Equilibrium of nuclear matter in QCD sum rules

Abstract

We calculate the nucleon parameters in symmetric nuclear matter employing the QCD sum rules approach. We focus on the average energy per nucleon and study the equilibrium states of the matter. We treat the matter as a relativistic system of interacting nucleons. Assuming the dependence of the nucleon mass on the light quark mass $m_q$ to be more important than that of nucleon interactions we find that the contribution of the relativistic nucleons to the scalar quark condensate can be expressed as that caused by free nucleons at rest multiplied by the density dependent factor $F(\rho)$. We demonstrate that there are no equilibrium states while we include only the condensates with dimension $d \leq 3$. There are equilibrium states if we include the lowest order radiative corrections and the condensates with $d \leq 4$. They manifest themselves for the nucleon sigma term $\sigma_N >60$ MeV. Including the condensates with $ d \leq 6$ we find equilibrium states of nuclear matter for $\sigma_N> 41$ MeV. In all cases the equilibrium states are due to influence of the relativistic motion of the nucleons composing the matter on the scalar quark condensate.