Chiral Limit of Nuclear Physics

We study nuclear physics in the chiral limit (mu, md = 0) in which the pion mass vanishes. We find that the deuteron mass is changed little, but that P–wave nucleon–nucleon scattering volumes are infinite. This motivates an investigation of the possibilities that there could be a two–nucleon 3P0 bound state, and that the nuclear matter ground state is likely to be a condensed state of nucleons paired to those quantum numbers. However, the short distance repulsion in the nucleon–nucleon potential is not affected by the chiral limit and prevents such new chiral possibilities. Thus the chiral limit physics of nuclei is very similar to that of nature. Using the chiral limit to simplify QCD sum rule calculations of nuclear matter properties seems to be a reasonable approximation. The derivative coupling of pions to nucleons, which results from spontaneously broken chiral symmetry, plays a major role in the structure of nuclei. This coupling, suppressed by the small momenta typical of nuclear physics, prevents the nuclear ground state, a system of strongly interacting hadrons, from being a pion soup. The net result is that the pion dominated internucleon interactions play a significant, but not dominant, role in the structure of the nuclei. The effects of the two pion exchange potential are believed to account for some of the needed mid–range attraction, but are not strong enough to induce a phase transition from the normal Fermi liquid that is believed to describe the ground state of heavy nuclei. During recent years there has been a renewed interest in applying chiral Lagrangian models and QCD sum rules towards the description of microscopic nuclear structure[1, 2]. An important element of these analyses is the implicit assumption that the chiral limit mq → 0, in which mπ → 0 as well, is smooth enough and does not change qualitatively properties of nuclei. This is reflected in an assertion that the major nuclear characteristics can be expressed through various vacuum condensates which can be determined in the mq → 0 limit. In particular, it was suggested that in this limit one can use the ω, σ–model where pion degrees of freedom are essentially irrelevant[3]. This assumption raises a question: What is the nature of nuclei in the mq → 0 limit? One can see immediately that the one pion exchange potential acquires a long range tensor interaction between nucleons ∝ r. This new interaction raises the possibility that in the chiral limit the structure of the nuclear ground state may be very different from that of actual nuclei. In the absence of quark masses the only scale in QCD is ΛQCD ≈ 200 MeV, so that one might naively expect that the binding energy of the deuteron and the binding energy per nucleon in nuclear matter might be of that order of magnitude. The purpose of the present note is to analyze nuclear properties in the chiral limit. This is based on the chiral limit of the nucleon–nucleon NN interaction. To take this limit we need to analyze the different scales. Our view is that the NN interaction can be understood in terms of two mass scales: the mπ scale which governs the long range physics and the mρ scale which governs short range physics. We explicitly set mπ to zero in the long range part of the nucleon–nucleon potential, but assume that the