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arXiv 1202.0208nucl-th
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从有效场论看π-氘散射中的多重散射级数和核子-核子势

The multiple-scattering series in pion-deuteron scattering and the nucleon-nucleon potential: perspectives from effective field theory

V. Baru, E. Epelbaum, C. Hanhart, M. Hoferichter, A. E. Kudryavtsev, D. R. Phillips

摘要:

介子-核散射的重要贡献是由多重散射系列中的项产生的,多重散射系列被定义为介子在离开核之前在一对静态核子之间来回散射的所有图的总和。特别是,这一系列的总和是需要一个精确的描述K介子-氘核散射,并出现作为核子-核子势的一部分。在这篇文章中,我们提出了一些有效场论(EFT)为基础的见解,这一系列的情况下,两个核子系统。特别是,我们讨论的事实是,如果介子-核子散射近似的散射长度项,该系列的个别条款是发散的,并增强相对于直接的期望从手征微扰理论($χ$ PT)。这显然表明存在类似增强的反条件。然而,我们表明,当一系列的离散取消,这样就不需要额外的信息,在短距离相互作用,以获得预测的观测后,remation。我们讨论的条件下,这种重申是合理的。我们发现,同样的问题出现在$NN$潜在的,在那里的mammed系列产生的极点,其外观表示该数量的$χ$ PT扩展的击穿规模。这明确地表明,$χ$ PT不能应用于计算距离小于$r \sim 1$ fm的$V(r)$,至少在理论上没有明确的Delta(1232)自由度。我们简要地讨论是否可以降低这个界限,如果三角洲共振是包括在EFT作为一个明确的自由度。

英文摘要:

Important contributions to meson-nucleus scattering are produced by terms in the multiple-scattering series, which is defined as the sum of all diagrams where the meson scatters back and forth between a pair of static nucleons before leaving the nucleus. In particular, the sum of this series is needed for an accurate description of kaon-deuteron scattering, and appears as part of the nucleon-nucleon potential. In this article we present some effective-field-theory (EFT)-based insights into this series in the case of two-nucleon systems. In particular, we discuss the fact that, if meson-nucleon scattering is approximated by the scattering-length term, individual terms of the series are divergent, and enhanced with respect to the straightforward expectation from chiral perturbation theory ($χ$PT). This apparently indicates the presence of similarly enhanced counterterms. However, we show that when the series is resummed the divergences cancel, such that no additional information on short-range interactions is needed to obtain predictions for observables after resummation. We discuss the conditions under which this resummation is justified. We show that the same issues arise in the $NN$ potential, where the resummed series produces poles whose appearance indicates the breakdown scale of the $χ$PT expansion for that quantity. This demonstrates unequivocally that $χ$PT cannot be applied to compute $V(r)$ for distances smaller than $r \sim 1$ fm at least in the theory without explicit Delta(1232) degrees of freedom. We briefly discuss whether this bound can be lowered if the Delta resonance is included in the EFT as an explicit degree of freedom.

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