Perturbative nuclear physics

TL;DR

This paper introduces a new perturbative effective field theory for nucleon-nucleon interactions that improves convergence and enables high-precision analytic calculations in nuclear physics.

Contribution

It develops a perturbative formulation of nuclear EFT treating pion interactions and addresses convergence issues by summing short-distance singularities to all orders.

Findings

Expansion converges satisfactorily to third order in s and d wave NN scattering.

Summing short-distance singularities improves convergence.

Enables high-precision analytic few-body nuclear calculations.

Abstract

We present a new formulation of effective field theory for nucleon-nucleon (NN) interactions which treats pion interactions perturbatively, and we offer evidence that the expansion converges satisfactorily to third order in the expansion, which we have computed analytically for s and d wave NN scattering. Starting with the Kaplan-Savage-Wise (KSW) expansion about the nontrivial fixed point corresponding to infinite NN scattering length, we cure the convergence problems with that theory by summing to all orders the singular short distance part of the pion tensor interaction. This method makes possible a host of high precision analytic few-body calculations in nuclear physics.