Topological susceptibility in full QCD: lattice results versus the prediction from the QCD partition function with granularity

Dürr, Stephan

doi:10.1016/s0550-3213(01)00325-x

Cited by 36 publications

(32 citation statements)

References 35 publications

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“…9 had not been obtained previously in dynamical fermion simulations, 25) except in an exploratory work by Kovács, 26) which utilized the same reweighting technique as in our work. The reason that this had not been observed is partly that the quark mass is not small enough to realize the -regime.…”

Section: Topological Susceptibilitymentioning

confidence: 70%

Effect of Low-Lying Fermion Modes in the isin-Regime of QCD

Ogawa

Hashimoto

2005

Progress of Theoretical Physics

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We investigate the effects of low-lying fermion eigenmodes on the QCD partition function in the -regime. The fermion determinant is approximated by a truncated product of lowlying eigenvalues of the overlap Dirac operator. With two flavors of dynamical quarks, we observe that the lattice results for the lowest eigenvalue distribution, eigenvalue sum rules and partition function reproduce the analytic predictions of Leutwyler and Smilga, which strongly depend on the topological charge of the background gauge configuration. The values of the chiral condensate extracted from these measurements are consistent. For one dynamical quark flavor, on the other hand, we find an apparent disagreement among the different determinations of the chiral condensate. This may suggest the failure of the -expansion in the absence of a massless Nambu-Goldstone boson. §1. Introduction Chiral perturbation theory (ChPT) is an effective field theory to describe the dynamics of quantum chromodynamics (QCD) at low energies ( Λ ∼ 1 GeV), where the Nambu-Goldstone pion excitations dominate the dynamics, while other particles are too heavy to be excited. In an infinite volume, ChPT provides a method to express low energy amplitudes of pions as an expansion in terms of the pion mass squared, m 2 π , and its momentum squared, p 2 . Thus it enables us to calculate low energy pion amplitudes in a systematic manner. When the system has a finite volume, such that for which the pion Compton wavelength (∼ 2π/m π ) is much larger than the linear extent L of the space-time, i.e. m π L 1, while L is large enough compared to the QCD scale, 1/Λ QCD , the low energy effective theory can still be constructed as an expansion in terms of small 2 ∼ m π /Λ ∼ p 2 /Λ 2 . This is known as the -expansion. 1) In this setup, the so-called -regime of ChPT, chiral symmetry is not spontaneously broken, and one must explicitly integrate over different vacua in the path integral. This yields the characteristic behavior of the partition function and other physical quantities. In particular, they depend strongly on the gauge field topology (or the existence of fermion zero modes). 2) Lattice QCD simulations are well suited to the study of finite volume physics. Because chiral symmetry plays an essential role in the -regime, one should use lattice fermion formulations that respect chiral symmetry. Such fermion formulations have been developed recently, namely the overlap fermion 3), 4) and domain-wall fermion formulation. 5), 6) These fermion formulations satisfy the Ginsparg-Wilson relation, 7) with which the fermion action can be shown to have exact chiral symmetry at finite lattice spacings. 8) Quenched lattice simulations have to this time been done in the at Monash University on June 15, 2015 http://ptp.oxfordjournals.org/ Downloaded from

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Section: Topological Susceptibilitymentioning

confidence: 70%

Effect of Low-Lying Fermion Modes in the isin-Regime of QCD

Ogawa

Hashimoto

2005

Progress of Theoretical Physics

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“…In numerical simulations of staggered fermions it is necessary to take fractional powers of the quark determinant to simulate a theory with the Of course, this result is valid only in leading order chiral perturbation theory, but at large quark mass it interpolates smoothly [5] to the quenched result predicted for pure gauge theory [6].…”

Section: Topological Susceptibility With Taste Symmetry Breakingmentioning

confidence: 99%

Topological susceptibility in staggered fermion chiral perturbation theory

2004

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The topological susceptibility of the vacuum in quantum chromodynamics has been simulated numerically using the Asqtad improved staggered fermion formalism. At nonzero lattice spacing the residual fermion doublers (fermion "tastes") in the staggered fermion formalism give contributions to the susceptibility that deviate from conventional continuum chiral perturbation theory. In this brief report we estimate the taste-breaking artifact and compare it with results of recent simulations, finding that it accounts for roughly half of the scaling violation.

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“…On the theoretical side, Ref. [16] conjectured for N f degenerate flavours in the large volume limit The first method used the theoretically predicted Σ value as an input to extract χ t . Now we try to evaluate Σ itself from our data.…”

Section: Methods 1 : Gaussian Summationmentioning

confidence: 99%

“…The essential practical question is the acceptance rate in the Metropolis step at the end of the HMC trajectories (it employs D ovHF to precision 10¡ 16 with light dynamical overlap fermionsin addition to the huge computation time request in QCD -is that the histories at weak gauge coupling perform only very few topological transitions (which require a temporary deformation to rough configurations). We refer to the clean definition, which identifies the topological charge with the fermionic index ν [6].…”

Section: Topological Summation With Dynamical Overlap Fermionsmentioning

confidence: 99%

Chiral condensate and topological susceptibility in the 2-flavour Schwinger model

Bietenholz¹,

Hip²

2009

Proceedings of the XXVI International Symposium on Lattice Field Theory — PoS(LATTICE 2008)

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HMC histories for light dynamical overlap fermions tend to stay in a fixed topological sector for many trajectories, so that the different sectors are not sampled properly. Therefore the suitable summation of observables, which have been measured in separate sectors, is a major challenge.We explore several techniques for this issue, based on data for the chiral condensate and the (analogue of the) pion mass in the 2-flavour Schwinger model with dynamical overlap-hypercube fermions.

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Topological susceptibility in full QCD: lattice results versus the prediction from the QCD partition function with granularity

Cited by 36 publications

References 35 publications

Effect of Low-Lying Fermion Modes in the isin-Regime of QCD

Effect of Low-Lying Fermion Modes in the isin-Regime of QCD

Topological susceptibility in staggered fermion chiral perturbation theory

Chiral condensate and topological susceptibility in the 2-flavour Schwinger model

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