Eur. Phys. J. A (2011) 47: 69
https://doi.org/10.1140/epja/i2011-11069-4

Regular Article - Theoretical Physics

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

¹ Institut für Kernphysik (Theorie), Institute for Advanced Simulation and Jülich Centre for Hadron Physics, Forschungszentrum Jülich, 52425, Jülich, Germany
² Institute for Theoretical and Experimental Physics, B. Cheremushkinskaya 25, 117218, Moscow, Russia

^* e-mail: a.nogga@fz-juelich.de

Received: 14 March 2011
Revised: 15 April 2011
Accepted: 15 April 2011
Published online: 31 May 2011

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.