Book/Report

FZJ-2018-04293

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Ein chiral symmetrisches Quarkmodell ohne freie Quarks

Buballa, M. (Corresponding author)FZJ*

1993
Forschungszentrum Jülich GmbH Zentralbibliothek Verlag Jülich

Please use a persistent id in citations: http://hdl.handle.net/2128/19396

Report No.: Juel-2788

Abstract: A chirally symmetric quark model is presented which contrary to the Nambu Jona-Lasinio (NJL) model does not lead to the presence of free quarks. In the model a non-local effective interaction is used as a schematic parameterization of the quark antiquark scattering kernel. The non-locality can be interpreted as phenomenologicallytaking into account an infinite number of elementary scattering processes, like the sum of all multi-gluon exchange processes in the particle-particle channel. Thebasic Lagrangian of the interaction shares all global internal symmetries with QCD. In particular in the limit of vanishing current quark masses it is chirally symmetric.Starting from the non-local scattering kernel the solution of the Dyson-Schwinger equation and the Bethe-Salpeter equation leads to a consistent description of thedressed quark propagators with the mesons as quark-antiquark states. Like in the NJL-model chiral symmetry is spontaneously broken. Because of the non-localityof the interaction, however, in our model the quarks do not acquire a constant constituent mass but a four momentum dependent selfenergy. The interaction can be parameterized in such a way that the quark propagator is pole free. That means that the quark mass shell is not defined and the quarks do not exist as free real but only as virtual particles. The solutions of the twobody equation, the quark-antiquark T-matrix, however, have got poles and mesons as bound quark-antiquark states exist as real particles within the model. Different from the NJL-model these mesons cannot decay into free quarks. It is shown that the description of mesons is consistent with the Goldstone theorem: In the chiral limit the pion is massless. In order to describe the coupling of vector and axial vector fields to the model gauge invariant Lagrangians are constructed. Since the non-local interaction is not gauge invariant, by itself one has to go beyond minimal substitution and to introducegauge fields also to the interaction Lagrangian. This leads to additional diagrams which correspond to the direct coupling of the gauge bosons to the non-local strongvertex. It is shown that Ward-Takahashi identities as well as the Gell-Mann Oakes Renner relation and a. generalized Goldberger Treiman relation hold. Finally the extension of the model to three quark flavours is discussed.

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Contributing Institute(s):

1. Publikationen vor 2000 (PRE-2000)

Research Program(s):

1. 899 - ohne Topic (POF3-899) (POF3-899)

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