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arXiv 2007.07360nucl-th
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具有浅S波共振的两体系统的有效场论

Effective Field Theory for Two-Body Systems with Shallow S-Wave Resonances

J. Balal Habashi, S. Sen, S. Fleming, U. van Kolck

摘要:

在量子力学中,共振对于复合粒子的散射具有特别重要的意义。建立了一个包含低能$S$波共振的二体散射的有效场论。我们的出发点是最一般的拉格朗日与短程相互作用。我们证明,这些相互作用可以组织成各种订单,以产生一个系统的扩展为$S$矩阵与两个低能量极点。极点的位置受到重正化的限制,在领导阶,其中的共同特点是一个非正的有效范围。我们进行了扩展,明确下一个领先的顺序,并说明它如何系统地占一个玩具模型的结果-一个在其边界的三角洲壳的球形井。

英文摘要:

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.

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