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

Abstract

We calculate the leading isospin conserving few-nucleon contributions to pion scattering on ${}^2$H, ${}^3$He, and ${}^4$He. 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 $\pi$-${}^3$He scattering length to be $(62\pm 4\pm 7)\times 10^{-3}{m}_{\pi }^{-1}$ where the uncertainties are due to ambiguities in the $\pi$-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 ${}^2$H. Furthermore, we investigate the relative size of the leading two-, three-, and four-nucleon contributions. For the numerical evaluation of the pertinent integrals, aMonte Carlo method suitable for momentum space is devised. Our results show that in general the power counting suggested by Weinberg is capable to properly predict the relative importance of $N$-nucleon operators, however, it fails to capture the relative strength of $N$- and $(N+1)$-nucleon operators, where we find a suppression by a factor of 5 compared to the predicted factor of 50. The relevance for the extraction of the isoscalar $\pi$-N scattering length from pionic ${}^2$H and ${}^4$He is discussed. As a side result, we show that beyond the calculation of the $\pi$-${}^2$H scattering length is already beyond the range of applicability of heavy pion effective field theory.

24 pages, 14 figures, 10 tables

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Cited by in corpus (23)

• Nuclear effective field theory: status and perspectives
• Hyperon-nucleon interaction at next-to-leading order in chiral effective field theory
• Roy-Steiner-equation analysis of pion-nucleon scattering
• Precision calculation of threshold pi^- d scattering, pi N scattering lengths, and the GMO sum rule
• Precision calculation of the pi^- deuteron scattering length and its impact on threshold pi-N scattering
• Convergence properties of {\itshape ab initio} calculations of light nuclei in a harmonic oscillator basis
• Electric Dipole Moments of Light Nuclei From Chiral Effective Field Theory
• P- and T-Violating Lagrangians in Chiral Effective Field Theory and Nuclear Electric Dipole Moments
• Remarks on the pion-nucleon sigma-term
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• First-principle calculations of Dark Matter scattering off light nuclei
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• On the role of isospin violation in the pion-nucleon $\sigma$-term
• Towards a high precision calculation for the pion-nucleus scattering lengths
• The magnetic form factor of the deuteron in chiral effective field theory
• Ab-initio electroweak corrections to superallowed $\beta$ decays and their impact on $V_{ud}$
• Effective Field Theory calculations of $NN\to NN\pi$
• Properties of infrared extrapolations in a harmonic oscillator basis
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• Threshold neutral pion photoproduction off the tri-nucleon to O(q^4)
• Pion absorption from the lowest atomic orbital in 2H, 3H and 3He
• Nucleon mass: trace anomaly and $\sigma$-terms
• Enhancement of deltaful two-pion exchange nuclear forces