Two-loop corrections for nuclear matter in a covariant effective field theory

Abstract

Although one-loop calculations provide a realistic description of bulk and single-particle nuclear properties, it is necessary to examine loop corrections to develop a systematic finite-density powercounting scheme for the nuclear many-body problem when loops are included. Moreover, it is imperative to study exchange and correlation corrections systematically to make reliable predictions for other nuclear observables. One must also verify that the natural sizes of the one-loop parameters are not destroyed by explicit inclusion of many-body corrections. The loop expansion is applied to a chiral effective hadronic lagrangian; with the techniques of Infrared Regularization, it is possible to separate out the short-range contributions and to write them as local products of fields that are already present in our lagrangian. (The appropriate field variables must be re-defined at each order in loops.) The corresponding parameters implicitly include short-range effects to all orders in the interaction, so these effects need not be calculated explicitly. The remaining (long-range) contributions that must be calculated are nonlocal and resemble those in conventional nuclear-structure calculations. Calculations at the two-loop level are carried out to illustrate these techniques at finite densities and to verify that the coupling parameters remain natural when fitted to the empirical properties of equilibrium nuclear matter.

Neutrinoproduction of photons and pions from nucleons in a chiral effective field theory for nuclei

“…For example, the interactions in the Eq. (18) lead to proper description of vector transition current at nonzero Q 2 and meanwhile it is relevant to two-body currents: suppose a photon is absorbed by one nucleon producing a ∆ which then interacts with other nucleon through the interactions mentioned above.…”

“…Explicit powercounting of loop diagrams in this EFT has been discussed in Refs. [17][18][19]. Here the contributions of the loops are assumed to be (mostly) saturated by heavy mesons and the ∆ resonance, so the couplings of contact interactions are viewed as being renormalized.…”

Effects of the Dirac sea on pion propagation in asymmetric nuclear matter

“…Currently, the non-linear chiral effective field theoretic approach seems to be quite successful in this respect. It might be recalled here, that, in such a framework, the explicit calculation of the Dirac vacuum is not required, rather, on the contrary, here, the short distance dynamics are absorbed into the parameters of the theory adjusted phenomenologically by fitting empirical data [30,31,42]. Now we proceed to calculate the effective pion masses in ANM in this approach.…”

Electroweak Interactions in a Chiral Effective Lagrangian for Nuclei

“…In principle, there are an infinite number of possible interaction terms in this lagrangian. However, power counting (Furnstahl et al, 1997;Hu et al, 2007;McIntire et al, 2007) and Naive Dimensional Analysis (NDA) (Georgi & Manohar, 1984;Georgi, 1993) enable us to truncate this series of interactions to achieve a good approximation. Following the discussion in Ref.…”

“…The motivation for this EFT and illustrations of some calculated results are discussed in Refs. (Furnstahl et al, 1997;Hu et al, 2007;Huertas, 2002;McIntire et al, 2007;McIntire, 2008;Serot, 2007;2010), for example. This QHD EFT has also been applied to a discussion of the isovector axial-vector current in nuclei (Ananyan et al, 2002).…”