标题： 手征对称性和核子-核子相互作用 显示英文标题

标题： Chiral Symmetry and the Nucleon Nucleon Interaction

摘要： 有效场论（EFT）在核子-核子（NN）相互作用中的应用的各个方面都被考虑。我们寻找超出一介子交换的贡献，这些贡献由手征对称性预测。使用威尔逊重整化群（RG）的形式理论，我们回顾了一个仅包含核子的简化EFT中的功率计数。对于低能弱散射，我们在RG的唯一平凡固定点周围找到了散射矩阵的自然展开。对于低能强散射，通过在对应于两个核子在阈值处束缚态的非平凡固定点周围展开势能，可以以一种有用且系统的方式进行计算。散射矩阵的逆的展开结果按顺序再现了有效范围展开。讨论了以符合手征对称性的方式将介子包含到这种EFT中的扩展。通过考虑修改的有效范围展开，我们发现S波散射的小动量展开如果收敛的话，收敛速度很慢。NN势能被写到了小动量的第三阶。在坐标空间中引入截断后，我们计算了EFT预测无需参数的外围部分波的相移，并且可以围绕平凡固定点进行展开。我们发现几个部分波中可以分离出两介子交换的影响，但在这一阶次中没有发现小动量展开收敛的有力证据。 显示英文摘要

摘要： Various aspects of the application of Effective Field Theory (EFT) to the Nucleon-Nucleon (NN) interaction are considered. We look for contributions beyond One Pion Exchange which are predicted by Chiral Symmetry. Using the formalism of the Wilson Renormalisation Group (RG) we review power counting in a simplified EFT containing only nucleons. For weak scattering at low energy, we find a natural expansion of the scattering matrix around the unique trivial fixed point of the RG. For strong scattering at low energy, the calculation can be organised in a useful and systematic way by expanding the potential around a non-trivial fixed point corresponding to a bound state of two nucleons at threshold. The resulting expansion of the inverse of the scattering matrix reproduces the effective range expansion order by order. The extension of this EFT to include pions in a manner consistent with chiral symmetry is discussed. By considering a modified effective range expansion, we find that the small momentum expansion in S-wave scattering converges slowly, if at all. The NN potential is written down to third order in small momenta. With a cut-off in coordinate space, we calculate phase shifts in peripheral partial waves for which the EFT predictions are parameter-free, and for which we may use the expansion around the trivial fixed point. We find several partial waves in which the effects of two-pion exchange can be isolated, but no strong evidence is found for the convergence of the small momentum expansion at this order.