Baryons and baryonic matter in the large Nc and heavy quark limits

This paper explores properties of baryons and finite density baryonic matter in an artificial world in which Nc, the number of colors, is large and the quarks of all species are degenerate and much larger than {\Lambda}_QCD. It has long been known that in large Nc QCD, baryons composed entirely of heavy quarks are accurately described in the mean-field approximation. However, the detailed properties of baryons in the combined large Nc and heavy quark 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 Nc and heavy quark expansions the baryon mass is computed explicitly as is the baryon form factor. Baryonic matter, the analog of nuclear matter in this artificial world, should also be well described in the mean-field approximation. In the special case where all baryons have an identical spin flavor structure, it is shown that in the formal heavy quark and large Nc 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 spin-flavor structure is dropped, a phase of baryonic matter exists with a density of 2Nf times that for the restricted case but with the same energy (where Nf is the number of degenerate flavors). It is shown that this phase is at least metastable.