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

Understand

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.