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Expectation values of four-quark operators in the nucleon

E. G. Drukarev·M. G. Ryskin·V. A. Sadovnikova·V. E. Lyubovitskij·Th. Gutsche·Amand Faessler
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Abstract

We calculate expectation values of QCD operators consisting of the products of the four operators of the light quarks corresponding to the scalar, pseudoscalar, vector, pseudovector (axial) and tensor Lorentz structures in the nucleon. All combinations of the light flavors are considered. For the evaluation we use elements of the Perturbative Chiral Quark Model (PCQM), approximating the contribution of the valence quarks by the contribution of the PCQM constituent quarks. The contribution of the sea quarks is treated by averaging over the QCD pions with the distribution of the pion field being determined by the PCQM. For quarks with the same flavor the expectation values are dominated by the contribution of the sea-quarks. In the scalar case the contribution of the sea quarks is dominated by the "disconnected terms" were one of the pairs of the quark operators acts on the vacuum while the other one acts on the quarks of the pion. The role of the interference terms with one of the quark pairs acting on the sea quarks and another one acting on the valence quarks increases for quarks with different flavors. The result for the scalar condensate is compared to the one obtained earlier in the framework of the Nambu -Jona-Lasinio model.

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E. G. Drukarev, M. G. Ryskin, V. A. Sadovnikova, V. E. Lyubovitskij, Th. Gutsche, Amand Faessler. 2003-06-16. Expectation values of four-quark operators in the nucleon. https://doi.org/10.1103/physrevd.68.054021

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