Baryons and baryonic matter in the large N_{c} and heavy quark limits
Abstract
This paper explores properties of baryons and finite density baryonic matter in an artificial world in which N_{c}, the number of colors, is large and the quarks of all species are degenerate and much larger than Λ_{QCD}. It has long been known that in large N_{c} quantum chromodynamics (QCD), baryons composed entirely of heavy quarks are accurately described in the meanfield approximation. However, the detailed properties of baryons in the combined large N_{c} and heavyquark limits have not been fully explored. Here some basic properties of baryons are computed using a variational approach. At leading order in both the large N_{c} and heavyquark expansions the baryon mass is shown to be M_{baryon}≈N_{c}M_{Q}(10.05426α∼_{s}^{2}), where α∼_{s}≡N_{c}α_{s}. The baryon form factor is also computed. Baryonic matter, the analog of nuclear matter in this artificial world, should also be well described in the meanfield approximation. In the special case where all baryons have an identical spinflavor structure, it is shown that in the formal heavyquark and large N_{c} limit interactions between baryons are strictly repulsive at low densities. The energy per baryon is computed in this limit and found to be exponentially small. It is shown that when the restriction to baryons with an identical spinflavor structure is dropped, a phase of baryonic matter exists with a density of 2N_{f} times that for the restricted case but with the same energy (where N_{f} is the number of degenerate flavors). It is shown that this phase is at least metastable.
 Publication:

Physical Review C
 Pub Date:
 July 2011
 DOI:
 10.1103/PhysRevC.84.015204
 arXiv:
 arXiv:1102.2197
 Bibcode:
 2011PhRvC..84a5204C
 Keywords:

 11.15.Pg;
 12.39.Hg;
 14.20.c;
 24.85.+p;
 Expansions for large numbers of components;
 Heavy quark effective theory;
 Baryons;
 Quarks gluons and QCD in nuclei and nuclear processes;
 Nuclear Theory;
 High Energy Physics  Phenomenology;
 High Energy Physics  Theory
 EPrint:
 19 pages