Abstract
We review on a novel chiral power counting scheme for in-medium chiral perturbation theory with nucleons and pions as degrees of freedom. It allows for a systematic expansion taking into account local as well as pion-mediated inter-nucleon interactions. Based on this power counting, one can identify classes of nonperturbative diagrams that require a resummation. As a method for performing those resummations we review on the techniques of Unitary Chiral Pertubation Theory for nucleon-nucleon interactions. We then apply both power counting and non-perturbative methods to the example of calculating the pion self-energy in asymmetric nuclear matter up-to-and-including next-to-leading order. It is shown that the leading corrections involving in-medium nucleon-nucleon interactions cancel between each other at given chiral orders.
Highlights
Ref.[18] considers the ground state of nuclear matter which, under the action of any time dependent operator at asymptotic times, behaves as Fermi seas of nucleons
At least one is needed, otherwise we would have a vacuum closed nucleon loop that in a low energy effective field theory is buried in the higher order counterterms
Denoting by k the on-shell four-momenta associated with one Fermi sea insertion in the in-medium generalized vertex” (IGV), the
Summary
Ref.[18] considers the ground state of nuclear matter which, under the action of any time dependent operator at asymptotic times, behaves as Fermi seas of nucleons. Ref.[18] establishes the concept of an “in-medium generalized vertex” (IGV) Such type of vertices result because one can connect several bilinear vacuum vertices through the exchange of baryon propagators with the flow through the loop of one unit of baryon number, contributed by the nucleon Fermi seas. At least one is needed, otherwise we would have a vacuum closed nucleon loop that in a low energy effective field theory is buried in the higher order counterterms It was stressed in ref.[12] that within a nuclear environment a nucleon propagator could have a “standard” or “non-standard” chiral counting. In order to treat chiral Lagrangians with an arbitrary number of baryon fields (bilinear, quartic, etc) ref.[1] considered firstly bilinear vertices like in refs.[12, 18], but the additional exchanges of heavy meson fields of any type are allowed.
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