Direct instantons and nucleon magnetic moments

Aw, M.; Banerjee, Manoj K.; Forkel, Hilmar

doi:10.1016/s0370-2693(99)00358-5

Cited by 14 publications

(12 citation statements)

References 27 publications

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“…Indeed, the spurious terms lead to different continuum factors as appeared in Ref. [15,16]. A similar discussion can be found in Ref.…”

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confidence: 72%

Use of the Double Dispersion Relation in QCD Sum Rules with External Fields

Kim¹

2000

Progress of Theoretical Physics

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In QCD sum rules with external fields, the double dispersion relation is often used to represent the correlation function. In this work, we point out that the double spectral density, when it is determined by successive applications of the Borel transformation, contains spurious terms which should be kept in the subtraction terms in the double dispersion relation. They are zero under the Borel transformation, but, if the dispersion integral is restricted with QCD duality, they contribute to the continuum. For the simple case with zero external momentum, it is shown that subtracting out the spurious terms is equivalent to the QCD sum rules represented by the single dispersion relation.The QCD sum rule 1) is widely used in studying hadronic properties based on QCD. 2) In this framework, a correlation function is introduced as a bridge between the hadronic and QCD representations. On the QCD side, the perturbative part and the power corrections are calculated in the deep space-like region (q 2 = −∞) using the operator product expansion (OPE), which is then used to extract the hadronic parameter of concern by matching with the corresponding hadronic representation.In matching the two representations, it is crucial to represent the correlator using a dispersion relation. Usually in the nucleon mass sum rule, as an example, the singlevariable dispersion relation is used. With this, the QCD correlator calculated in the deep space-like region can be related to its imaginary part defined in the time-like region, which is then compared with the corresponding hadronic spectral density to extract the hadronic parameter of concern. The hadronic spectral density contains contributions from higher resonances as well as the pole from the low-lying resonance of concern. To subtract out the continuum, QCD duality is invoked above a certain threshold, where the continuum contribution is equated to the perturbative part of QCD. This duality restricts the dispersion integral below the continuum threshold in the matching. Therefore, the predictive power of the QCD sum rules relies heavily on the duality assumption. Indeed, in quantum mechanical examples, the partonhadron duality works well for two-point correlation functions. 3) Often, within the QCD sum rule framework, a correlation function with an external field is considered to calculate, for examples, pion-nucleon couplings 4) -6) and nucleon magnetic moments. 7) In such a case, as the two baryonic lines propagate through the correlator at the tree level, the double-variable dispersion relation 8) can * ) JSPS fellow.

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“…Indeed, the spurious terms lead to different continuum factors as appeared in Ref. [15,16]. A similar discussion can be found in Ref.…”

supporting

confidence: 72%

Use of the Double Dispersion Relation in QCD Sum Rules with External Fields

Kim¹

2000

Progress of Theoretical Physics

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“…Furthermore, although the SIA has been used in several phenomenological studies (e.g. [1], [5,6,7], and references therein), its derivation was never discussed in detail, its range of applicability was never quantitatively checked, and the values of relevant effective masses well specified. And indeed, if one uses the value m * ≃ 170M eV the correlation functions, evaluated in the SIA, do not agree with the results of the random and interacting instanton liquid [3].…”

Section: Introductionmentioning

confidence: 99%

Systematic study of the single instanton approximation in QCD

Faccioli

Shuryak

2001

Phys. Rev. D

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Single-instanton approximation (SIA) is often used to evaluate analytically instanton contributions euclidean correlation function in QCD at small distances. We discuss how this approximation can be consistently derived from the theory of instanton ensemble and give precise definitions to a number of different "quark effective masses", generalizing the parameter m * , which was introduced long ago to account for the collective contribution of the whole ensemble. We test numerically the range of applicability of the SIA for different quantities. Furthermore, we determine all the effective masses (for random and interacting instanton liquid models) as well as from phenomenology, and discuss to what extent those are universal.lan

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“…g A previously contemplated connection between the instability of the original Π 3 sum rule and the perturbative infrared singularities of the "pragmatic" OPE seems, in view of newer results 18 , unlikely 6 . the nucleon state, 0|η|N = λ N u.…”

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confidence: 99%

“…In this talk, I will report on an investigation 6 which takes a step towards uncovering the hidden role of glue in the response to electromagnetic fields by studying the impact of instantons on the nucleon magnetic moments in the recently developed IOPE sum-rule approach 4,7 . While in general the range of applicability of the IOPE (as a short-distance expansion) is more limited than that of instanton vacuum models or lattice calculations, it profits from the transparency of an analytical (yet largely model-independent) method and takes, in contrast to instanton models, all long-wavelength vacuum fields and also perturbative fluctuations into account.…”

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confidence: 99%

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Instantons and Nucleon Magnetism

Forkel

2001

Hadron Physics 2000

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We construct improved QCD sum rules for the nucleon magnetic moments by implementing direct-instanton contributions to the operator product expansion of the nucleon correlator in a magnetic background field. The instanton contributions are found to affect only those sum rules which had previously been considered unstable. The new sum rules show a high degree of stability and reproduce the experimental values of the nucleon magnetic moments for values of the magnetic quark condensate susceptibility which are consistent with other estimates. (Invited talk given at "

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Direct instantons and nucleon magnetic moments

Cited by 14 publications

References 27 publications

Use of the Double Dispersion Relation in QCD Sum Rules with External Fields

Use of the Double Dispersion Relation in QCD Sum Rules with External Fields

Systematic study of the single instanton approximation in QCD

Instantons and Nucleon Magnetism

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