Determination of the chiral condensate from QCD Dirac spectrum on the lattice

Fukaya, Hidenori; Aoki, Sadao; Chiu, Ting‐Wai; Hashimoto, S.; Kaneko, T.; Noaki, J.; Onogi, Tetsuya; Yamada, Norikazu

doi:10.1103/physrevd.83.074501

Cited by 46 publications

(53 citation statements)

References 68 publications

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“…The final results, however, are independent of this intermediate step: they are expressed as ratios of quantities of the two-flavor theory only. It is worth noting that there were several exploratory studies of the spectral density of the Dirac operator in QCD; see for instance [4,9,10]. The approach pursued here is rather general (preliminary results were presented in Ref.…”

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confidence: 99%

Chiral Symmetry Breaking in QCD with Two Light Flavors

et al. 2015

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A distinctive feature of the presence of spontaneous chiral symmetry breaking in QCD is the condensation of low modes of the Dirac operator near the origin. The rate of condensation must be equal to the slope of M 2 π F 2 π =2 with respect to the quark mass m in the chiral limit, where M π and F π are the mass and the decay constant of the Nambu-Goldstone bosons. We compute the spectral density of the (Hermitian) Dirac operator, the quark mass, the pseudoscalar meson mass, and decay constant by numerical simulations of lattice QCD with two light degenerate Wilson quarks. We use lattices generated by the Coordinated Lattice Simulation (CLS) group at three values of the lattice spacing in the range 0.05-0.08 fm, and for several quark masses corresponding to pseudoscalar mesons masses down to 190 MeV. Thanks to this coverage of parameters space, we can extrapolate all quantities to the chiral and continuum limits with confidence. The results show that the low quark modes do condense in the continuum as expected by the Banks-Casher mechanism, and the rate of condensation agrees with the GellMann-Oakes-Renner relation. For the renormalization-group-invariant ratios we obtain ½Σ RGI 1=3 =F ¼ 2.77ð2Þð4Þ and ΛM S =F ¼ 3.6ð2Þ, which correspond to ½ΣM S ð2 GeVÞ 1=3 ¼ 263ð3Þð4Þ MeV and F ¼ 85.8ð7Þð20Þ MeV if F K is used to set the scale by supplementing the theory with a quenched strange quark.

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confidence: 99%

Chiral Symmetry Breaking in QCD with Two Light Flavors

et al. 2015

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“…Figure 3 shows the lattice data obtained at the same parameters other than the lattice volume, 32 3 is about 2.6 fm and 3.9 fm, respectively. The data are consistent with each other within the statistical error.…”

Section: Lattice Results and Chiral Fitsmentioning

confidence: 99%

“…massless quark limit after taking the infinite volume limit. In our previous work using the overlap fermion formulation [2,3] we calculated the low-lying eigenvalues of the Dirac operator on lattice ensembles at several quark masses. Analyzing the lattice data using the analytic formulae calculated within one-loop chiral perturbation theory in the p-regime and ε-regime [4], we extracted the chiral condensate, though the uncertainty due to finite lattice spacing and finite lattice volume was yet unexplored.…”

Section: Introductionmentioning

confidence: 99%

Determination of chiral condensate from low-lying eigenmodes of Mobius domain-wall Dirac operator

Cossu¹,

Fukaya²,

Hashimoto³

et al. 2017

Proceedings of 34th Annual International Symposium on Lattice Field Theory — PoS(LATTICE2016)

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We calculate the spectral function of the Mobius domain-wall Dirac operator utilizing a stochastic eigenvalue counting technique. From the low-end of the spectrum we extract the chiral condensate in 2+1-flavor QCD, and take the chiral and continuum limits. Lattice ensembles are those generated with Mobius domain-wall fermions at a ∼ 0.080, 0.055 and 0.044 fm.34th annual International Symposium on Lattice Field Theory

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“…Our results are thus marginally compatible with the latter, within uncertainties of both results. Note, however, that various recent lattice results vary in a wider range for n f = 3, as compiled from [2]: from 214 ± 6 ± 24 [56] to 290 ± 15 [57]. This is largely due to the still difficult required extrapolation of lattice results to the chiral limit, which for the SU (3) case is affected by large uncertainties.…”

Section: Qq (µ = 2 Gev) and Comparison With Other Determinationsmentioning

confidence: 99%

Chiral condensate and spectral density at full five-loop and partial six-loop orders of renormalization group optimized perturbation theory

Kneur

Neveu

2020

Phys. Rev. D

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We reconsider our former determination of the chiral quark condensate qq from the related QCD spectral density of the Euclidean Dirac operator, using our Renormalization Group Optimized Perturbation (RGOPT) approach. Thanks to the recently available complete five-loop QCD RG coefficients, and some other related four-loop results, we can extend our calculations exactly to N 4 LO (five-loops) RGOPT, and partially to N 5 LO (six-loops), the latter within a well-defined approximation accounting for all six-loop contents exactly predictable from five-loops RG properties. The RGOPT results overall show a very good stability and convergence, giving primarily the RG invariant (RGI) condensate, qq 1/3 RGI (n f = 0) = −(0.840 +0.020 −0.016 )Λ0, qq 1/3 RGI (n f = 2) = −(0.781 +0.019 −0.009 )Λ2, qq 1/3 RGI (n f = 3) = −(0.751 +0.019−.010 )Λ3, whereΛn f is the basic QCD scale in the M S-scheme for n f quark flavors, and the range spanned is our rather conservative estimated theoretical error. This leads e.g. to qq 1/3 n f =3 (2 GeV) = −(273 +7 −4 ± 13) MeV, using the latestΛ3 values giving the second uncertainties. We compare our results with some other recent determinations. As a by-product of our analysis we also provide complete five-loop and partial six-loop expressions of the perturbative QCD spectral density, that may be useful for other purposes.

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Determination of the chiral condensate from QCD Dirac spectrum on the lattice

Cited by 46 publications

References 68 publications

Chiral Symmetry Breaking in QCD with Two Light Flavors

Chiral Symmetry Breaking in QCD with Two Light Flavors

Determination of chiral condensate from low-lying eigenmodes of Mobius domain-wall Dirac operator

Chiral condensate and spectral density at full five-loop and partial six-loop orders of renormalization group optimized perturbation theory

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