Expectation values of four-quark operators in the nucleon

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.Comment: 40 pages, 3 PS figure

Charmed baryon Λc in nuclear matter

“…We specifically consider two types of density dependences. The first one is based on the factorization hypothesis and the second is estimated from the perturbative chiral quark model (PCQM) [77,78].…”

Role of the in-medium four-quark condensates reexamined

“…As noted in [13], the latter contribution was overlooked in [9]. The matrix element R XY can obtain a nonzero value also in the axialpseudoscalar channel with Γ X = γ 0 γ 5 , Γ Y = γ 5 .…”

“…Inclusion of nonlocality of the vector condensate and of some other small corrections [9] changes the last equation to (see Appendix B)…”

“…(17) can be obtained by straightforward calculations (see Appendix C). We find the numerical values for the 4u case [9] A q S = −0.05 + 0.04α; A …”

Operator product expansion and quark–hadron duality: facts and riddles

“…A simple and beautiful discussion of the ρ meson (positive) mass shift in nuclei is, however, given in [120]. New developments concerning the treatment of nucleon matrix elements,in particular the ones of four-quark operators, deserve a review article in their own right, for a recent publication relying on the perturbative chiral quark model see [118]. Here we focus on interesting OPE aspects at finite density which hint on a fundamental manifestation of strong interactions at purely Euclidean external momenta in both vacuum and hadron properties: the occurrence of strong nonperturbative correlations characterized by mass scales considerably larger than the perturbative scale Λ QCD .…”