arXiv 1201.43312012-01-20nucl-th

手征有效场论中核子-核子碰撞中π介子的产生：次次领头阶贡献

Pion production in nucleon-nucleon collisions in chiral effective field theory: next-to-next-to-leading order contributions

A. A. Filin, V. Baru, E. Epelbaum, C. Hanhart, H. Krebs, A. E. Kudryavtsev, F. Myhrer

备注：: 28 pages, 7 figures, 2 tables
DOI：: 10.1103/PhysRevC.85.054001

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摘要：

本文给出了手征有效场论中对$NN\to NNπ$达到并包括次次领头阶（$^2$ LO）跃迁算符有贡献的π-核子环在阈附近的完整计算.评估是基于所谓的动量计数计划，考虑到相对较大的动量的初始核子固有的π介子生产反应。我们发现，在下一个到领先的顺序（NLO）在早期的研究中发现的循环之间的显着取消也在N $^2$ LO操作。特别是，对环图的$1/m_N$修正（$m_N$是核子质量）在N $^2$ LO处抵消，涉及低能常数$c_i$的π环的贡献也是如此，i=1. 4.然而，与NLO计算相反，在N $^2$ LO处的环路的消除是不完整的，从而产生对过渡幅度的非零贡献。连同一π交换树级运营商，环路的贡献提供了生产运营商的长程部分。最后，我们讨论了这些发现的现象学意义。特别是，我们发现，产生的振幅的N $^2$ LO π介子环产生的贡献的大小与最重要的现象学重介子交换振幅。

英文摘要：

A complete calculation of the pion-nucleon loops that contribute to the transition operator for $NN\to NNπ$ up-to-and-including next-to-next-to-leading order (N$^2$LO) in chiral effective field theory near threshold is presented. The evaluation is based on the so-called momentum counting scheme, which takes into account the relatively large momentum of the initial nucleons inherent in pion-production reactions. We show that the significant cancellations between the loops found at next-to-leading order (NLO) in the earlier studies are also operative at N$^2$LO. In particular, the $1/m_N$ corrections (with $m_N$ being the nucleon mass) to loop diagrams cancel at N$^2$LO, as do the contributions of the pion loops involving the low-energy constants $c_i$, i=1...4. In contrast to the NLO calculation however, the cancellation of loops at N$^2$LO is incomplete, yielding a non-vanishing contribution to the transition amplitude. Together with the one-pion exchange tree-level operators, the loop contributions provide the long-range part of the production operator. Finally, we discuss the phenomenological implications of these findings. In particular, we find that the amplitudes generated by the N$^2$LO pion loops yield contributions comparable in size with the most important phenomenological heavy-meson exchange amplitudes.

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