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

Bijnens, Johan LU orcid ; de Rafael, Eduardo and Zheng, Hanqing (1994) In Zeitschrift für Physik C Particles and Fields 62(3). p.437-454
Abstract

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... (More)

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 + -π 0 electromagnetic mass difference and find good agreement with the measured value.

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type
Contribution to journal
publication status
published
subject
in
Zeitschrift für Physik C Particles and Fields
volume
62
issue
3
pages
18 pages
publisher
Springer Nature
external identifiers
  • scopus:0000392110
ISSN
0170-9739
DOI
10.1007/BF01555904
language
English
LU publication?
no
id
e44feb84-ab11-4d5d-9cdd-e8a07f76d993
date added to LUP
2019-05-03 09:31:06
date last changed
2025-04-04 14:40:27
@article{e44feb84-ab11-4d5d-9cdd-e8a07f76d993,
  abstract     = {{<p>                            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                            <sub>c</sub>                             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                            <sub>s</sub>                            =2 M                            <sub>Q</sub>                             independent of the regularization scheme. In the end, we calculate fully an example of a nonleptonic matrix element in the ENJL-model, the π                            <sup>+</sup>                            -π                            <sup>0</sup>                             electromagnetic mass difference and find good agreement with the measured value.</p>}},
  author       = {{Bijnens, Johan and de Rafael, Eduardo and Zheng, Hanqing}},
  issn         = {{0170-9739}},
  language     = {{eng}},
  month        = {{09}},
  number       = {{3}},
  pages        = {{437--454}},
  publisher    = {{Springer Nature}},
  series       = {{Zeitschrift für Physik C Particles and Fields}},
  title        = {{Low-energy behaviour of two-point functions of quark currents}},
  url          = {{http://dx.doi.org/10.1007/BF01555904}},
  doi          = {{10.1007/BF01555904}},
  volume       = {{62}},
  year         = {{1994}},
}