Weinbergʼs approach to nucleon–nucleon scattering revisited

E Epelbaum,J Gegelia

doi:10.1016/j.physletb.2012.08.025

E Epelbaum, J Gegelia

Open Access

https://doi.org/10.1016/j.physletb.2012.08.025

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Abstract

We propose a new, renormalizable approach to nucleon–nucleon scattering in chiral effective field theory based on the manifestly Lorentz invariant form of the effective Lagrangian without employing the non-relativistic expansion. For the pion-less case and for the formulation based on perturbative pions, the new approach reproduces the known results obtained by Kaplan, Savage and Wise. Contrary to the standard formulation utilizing the non-relativistic expansion, the non-perturbatively resummed one-pion exchange potential can be renormalized by absorbing all ultraviolet divergences into the leading S-wave contact interactions. We explain in detail the differences to the non-relativistic formulation and present numerical results for two-nucleon phase shifts at leading order in the low-momentum expansion.

Highlights

The last two decades have witnessed a renewed interest in the nuclear force problem and nuclear physics thanks to the development and application of effective field theory (EFT) methods
Based on the KSW approach at next-to-leading order (NLO) in the EFT expansion, we demonstrate in section 3 the consistency of this scheme with respect to the power counting
In this paper we applied the manifestly Lorentz-invariant form of the effective Lagrangian to the problem of nucleon-nucleon scattering without relying on the heavy-baryon expansion

Summary

Introduction

The last two decades have witnessed a renewed interest in the nuclear force problem and nuclear physics thanks to the development and application of effective field theory (EFT) methods. The potentially enhanced contributions of these higher-order Mπ2-dependent operators might become an issue if one is interested in the quark mass dependence of nucleon-nucleon scattering but do not affect the predictive power of the theory in terms of describing the energy dependence of the phase shift at the physical values of the quark masses. The appearance of such divergences seems to indicate that the same enhancement, which is responsible for non-perturbativeness of the OPE potential 2 , applies to higher-order shortrange operators This feature is sometimes referred to as inconsistency of Weinberg’s approach.

The framework

Perturbative pions at next-to-leading order

Non-perturbative pions at leading order

Summary and conclusions