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

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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 −1π 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.

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Authors and Affiliations

  1. Institut für Kernphysik (Theorie), Institute for Advanced Simulation and Jülich Centre for Hadron Physics, Forschungszentrum Jülich, 52425, Jülich, Germany

    S. Liebig, V. Baru, F. Ballout, C. Hanhart & A. Nogga

  2. Institute for Theoretical and Experimental Physics, B. Cheremushkinskaya 25, 117218, Moscow, Russia

    V. Baru

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  1. S. Liebig
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  2. V. Baru
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  3. F. Ballout
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  4. C. Hanhart
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  5. A. Nogga
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Correspondence to A. Nogga.

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Communicated by J. Bijnens

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Liebig, S., Baru, V., Ballout, F. et al. Towards a high-precision calculation for the pion-nucleus scattering lengths. Eur. Phys. J. A 47, 69 (2011). https://doi.org/10.1140/epja/i2011-11069-4

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