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Towards a high precision calculation for the pion-nucleus scattering lengths | | S. Liebig
; V. Baru
; F. Ballout
; C. Hanhart
; A. Nogga
; | | Date: |
19 Mar 2010 | | 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 $(62 pm 4pm 7) imes 10^{-3} m_{pi}^{-1}$ 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. | | Source: | arXiv, 1003.3826 | | Services: | Forum | Review | PDF | Favorites | |
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