The Contribution of the Quark Condensate to the πN Sigma Term

Abstract

There has been a discrepancy between values of the pion-nucleon sigma term extracted by two different methods for many years. Analysis of recent high precision pion-nucleon data has widened the gap between the two determinations. We argue that the two extractions correspond to different definitions and that the difference between them can be understood and calculated. The sigma term is directly related to explicit chiral symmetry breaking in the nucleon. The conventional view has been that its value can be obtained by either an extrapolation of the isospin zero pion-nucleon scattering amplitude to a defined subthreshold point or by comparing masses of members of the baryon octet. There has long been a problem that the two determinations do not result in the same value. We argue that they should not have the same value and that the difference is about what one should expect. The value extracted from the comparison of masses (ΣM) is commonly thought to be around 35 MeV while the value of the sigma term extracted from pion-nucleon scattering (ΣS) was given by Koch as 64 ± 8 MeV [1] using dispersion analysis and the KarlsruheHelsinki phase shifts. While this difference was disturbing, there were theoretical corrections to be made and the pion-nucleon data at that time were not of high quality, especially at low energy. It was suggested that the difference could be interpreted as evidence for a large component of strangeness in the nucleon [3, 2]. Estimates of the strangeness content from the strange meson cloud give around 7.6% [4]. From neutrino induced reactions the strangeness content has been reported as 6.4 % [5] and 9.9 % [6] (although corrections to these numbers may be significant [7]), making the 20% required for this explanation of the discrepancy questionable. The πN data base has been improved recently (see Ref. [8] for an analysis). New sigmaterm extractions with this data, however, did not reduce the discrepancy, but increased it. Kaufmann and Hite[9] used interior and fixed t dispersion relations to map out the subthreshold amplitude. They obtained a value of ΣS = 88± 15 MeV. Recently Olsson and

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Cite this paper

@inproceedings{Kaufmann2003TheCO, title={The Contribution of the Quark Condensate to the πN Sigma Term}, author={William Kaufmann}, year={2003} }