Towards a power counting in nuclear energy–density–functional theories through a perturbative analysis

Abstract

We illustrate a step towards the construction of a power counting in energy–density–functional (EDF) theories, by analyzing the equations of state (EOSs) of both symmetric and neutron matter. Within the adopted strategy, next–to–leading order (NLO) EOSs are introduced which contain renormalized first–order–type terms and an explicit second–order finite part. Employing as a guide the asymptotic behavior of the introduced renormalized parameters, we focus our analysis on two aspects: (i) With a minimum number of counterterms introduced at NLO, we show that each energy contribution entering in the EOS has a regular evolution with respect to the momentum cutoff (introduced in the adopted regularization procedure) and is found to converge to a cutoff–independent curve. The convergence features of each term are related to its Fermi–momentum dependence. (ii) We find that the asymptotic evolution of the second–order finite–part coefficients is a strong indication of a perturbative behavior, which in turns confirms that the adopted strategy is coherent with a possible underlying power counting in the chosen Skyrme–inspired EDF framework.