Evidence of instanton effects in hadrons from the study of low eigenfunctions of the Dirac operator

Ivanenko, T.L.; Negele, John W.

doi:10.1016/s0920-5632(97)00815-3

Cited by 35 publications

(65 citation statements)

References 13 publications

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“…4 we present the results of our calculations for the nucleon mass as a function of the pion mass squared for different choices of the cut-offρ. Comparing these IILM data at differentρ with the lattice data collaborations [27,28] clearly shows that agreement between IILM and lattice QCD predictions is obtained only for a unique value of the cut-off scale, corresponding to an average instanton size of 0.32 fm, in excellent agreement with the early phenomenological estimateρ ≃ 1/3 fm [4] and recent lattice results [6,29,30,31,32]. The complete set of values of masses extracted from our IILM calculations is presented in Table I.…”

Section: Pion and Nucleon Mass In The Iilmsupporting

confidence: 82%

Exploring the chiral regime of QCD in the interacting instanton liquid model

et al. 2007

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The Interacting Instanton Liquid Model is used to explore the role of instanton induced dynamics in hadron structure. To support the validity of this model in the chiral regime, the quark mass dependencies of several properties are shown to agree with chiral perturbation theory, including the density of eigenmodes of the Dirac operator and the masses of the pion and nucleon. A quark mass m * = 80 MeV emerging naturally from the model is shown to specify the mass scale above which the fermion determinant is suppressed, the zero modes become subdominant, and the density of quasi-zero modes become independent of the quark mass.

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Section: Pion and Nucleon Mass In The Iilmsupporting

confidence: 82%

Exploring the chiral regime of QCD in the interacting instanton liquid model

et al. 2007

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“…Since instantons play a major role in the physics of light quarks [6,7], we also would like to understand their role in hadron structure functions. Especially interesting from this perspective is the spin structure of a proton.…”

Section: Motivationmentioning

confidence: 99%

Study of instanton contributions to moments of nucleon spin-dependent structure functions

Dolgov¹,

Brower²,

Negele³

et al. 1999

Nuclear Physics B - Proceedings Supplements

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Instantons are the natural mechanism in non-perturbative QCD to remove helicity from valence quarks and transfer it to gluons and quark-antiquark pairs. To understand the extent to which instantons explain the so-called "spin crisis" in the nucleon, we calculate moments of spin-dependent structure functions in quenched QCD and compare them with the results obtained with cooled configurations from which essentially all gluon contributions except instantons have been removed. Preliminary results are presented. MOTIVATIONIn recent years there has been a major experimental effort to measure structure functions which characterize the distribution of quarks in the nucleon. The challenge for theorists is now to understand the data which already exist and to predict the structure functions which will be measured in currently planned experiments. Lattice QCD provides the only known framework for non-perturbative calculation of hadron structure, and although it cannot address the intrinsically Minkowski structure functions themselves, through the operator product expansion it is possible to calculate their moments. There have been several calculations of these moments in recent years, including calculation of all moments of the spin independent and longitudinal spin dependent structure functions through order four [1] and the tensor charge [2] by the QCDSF collaboration, as well as calculation of connected and disconnected contributions to the axial charge [3,4] and to the tensor charge [5]. These results agree qualitatively with experiment and discrepancies may plausibly be attributed to a combination of finite lattice size effects, and the omission of sea quarks and disconnected diagrams.However, in addition to showing that numeri- * Based on the poster presented by D.Dolgov. Work supported by the U.S. Department of Energy (DOE) under cooperative research agreement DE-FC02-94ER40818.cal solution of QCD reproduces the experimental results, we want to understand as fully as possible the physical origin of the observed structure. Since instantons play a major role in the physics of light quarks [6,7], we also would like to understand their role in hadron structure functions. Especially interesting from this perspective is the spin structure of a proton.is the only known vertex in QCD that directly removes helicity from valence quarks and transfers it to gluons and quark-antiquark pairs, thereby rendering instantons the natural mechanism to explain the so-called "spin crisis".Hence it is important to identify the instanton contribution to the proton spin structure functions. On the lattice, a practical way of extracting the instanton content is "cooling" [8,6], in which one sequentially minimizes the action locally on each link and iteratively approaches a stationary solution.In this work we calculate the zeroth moments of the g 1 (x) and h 1 (x) structure functions with and without cooling for u and d quarks in quenched lattice QCD. The zeroth moment of g 1 (x) is proportional to the quark's spin contribution to the total ...

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“…Lattice calculations have helped to corroborate these ideas. Recently several studies of the zero-modes and near zeromodes of the Dirac operator [2][3][4] which provide a powerful and natural filter retaining the infrared fluctuations of the underlying gauge field were presented. It was established that the vacuum has a lumpy structure and the lumps are locally chiral [3] and (anti) self-dual [4].…”

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confidence: 99%

Calorons, instantons, and constituent monopoles in SU(3) lattice gauge theory

Gattringer

2003

Phys. Rev. D

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We analyze the zero-modes of the Dirac operator in quenched SU(3) gauge configurations at nonzero temperature and compare periodic and anti-periodic temporal boundary conditions for the fermions. It is demonstrated that for the different boundary conditions often the modes are localized at different space-time points and have different sizes. Our observations are consistent with patterns expected for Kraan -van Baal solutions of the classical Yang-Mills equations. These solutions consist of constituent monopoles and the zero-modes are localized on different constituents for different boundary conditions. Our findings indicate that the excitations of the QCD vacuum are more structured than simple instanton-like lumps.PACS numbers: 11.15.HaUnderstanding the relevant excitations of the QCD vacuum is a major scientific goal and lattice calculations can contribute valuable non-perturbative information. A prominent candidate for such relevant excitations are instantons which are particularly successful in providing a mechanism for chiral symmetry breaking [1]. Lattice calculations have helped to corroborate these ideas. Recently several studies of the zero-modes and near zeromodes of the Dirac operator [2-4] which provide a powerful and natural filter retaining the infrared fluctuations of the underlying gauge field were presented. It was established that the vacuum has a lumpy structure and the lumps are locally chiral [3] and (anti) However, it is generally believed, that instantons are not responsible for confinement. On the other hand all lattice calculations show that the deconfinement transition and the restoration of chiral symmetry coincide at a single critical temperature which suggests that there is an underlying mechanism linking the two phenomena. In recent years Kraan and van Baal [5] have constructed new solutions for the classical SU(N) Yang Mills equations with compactified time, i.e. at finite temperature (KvB solutions). The KvB solutions generalize the caloron solution [6] and a lump of topological charge 1 is built of N constituent monopoles, a feature which might provide a link to the confinement problem. Note that for KvB solutions the monopole lumps appear in multiples of N. A single lump is not an independent object and only N lumps together have topological charge ±1. Strong evidence for SU(2) KvB solutions in cooled lattice gauge configurations were given for twisted [7] and periodic boundary conditions [8]. The zero-mode for the KvB solution [9] shows characteristic features which should allow to use the eigenvectors of the Dirac operator as a filter retaining infrared fluctuations and search for traces of KvB solutions also in thermalized configurations.Before presenting our lattice calculations we briefly discuss a few properties of SU(3) KvB solutions and their zero-mode. KvB solutions [5] are characterized by the Polyakov loop at spatial infinity which in a suitable gauge can be expressed as P ∞ = exp(i2πdiag(µ 1 , µ 2 , µ 3 )) with µ 1 + µ 2 + µ 3 = 0 and µ 1 ≤ µ 2 ≤ µ 3 ≤ µ 4 ≡ 1 + µ ...

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Evidence of instanton effects in hadrons from the study of low eigenfunctions of the Dirac operator

Cited by 35 publications

References 13 publications

Exploring the chiral regime of QCD in the interacting instanton liquid model

Exploring the chiral regime of QCD in the interacting instanton liquid model

Study of instanton contributions to moments of nucleon spin-dependent structure functions

Calorons, instantons, and constituent monopoles in SU(3) lattice gauge theory

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