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Towards a high-precision calculation for the pion-nucleus scattering lengths

  • S. Liebig
  • V. Baru
  • F. Ballout
  • C. Hanhart
  • A. NoggaEmail author
Regular Article - Theoretical Physics

Abstract

We calculate the leading isospin-conserving few-nucleon contributions to pion scattering off 2H, 3He, and 4He. We demonstrate that the strong contributions to the pion-nucleus scattering lengths can be controlled theoretically to an accuracy of a few percent for isoscalar nuclei and of 10% for isovector nuclei. In particular, we find the π-3He scattering length to be (62 ± 4 ± 7) × 10−3 m π −1 where the uncertainties are due to ambiguities in the π-N scattering lengths and few-nucleon effects, respectively. To establish this accuracy we need to identify a suitable power counting for pion-nucleus scattering. For this purpose we study the dependence of the two-nucleon contributions to the scattering length on the binding energy of 2H. Furthermore, we investigate the relative size of the leading two-, three-, and four-nucleon contributions. For the numerical evaluation of the pertinent integrals, a Monte Carlo method suitable for the momentum space is devised. We observe that, so far, no power counting is able to provide a quantitative understanding of the relative strength of N- and (N + 1)]]-nucleon operators. Empirically, we find a relative suppression by a factor of 5 compared to a factor of 50 predicted from dimensional analysis. On the other hand, the relative importance of different contributions within each class of N-nucleon operators can be understood within Weinberg counting. The relevance of our findings for the extraction of the isoscalar π-N scattering length from pionic 2H and 4He is outlined. We also discuss the applicability of heavy pion effective field to the π-2H system.

Keywords

Wave Function Monte Carlo Power Counting Deuteron Binding Energy Pion Scattering 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© SIF, Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • S. Liebig
    • 1
  • V. Baru
    • 1
    • 2
  • F. Ballout
    • 1
  • C. Hanhart
    • 1
  • A. Nogga
    • 1
    Email author
  1. 1.Institut für Kernphysik (Theorie), Institute for Advanced Simulation and Jülich Centre for Hadron PhysicsForschungszentrum JülichJülichGermany
  2. 2.Institute for Theoretical and Experimental PhysicsMoscowRussia

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