Use of the Nambu-Jona-Lasino model in the calculation of the density dependence of four-quark condensates.

Abstract

Recent works concerning QCD sum rules in nuclear matter have provided a new method for the calculation of the nucleon self-energy in matter. The results of that program depend strongly on assumptions made concerning the density dependence of four-quark condensates. If a factorization scheme is used to express the four-quark condensate values in terms of the two-quark condensates, the (Lorentz) scalar self-energy of the nucleon is small. However, if the four-quark condensates have only a weak density dependence, the nucleon scalar self-energy is large and attractive, and is in accordance with Dirac phenomenology. In this paper our goal is to show how the Nambu--Jona-Lasinio model may be used to calculate the density dependence of four-quark condensates. As an elementary example we calculate some of the contributions to a four-quark condensate containing scalar-isoscalar [ital [bar q]q] pairs. These calculations suggest only a very small modification of the value of the scalar-isoscalar condensate in matter relative to the value obtained in the factorization scheme. However, when we continue our study of the correlator of operators with the quantum numbers of the nucleon, we encounter some new and important terms among the four-quark condensates. These have their origin in an exchange process betweenmore » diquarks in the nucleon and diquarks present in the nucleons of the nuclear medium (nuclear matter). These terms may be taken to represent the effects of diquark condensates'' they are present in nuclear matter. If we use the interpolating field advocated by Ioffe we obtain a correction that eliminates the problematic density dependence of the four-quark condensates described above, if nuclear matter contains a similar amount of scalar ([ital T]=0) diquarks and axial-vector ([ital T]=1) diquarks. We believe that our paper provides increased confidence in the use of QCD sum rules in the study of the properties of hadrons in matter.« less