Low-energy behaviour of two-point functions of quark currents

Johan Bijnens, Eduardo de Rafael, Hanqing Zheng

Research output: Contribution to journalArticlepeer-review


We discuss vector, axial-vector, scalar and pseudoscalar two-point functions at low and intermediate energies. We first review what is known from chiral perturbation theory, as well as from a heat kernel expansion within the context of an extended Nambu-Jona-Lasinio (ENJL) model. We derive then these two-point functions to all orders in the momenta and to leading order in 1/N c within the framework of this model. We find an improved high-energy behaviour and a general way of parametrizing them that shows relations between some of the two-point functions, which are also valid in the presence of gluonic interactions. The similarity between the shape of the experimentally known spectral functions and the ones we derive, is greatly improved with respect to those predicted by the usual constituent quark like models. We also obtain the scalar mass M s =2 M Q independent of the regularization scheme. In the end, we calculate fully an example of a nonleptonic matrix element in the ENJL-model, the π +0 electromagnetic mass difference and find good agreement with the measured value.

Original languageEnglish
Pages (from-to)437-454
Number of pages18
JournalZeitschrift für Physik C Particles and Fields
Issue number3
Publication statusPublished - 1994 Sep 1
Externally publishedYes

Subject classification (UKÄ)

  • Subatomic Physics


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