Deuteron electromagnetic form factors in a renormalizable formulation of chiral effective field theory

E Epelbaum,M R Schindler,A M Gasparyan,J Gegelia

doi:10.1140/epja/i2014-14051-8

Abstract

We calculate the deuteron electromagnetic form factors in a modified version of Weinberg's chiral effective field theory approach to the two-nucleon system. We derive renormalizable integral equations for the deuteron without partial wave decomposition. Deuteron form factors are extracted by applying the Lehmann-Symanzik-Zimmermann reduction formalism to the three-point correlation function of deuteron interpolating fields and the electromagnetic current operator. Numerical results of a leading-order calculation with removed cutoff regularization agree well with experimental data.

Highlights

The seminal papers by Weinberg on chiral effective field theory (EFT) of nuclear forces [1,2] have triggered an intense activity starting with ref
One of the most discussed aspects of the application of chiral effective field theory to twoand few-body problems is related to the question of how to properly renormalize the resulting integral equations
We extend our recently suggested renormalizable formulation of nuclear chiral EFT with non-perturbative pions [6] to calculate the electromagnetic form factors of the deuteron at lowest order

Summary

Introduction

The seminal papers by Weinberg on chiral effective field theory (EFT) of nuclear forces [1,2] have triggered an intense activity starting with ref. [3]. [6], which is based on the manifestly Lorentzinvariant effective Lagrangian and time-ordered perturbation theory Within this scheme the leading-order (LO) nucleon-nucleon scattering amplitude is obtained by solving an integral equation (known as the Kadyshevsky equation [7]), and corrections are calculated perturbatively. We extend our recently suggested renormalizable formulation of nuclear chiral EFT with non-perturbative pions [6] to calculate the electromagnetic form factors of the deuteron at lowest order. The crucial new feature of our framework is its explicit renormalizability in spite of the nonperturbative treatment of the one-pion–exchange (OPE) potential This allows us to take the cutoff parameter to infinity when calculating the two-nucleon amplitude both perturbatively as well as non-perturbatively.

The deuteron form factors

The deuteron equation

Discussion and summary