Chiral Symmetry, Quark Mass, and Scaling of the Overlap Fermions

Sj, Dong; Lee, Frank; Liu, KF; Jb, Zhang

doi:10.1103/physrevlett.85.5051

Phys. Rev. Lett.

2000

DOI: 10.1103/physrevlett.85.5051

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Chiral Symmetry, Quark Mass, and Scaling of the Overlap Fermions

Dong Sj

Frank Lee²,

KF Liu³

et al.

Abstract: The chiral symmetry relation and scaling of the overlap fermions are studied numerically on the quenched lattices at 3 couplings with about the same physical volume. We find that the generalized Gell-Mann-Oakes-Renner relation is satisfied to better than 1% down to the smallest quark mass at m 0 a = 0.006. We also obtain the quark mass from the PCAC relation and the pseudoscalar masses. The renormalization group invariant quark mass is shown to be fairly independent of scale. The π and ρ masses at a fixed m π … Show more

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Cited by 57 publications

(89 citation statements)

References 27 publications

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“…For T ≥ 1.25T c , M P S is constant and non-vanishing for ma < ∼ 0.1. In the same temperature range, the ratio m P S (T )/m V (T ) is within 10% of unity and quite different from the measured values at T = 0 at nearby couplings β [15]. Thus, the simple picture that emerges is a property of the high temperature phase of (quenched) QCD.…”

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confidence: 69%

“…The configurations were separated by 1000 sweeps of a Cabibo-Marinari update. A previous computation [15] with T = 0 quenched overlap quarks at the nearby couplings of β = 5.85 and 6.0 allows us to compare finite and zero temperature physics.For the matrix M = D † w D w , and a given source vector b, we computed y = M −1/2 b by a conjugate gradient (CG) version of a proposed Lanczös method [16]. CG gives better control over errors than Lanczös or other methods based on approximations using Chebychev or Reeves polynomials.…”

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confidence: 99%

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Quenched QCD at finite temperature with chiral fermions

2002

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We study physics at temperatures just above the QCD phase transition (Tc) using chiral (overlap) Fermions in the quenched approximation of lattice QCD. Exact zero modes of the overlap Dirac operator are localized and their frequency of occurrence drops with temperature. This is closely related to axial U (1) symmetry, which remains broken up to 2Tc. After subtracting the effects of these zero modes, chiral symmetry is restored, as indicated by the behavior of the chiral condensate ( ψψ ). The pseudoscalar and vector screening masses are close to ideal gas values.11.15.Ha, 12.38.Mh TIFR/TH/01-27, t01/076, hep-lat/0107022With new results from the Brookhaven heavy-ion collider appearing thick and fast [4], the time seems ripe for making a concerted effort to understand the dynamics of the high-temperature phase of quantum chromodynamics, namely the quark-gluon plasma. There are several puzzles that seem to have resisted a decade of efforts to understand them. The one we focus on involves the static screening of certain excitations of the plasma.It has long been understood that the screening of currents in a plasma would give us information on its excitations. Currents with certain quantum numbers excite mesons from the vacuum at low temperatures, and should exhibit deconfinement related changes above the QCD phase transition temperature (T c ) [5]. Detailed studies have shown that this indeed does happen in the vector, and axial-vector channels: the screening above T c is clearly due to nearly non-interacting quark anti-quark pairs in the medium [6,7]. On the other hand, the scalar and pseudo-scalar screening masses show more complicated behavior-strong deviations from the ideal Fermi gas, and a strong temperature dependence. This puzzling behavior is generic-it has been seen in quenched [8] and dynamical simulations with two [9] and four flavors [5][6][7]10] of staggered quarks, as well as with Wilson quarks [11]. This is the puzzle that we address and solve in this letter.The new technique we bring to bear on this problem is to use a version of lattice Fermions called overlap Fermions [12]. It has the advantage of preserving chiral symmetry on the lattice for any number of massless flavors of quarks [13]. This is in contrast to other formulations such as Wilson Fermions which break all chiral symmetries or staggered Fermions which break them partially. Since the number of pions and their nature is intimately related to the actually realized chiral symmetry on the lattice, we should expect any realization of chiral Fermions on the lattice to provide insight into the question we address.The overlap Dirac operator (D) can be defined [14] in terms of the Wilson-Dirac operator (D w ) by the relationThe computation of D −1 needs a nested series of two matrix inversions for its evaluation (each step in the numerical inversion of D involves the inversion of D † w D w ). This squaring of effort makes a study of QCD with dynamical overlap quarks very expensive. As a first step in this direction, we chose to work with quen...

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Quenched QCD at finite temperature with chiral fermions

2002

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“…In addition to having small O(a 2 ) discretization errors [23,24], the overlap fermion that we use for the valence quarks in the nucleon can also be used for the light and charm quarks in the loop insertion with small O(m 2 a 2 ) error [25,26]. This allows us to calculate both f Ts and f Tc .…”

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confidence: 99%

Strangeness and charmness content of the nucleon from overlap fermions on2+1-flavor domain-wall fermion configurations

et al. 2013

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We present a calculation of the strangeness and charmness contents N |ss|N and N |cc|N of the nucleon from dynamical lattice QCD with 2 + 1 flavors. The calculation is performed with overlap valence quarks on 2+1-flavor domain-wall fermion gauge configurations. The configurations are generated by the RBC collaboration on a 24 3 × 64 lattice with sea quark mass am l = 0.005, am s = 0.04, and inverse lattice spacing a −1 = 1.73 GeV. Both actions have chiral symmetry which is essential in avoiding contamination due to the operator mixing with other flavors. Nucleon propagator and the quark loops are both computed with stochastic grid sources, while low-mode substitution and low-mode averaging methods are used respectively which substantially improve the signal to noise ratio. We obtain the strangeness matrix element f Ts = m s N |ss|N /M N = 0.0334(62), and the charmness content f Tc = m c N |cc|N /M N = 0.094(31) which is resolved from zero by 3 σ precision for the first time.

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“…What χ 2 couples to remains an open question. The lattice size we use is 16 3 × 28 with the scale of a = 0.202(1) fm set from f π , which is our preferred choice for scale [11]. We consider a wide range of quark masses: 26 masses with the lowest m π = 180 MeV (or m π /m ρ =0.248), very close to the physical limit, and with 18 masses below the strange quark mass.…”

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Excited baryons from Bayesian priors and overlap fermions

Lee

Dong

Draper

et al. 2003

Nuclear Physics B - Proceedings Supplements

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Using the constrained-fitting method based on Bayesian priors, we extract the masses of the two lowest states of octet and decuplet baryons with both parities. The calculation is done on quenched 163 × 28 lattices of a = 0.2 fm using an improved gauge action and overlap fermions, with the pion mass as low as 180 MeV. The rich structure of the excited baryon spectrum, as documented by the particle data group [1], provides a fertile ground for exploring the nature of quark-quark interactions. One outstanding example is the ordering of the lowestlying states which has the order of positive and negative-parity excitations inverted between N , ∆ and Λ channels. Conventional quark models have difficulty explaining the ordering in a consistent manner. There are two contrasting views. One is from the constituent quark model [2,3] which has the interaction dominated by onegluon-change type, i.e., color-spin λ c

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Chiral Symmetry, Quark Mass, and Scaling of the Overlap Fermions

Cited by 57 publications

References 27 publications

Quenched QCD at finite temperature with chiral fermions

Quenched QCD at finite temperature with chiral fermions

Strangeness and charmness content of the nucleon from overlap fermions on2+1-flavor domain-wall fermion configurations

Excited baryons from Bayesian priors and overlap fermions

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