arXiv 1003.38262010-03-19nucl-th

高精度计算π-核散射长度

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

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

备注：: 24 pages, 14 figures, 10 tables
DOI：: 10.1140/epja/i2011-11069-4

摘要：

计算了主导同位旋守恒的少核子对$^2$ H、$^3$ He和$^4$ He上π介子散射的贡献。我们表明，强贡献的π-核散射长度可以控制理论上的百分之几的准确度为isoscillate核和isovector核的10%。特别是，我们发现$π$ - $^3$ He散射长度是$(62 \pm 4\pm 7)\times 10^{-3} m_π^{-1}$，其中的不确定性是由于在$π$ -N散射长度和少核子效应，分别模糊。为了建立这种精度，我们需要确定一个合适的功率计数的π-核散射。为此，我们研究了两核子对散射长度的贡献与$^2$ H的结合能的关系。此外，我们调查的相对大小的领先的两个，三个和四个核子的贡献。对于有关积分的数值计算，本文提出了一种适用于动量空间的MonteCarlo方法。我们的研究结果表明，在一般情况下，由温伯格建议的功率计数是能够正确地预测的相对重要性的$N$ -核子算子，但是，它未能捕获的相对强度的$N$ -和$(N+1)$ -核子算子，在那里我们发现了一个抑制因子为5相比，预测的因子为50。讨论了从π介子$^2$ H和$^4$ He中提取等序$π$ -N散射长度的相关性.作为一个附带的结果，我们证明了超出$π$ - $^2$ H散射长度的计算已经超出了重π有效场论的适用范围。

英文摘要：

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 $π$-$^3$He scattering length to be $(62 \pm 4\pm 7)\times 10^{-3} m_π^{-1}$ 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 $^2$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 $π$-N scattering length from pionic $^2$H and $^4$He is discussed. As a side result, we show that beyond the calculation of the $π$-$^2$H scattering length is already beyond the range of applicability of heavy pion effective field theory.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

相关论文