Analytic structure of meson propagators in the proper-time regularized Nambu-Jona-Lasinio model

Broniówski, Wojciech; Ripka, G.; Nikolov, Emil N.; Goeke, K.

doi:10.1007/bf02769546

Cited by 13 publications

(23 citation statements)

References 35 publications

(20 reference statements)

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“…As a matter of fact, even in local models, such as in those with the proper-time regularization, dispersion relations do not hold [35] due to the presence of essential singularities generating nonanalytic structure in the complex q 2 -plane.…”

Section: B Vertices With Two Currentsmentioning

confidence: 99%

Spectral quark model and low-energy hadron phenomenology

Arriola

Broniowski

2003

Phys. Rev. D

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We propose a spectral quark model which can be applied to low energy hadronic physics. The approach is based on a generalization of the Lehmann representation of the quark propagator. We work at the one-quark-loop level. Electromagnetic and chiral invariance are ensured with help of the gauge technique which provides particular solutions to the Ward-Takahashi identities. General conditions on the quark spectral function follow from natural physical requirements. In particular, the function is normalized, its all positive moments must vanish, while the physical observables depend on negative moments and the so-called log-moments. As a consequence, the model is made finite, dispersion relations hold, chiral anomalies are preserved, and the twist expansion is free from logarithmic scaling violations, as requested of a low-energy model. We study a variety of processes and show that the framework is very simple and practical. Finally, incorporating the idea of vector-meson dominance, we present an explicit construction of the quark spectral function which satisfies all the requirements. The corresponding momentum representation of the resulting quark propagator exhibits only cuts on the physical axis, with no poles present anywhere in the complex momentum space. The momentum-dependent quark mass compares very well to recent lattice calculations. A large number of predictions and relations, valid at the low-energy scale of the model, can be deduced from our approach for such quantities as the pion light-cone wave function, non-local quark condensate, pion transition form factor, pion valence parton distribution function, etc. These quantities, obtained at a low-energy scale of the model, have correct properties, as requested by symmetries and anomalies. They also have pure twist expansion, free of logarithmic corrections, as requested by the QCD factorization property.

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Section: B Vertices With Two Currentsmentioning

confidence: 99%

Spectral quark model and low-energy hadron phenomenology

Arriola

Broniowski

2003

Phys. Rev. D

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“…Also, let us remind the reader that in ref [17], scaling for the pion structure functions was accomplished in the Pauli-Villars regularization, and not in the proper-time regularization. In this context, it has been shown [19] that in the Pauli-Villars regularization, unlike the more customary proper-time scheme where cuts in the complex plane appear [20,9], dispersion relations are fulfilled.…”

Section: Pauli-villars Regularization For the Njl Modelmentioning

confidence: 99%

“…The only point is to identify the operators A and B. Using eq (B.7), we get 20) where in the second line we have used that Mγ µ = γ µ M 5 . Several cases for A and B have to be considered.…”

Section: Appendix B: Separation Into Free-massless and Full Quark Promentioning

confidence: 99%

Hadron structure functions in a chiral quark model: Regularization, scaling and sum rules

1999

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We provide a consistent regularization procedure for calculating hadron structure functions in a chiral quark model. The structure functions are extracted from the absorptive part of the forward Compton amplitude in the Bjorken limit. Since this amplitude is obtained as a time-ordered correlation function its regularization is consistently determined from the regularization of the bosonized action. We find that the Pauli-Villars regularization scheme is most suitable because it preserves both the anomaly structure of QCD and the leading scaling behavior of hadron structure functions in the Bjorken limit. We show that this procedure yields the correct pion structure function. In order to render the sum rules of the regularized polarized nucleon structure functions consistent with their corresponding axial charges we find it mandatory to further specify the regularization procedure. This specification goes beyond the double subtraction scheme commonly employed when studying static hadron properties in this model. In particular the present approach serves to determine the regularization prescription for structure functions whose leading moments are not given by matrix elements of local operators. In this regard we conclude somewhat surprisingly that in this model the Gottfried sum rule does not undergo regularization.

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“…These sorts of problems are well known and arguments have been put forward and tricks invented to deal with such problems-for a discussion on these issues, see, for example, Refs. [13][14][15]. Obviously, this situation is unsatisfactory since one would like that the regularization scheme play a secondary role in the process of making predictions with the model.…”

Section: Introductionmentioning

confidence: 99%

Predictive formulation of the Nambu–Jona-Lasinio model

2008

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A novel strategy to handle divergences typical of perturbative calculations is implemented for the Nambu-Jona-Lasinio model and its phenomenological consequences investigated. The central idea of the method is to avoid the critical step involved in the regularization process, namely, the explicit evaluation of divergent integrals. This goal is achieved by assuming a regularization distribution in an implicit way and making use, in intermediary steps, only of very general properties of such regularization. The finite parts are separated from the divergent ones and integrated free from effects of the regularization. The divergent parts are organized in terms of standard objects, which are independent of the (arbitrary) momenta running in internal lines of loop graphs. Through the analysis of symmetry relations, a set of properties for the divergent objects are identified, which we denominate consistency relations, reducing the number of divergent objects to only a few. The calculational strategy eliminates unphysical dependencies of the arbitrary choices for the routing of internal momenta, leading to ambiguity-free, and symmetry-preserving physical amplitudes. We show that the imposition of scale properties for the basic divergent objects leads to a critical condition for the constituent quark mass such that the remaining arbitrariness is removed. The model becomes predictive in the sense that its phenomenological consequences do not depend on possible choices made in intermediary steps. Numerical results are obtained for physical quantities at the one-loop level for the pion and sigma masses and pion-quark and sigmaquark coupling constants.

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Analytic structure of meson propagators in the proper-time regularized Nambu-Jona-Lasinio model

Cited by 13 publications

References 35 publications

Spectral quark model and low-energy hadron phenomenology

Spectral quark model and low-energy hadron phenomenology

Hadron structure functions in a chiral quark model: Regularization, scaling and sum rules

Predictive formulation of the Nambu–Jona-Lasinio model

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