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Perturbative calculations of nucleon-deuteron elastic scattering in chiral effective field theory

Lin Zuo, Wendi Chen, Dan-Yang Pang, Bingwei Long

Abstract

We develop a framework for calculating nucleon-deuteron scattering using strict perturbation theory for treating subleading interactions in chiral effective field theory (ChEFT). Rather than using direct evaluations in the distorted-wave expansion, our approach solves a hierarchy of integral equations to obtain subleading scattering amplitudes. A benchmark with the wave packet continuum-discretization is performed. This framework benefits from the fact that the renormalization-group invariance chiral forces involves only a limited number of two-body partial waves at leading order. We use it to calculate nucleon-deuteron elastic scattering differential cross sections and analyzing powers up to next-to-leading order.

Perturbative calculations of nucleon-deuteron elastic scattering in chiral effective field theory

Abstract

We develop a framework for calculating nucleon-deuteron scattering using strict perturbation theory for treating subleading interactions in chiral effective field theory (ChEFT). Rather than using direct evaluations in the distorted-wave expansion, our approach solves a hierarchy of integral equations to obtain subleading scattering amplitudes. A benchmark with the wave packet continuum-discretization is performed. This framework benefits from the fact that the renormalization-group invariance chiral forces involves only a limited number of two-body partial waves at leading order. We use it to calculate nucleon-deuteron elastic scattering differential cross sections and analyzing powers up to next-to-leading order.
Paper Structure (9 sections, 52 equations, 8 figures, 3 tables)

This paper contains 9 sections, 52 equations, 8 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Faddeev equation with Deformed Contour
  3. Jacobi partial-wave basis
  4. Inhomogeneous Faddeev equation
  5. Deformed Contour
  6. Perturbation theory for subleading order
  7. Benchmarks
  8. Results
  9. Summary

Figures (8)

  • Figure 1: The diagrammatic representation of the Faddeev equation. The solid line represents the nucleons, the solid circle the two-body off-shell $T$-matrix, the blue half circle the deuteron, the yellow blob the Faddeev breakup amplitude. Not all the particle-exchange topologies are shown.
  • Figure 2: Diagram showing the analytic structure of $V^{1\pi}(p',p")$ when the integration contours for both $p'$ and $p"$ are rotated by an angle $\theta$. The red lines indicate the trajectories of the two branch points at $p"=p'\pm im_{\pi}$, which originate from the end-point singularities of the integral.
  • Figure 3: Analytic structure of $V^{1\pi}(k,p")$ with the $p"$ contour rotated by an angle $\theta$. The solid dots points indicate the end-point singularities of the integral.
  • Figure 4: Comparison of the $nd$ elastic scattering differential cross sections and neutron analyzing powers. Results obtained with the contour-deformation and the WPCD method are shown as solid and dashed curves, respectively.
  • Figure 5: The doublet and quadruplet $S$-wave phase shifts as functions of $E_N$ for various cutoff $\Lambda$. Top and bottom panels correspond to the $^2S_{\frac{1}{2}}$ and $^4S_{\frac{3}{2}}$ channels, respectively.
  • ...and 3 more figures