论文标题
具有浅s波共振的两体系统的有效现场理论
Effective Field Theory for Two-Body Systems with Shallow S-Wave Resonances
论文作者
论文摘要
共振对于量子力学中复合颗粒的散射特别重要。我们为两体散射建立了一个有效的现场理论，其中包括低能$ S $波的共鸣。我们的起点是最通用的拉格朗日，具有短距离交互。我们证明可以将这些相互作用组织到各种订单中，以便为带有两个低能杆的$ s $矩阵产生系统扩展。 POL位置受到领先顺序重新归一化的限制，其中共同特征是非阳性有效范围。我们明确地进行了扩展到近代领先的顺序，并说明了它如何系统地解释玩具模型的结果 - 球形井在其边界处有三角洲外壳。
Resonances are of particular importance to the scattering of composite particles in quantum mechanics. We build an effective field theory for two-body scattering which includes a low-energy $S$-wave resonance. Our starting point is the most general Lagrangian with short-range interactions. We demonstrate that these interactions can be organized into various orders so as to generate a systematic expansion for an $S$ matrix with two low-energy poles. The pole positions are restricted by renormalization at leading order, where the common feature is a non-positive effective range. We carry out the expansion explicitly to next-to-leading order and illustrate how it systematically accounts for the results of a toy model -- a spherical well with a delta shell at its border.
