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arXiv 1602.02640nucl-th
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手征微扰理论中的π-核子弹性散射:新的观点

Elastic pion-nucleon scattering in chiral perturbation theory: A fresh look

D. Siemens, V. Bernard, E. Epelbaum, A. Gasparyan, H. Krebs, Ulf-G. Meißner

摘要:

在手征微扰理论的框架内,重子展开和协变方法的基础上扩展的质量壳重正化方案的四阶弹性π介子核子散射分析。我们详细讨论了重整化的各种低能量常数,并提供明确的表达式相关的$β$ -功能和有限的减法的功率计数打破条款内的协变配方。为了估计手征展开截断的理论不确定性,我们采用了一种已成功应用于最近的核力分析的方法。这使我们能够可靠地提取相关的低能量常数从可用的散射数据在低能量。所得结果提供了一个明确的证据表明,该反应的手性扩展的崩溃规模与$Δ$共振。明确列入领先的贡献的$Δ$ -同量异位素被证明大大增加了适用范围的有效场论。由此产生的预测的相移是在一个很好的协议与最近的罗伊-施泰纳方程分析的π-核子散射。

英文摘要:

Elastic pion-nucleon scattering is analyzed in the framework of chiral perturbation theory up to fourth order within the heavy-baryon expansion and a covariant approach based on an extended on-mass-shell renormalization scheme. We discuss in detail the renormalization of the various low-energy constants and provide explicit expressions for the relevant $β$-functions and the finite subtractions of the power-counting breaking terms within the covariant formulation. To estimate the theoretical uncertainty from the truncation of the chiral expansion, we employ an approach which has been successfully applied in the most recent analysis of the nuclear forces. This allows us to reliably extract the relevant low-energy constants from the available scattering data at low energy. The obtained results provide a clear evidence that the breakdown scale of the chiral expansion for this reaction is related to the $Δ$-resonance. The explicit inclusion of the leading contributions of the $Δ$-isobar is demonstrated to substantially increase the range of applicability of the effective field theory. The resulting predictions for the phase shifts are in an excellent agreement with the ones from the recent Roy-Steiner-equation analysis of pion-nucleon scattering.

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