continuum limit. | result 0.98 | 0.95 | 0.43 | asserted 1.00 |
| Renormalization factors for the pseudo scalar density and the axial vector current are also evaluated for the same action and the bare couplings as two recent large scale Nf=2+1 simulations; previous work of the CP-PACS/JLQCD collaboration, which covered the up-down quark mass range heavier than $m_\pi\sim 500$ MeV and that of PACS-CS collaboration for much lighter quark masses down to $m_\pi=155$ MeV. | contribution 0.55 | 0.82 | 0.06 | asserted 1.00 |
| The quark mass renormalization factor is used to renormalize bare PCAC masses in these simulations. | contribution 0.51 | 0.74 | 0.11 | asserted 1.00 |
What kind of paper the classifier reports this is: simulation study 1.00 · evidence from simulation or computation 0.99
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,837 input tokens, $0.0002 reported.
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Cited by 10 Pith papers
Reviewed papers on Pith that cite this one. The full citation record
- Confirming the Existence of the strong CP Problem in Lattice QCD with the Gradient Flow hep-lat · Feb 2019
- The gradient flow coupling in the Schr\"odinger Functional hep-lat · Jan 2013
- Exploring Nf=2+1 QCD thermodynamics from the gradient flow hep-lat · Sep 2016
- Quark masses and low energy constants in the continuum from the tadpole improved clover ensembles hep-lat · Oct 2023
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- FLAG Review 2021 hep-lat · Nov 2021
- FLAG Review 2019 hep-lat · Feb 2019
- Review of lattice results concerning low-energy particle physics hep-lat · Jul 2016
- Review of lattice results concerning low energy particle physics hep-lat · Oct 2013
- FLAG Review 2024 hep-lat · Nov 2024
How the literature uses it
15 arXiv papers cite this in 21 sentences
Papers whose main result relates to this one's
States the same result 1 paper
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The regularization independent step scaling function of the quark mass is obtained in the continuum limit.
Non-perturbative renormalization of quark mass in Nf=2+1 QCD with the Schroedinger functional scheme · 0.99
Papers citing it · 10 sentences without a confident label
Uses its method or tool 2 papers
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Combining the RG evolutions for $Z_P$ and the coupling in both schemes, we can extract the mass renormalization constant $Z^MS_m(g_0,μ)$ in the MS scheme [ref] by [equation] where $L_max=4a$ will be applied.
Mass and Axial current renormalization in the Schr\"odinger functional scheme for the RG-improved gauge and the stout smeared $O(a)$-improved Wilson quark actions · Scale setting and mass renormalization · 0.89
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Since the coefficient respecting our SF setup is not available, we follow the prescription adopted in Ref. [ref] and determine it by fitting $δ_P,0$ to a linear function of $u$.
Running coupling constant and mass anomalous dimension of six-flavor SU(2) gauge theory · Step scaling function and its improvement · 1.00
Uses its data or values 4 papers
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In order to evaluate the mass renormalization constant $Z^MS_m(g_0,μ)$, we employ $σ_P(u)$ from Ref. [ref] and $σ(u)$ from Ref. [ref] .
Mass and Axial current renormalization in the Schr\"odinger functional scheme for the RG-improved gauge and the stout smeared $O(a)$-improved Wilson quark actions · Scale setting and mass renormalization · 0.96
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They have been generated [ref] using $N_f=2+1$ dynamical fermion flavors all regulated with a non-perturbative O($a$) clover-improved lattice fermion action and the Iwasaki gauge action.
Machine learning mapping of lattice correlated data · Correlation maps and translation invariance · 0.82
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In this work, as illustration, we use the values of $Z_P$ determined using the Schrödinger Functional scheme in Ref. [ref] at some low-energy scale.
Nonperturbative Renormalization of the Quark Chromoelectric Dipole Moment with the Gradient Flow:Power Divergences · Numerical Analysis · 1.00
Compares with it 2 papers
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This is a major achievement compared to a similar determinations in the past [ref] .
Non-perturbative running of quark masses in three-flavour QCD · Conclusions · 1.00
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This is in contrast with the quite strong time-dependence observed in [ref] for the correlators entering the definition of $$.
Non-perturbative renormalization of the axial current in $N_f = 3$ lattice QCD with Wilson fermions and tree-level improved gauge action · Results · 1.00
Cites it as background 1 paper
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Beside a successful application of the finite-size scaling technique in the case of pure Yang-Mills theory [ref] , the running coupling [ref] and quark mass [ref] have been computed non-perturbatively in QCD with different flavour content by ALPHA and other collaborations.
The gradient flow coupling in the Schr\"odinger Functional · Introduction · 0.93
What it cites · 34 sentences without a confident label
Uses the method or tool of 8 papers
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Since the step scaling function (SSF) $σ(u)$ for the running coupling has already been obtained [ref] , an evaluation of the RGI mass renormalization factor proceeds in the same way as given in Ref. [ref] , which we briefly summarize here. * We start by preparing the coupling step scaling function $σ(u)$, which gives the relation between the renormalized coupling constants when the renormalization scale is changed by a factor two, [equation] The renormalization scale is defined through a physical box size $L$ where the renormalized coupling $u=g^2(L)$ is evaluated in the SF scheme.
Precise determination of the strong coupling constant in Nf=2+1 lattice QCD with the Schr\"odinger functional scheme · Our strategy · 0.80
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Since the step scaling function (SSF) $σ(u)$ for the running coupling has already been obtained [ref] , an evaluation of the RGI mass renormalization factor proceeds in the same way as given in Ref. [ref] , which we briefly summarize here. * We start by preparing the coupling step scaling function $σ(u)$, which gives the relation between the renormalized coupling constants when the renormalization scale is changed by a factor two, [equation] The renormalization scale is defined through a physical box size $L$ where the renormalized coupling $u=g^2(L)$ is evaluated in the SF scheme.
Non-perturbative quark mass renormalization in two-flavor QCD · Our strategy · 0.80
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Since the step scaling function (SSF) $σ(u)$ for the running coupling has already been obtained [ref] , an evaluation of the RGI mass renormalization factor proceeds in the same way as given in Ref. [ref] , which we briefly summarize here. * We start by preparing the coupling step scaling function $σ(u)$, which gives the relation between the renormalized coupling constants when the renormalization scale is changed by a factor two, [equation] The renormalization scale is defined through a physical box size $L$ where the renormalized coupling $u=g^2(L)$ is evaluated in the SF scheme.
Non-perturbative quark mass renormalization in quenched lattice QCD · Our strategy · 0.80
Uses data or values from 5 papers
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The renormalization scale $μ$ is introduced through the RGI scale $Λ_MS$ evaluated in Ref. [ref] .
Precise determination of the strong coupling constant in Nf=2+1 lattice QCD with the Schr\"odinger functional scheme · Our strategy · 0.83
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Our goal is to renormalize the bare light quark masses and meson decay constants evaluated in two recent large-scale $N_f=2+1$ lattice QCD simulations employing non-perturbatively O(a) improved Wilson quark action; the work of CP-PACS/JLQCD Collaboration with relatively heavy pion mass of $m_π∼500$ MeV [ref] and that of PACS-CS collaboration with much lighter quark masses down to $m_π=155$ MeV [ref] .
2+1 Flavor Lattice QCD toward the Physical Point · Introduction · 0.83
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Our goal is to renormalize the bare light quark masses and meson decay constants evaluated in two recent large-scale $N_f=2+1$ lattice QCD simulations employing non-perturbatively O(a) improved Wilson quark action; the work of CP-PACS/JLQCD Collaboration with relatively heavy pion mass of $m_π∼500$ MeV [ref] and that of PACS-CS collaboration with much lighter quark masses down to $m_π=155$ MeV [ref] .
Light quark masses from unquenched lattice QCD · Introduction · 0.83
Compares with 1 paper
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For the old CP-PACS/JLQCD work of Ref. [ref] results with $K$ and $ϕ$ meson input are plotted (filled squares and triangles) together with perturbatively renormalized masses using tadpole improved renormalization factor (open squares and circles).
Light quark masses from unquenched lattice QCD · RGI mass renormalization factor · 0.85
Cites as background 1 paper
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Some years ago CP-PACS and JLQCD Collaborations jointly performed an $N_f=2+1$ simulation with the $O(a)$ improved Wilson action and the Iwasaki gauge action [ref] .
Light quark masses from unquenched lattice QCD · $Z_P$ at low energy scale · 0.90
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