Fully Perturbative Calculation of $nd$ Scattering to Next-to-next-to-leading-order

TL;DR

This paper presents a new perturbative method for calculating neutron-deuteron scattering up to NNLO in pionless EFT, avoiding full off-shell amplitude calculations and showing good agreement with potential models.

Contribution

A novel technique for perturbative corrections in $nd$ scattering that simplifies calculations and includes a complete phase-shift analysis up to NNLO.

Findings

Good agreement with potential models at low energies.

Successful calculation of SD-mixing term at NNLO.

Complete phase-shift analysis including eigen-phases and mixing angles.

Abstract

We introduce a new technique to calculate perturbative corrections to neutron-deuteron ($nd$) scattering that does not require calculation of the full off-shell scattering amplitude. Its relation to the more familiar partial-resummation technique is explained. Also included is a calculation of the SD-mixing term that occurs at next-to-next-to-leading-order (NNLO) in pionless effective field theory $\mathrm{EFT}_{\not{\pi}}$\xspace. Using the new technique with the SD-mixing term a complete strictly perturbative phase-shift analysis of $nd$ scattering is performed up to NNLO including eigen-phases and mixing angles. This is compared to potential model calculations and good agreement is found with the eigen-phases and some of the mixing angles at low energies.