Relativistic self-energy decomposition of nuclear symmetry energy and equation of state of neutron matter within QCD sum rules

Abstract

Properties of the relativistic nucleon self-energy decomposition of the symmetry energy as well as the equation of state (EOS) of pure neutron matter (PNM) are explored systematically within the QCD sum rules (QCDSR). Our main conclusions are as follows: (1) The five self-energy decomposition terms of the symmetry energy according to the nucleon Lorentz structure are carefully studied, leading to the conclusion that the symmetry energy increases as the nucleon sigma term ${\ensuremath{\sigma}}_{\mathrm{N}}$ increases and the contributions to the symmetry energy due to the momentum dependence of the self-energies in symmetric nuclear matter (SNM) are very small compared with those from other decomposition terms. (2) A smaller strange quark mass is found to generate a larger symmetry energy, and this correlation is useful for understanding the origins of the uncertainties on the (nucleonic matter) symmetry energy from quark level. (3) The EOS of PNM at low densities can be effectively approximated by ${E}_{\mathrm{n}}(\ensuremath{\rho})\ensuremath{\approx}{E}_{\mathrm{n}}^{\mathrm{FFG}}(\ensuremath{\rho})+(M\ensuremath{\rho}/2{\ensuremath{\langle}\overline{q}q\ensuremath{\rangle}}_{\mathrm{vac}})[(1\ensuremath{-}\ensuremath{\xi})({\ensuremath{\sigma}}_{\mathrm{N}}/2{m}_{\mathrm{q}})\ensuremath{-}5]$ which depends only on several physical quantities such as ${m}_{\mathrm{q}},{\ensuremath{\sigma}}_{\mathrm{N}}$ and ${\ensuremath{\langle}\overline{q}q\ensuremath{\rangle}}_{\mathrm{vac}}$, and this formula already has predictive power and the results are found to be consistent with those from other celebrated microscopic many-body theories at low densities. (4) The higher order density terms in quark condensates are shown to be important to describe the empirical EOS of PNM in the density region around and above nuclear saturation density, and these higher order density terms are also found to hinder the appearance of chiral symmetry restoration in PNM at high densities. (5) The symmetry energy is shown to depend strongly on the five-dimensional condensate ${\ensuremath{\langle}{g}_{\mathrm{s}}{q}^{\ifmmode\dagger\else\textdagger\fi{}}\ensuremath{\sigma}\mathcal{G}q\ensuremath{\rangle}}_{\ensuremath{\rho},\ensuremath{\delta}}$, providing a useful approach to explore the symmetry energy through knowledge on the condensates which can be extracted from hadronic physics. (6) The twist-4 four-quark condensates are shown to have significant effects on the EOS of both SNM and PNM but have minor effects on the symmetry energy, and combined with the analyses on the effects of the higher order density terms in the chiral condensates, three parameter sets of QCDSR are constructed and they are shown to be able to describe the EOS of PNM and the symmetry energy within a wide range of densities. Our results in the present work demonstrate that the QCDSR approach can provide a useful way to understand the properties of dense nucleonic matter from nonperturbative QCD vacuum.