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arXiv 2408.09375hep-phcond-mat.quant-gashep-latnucl-th
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长程力下的有效力程展开

Effective range expansion with a long-range force

Meng-Lin Du, Feng-Kun Guo, Bing Wu

AI总结:

针对左支割线限制有效力程展开适用性的问题,提出一种包含非解析项的类Padé参数化方法,可推广有效力程展开并广泛适用于Yukawa型相互作用系统,尤其有助于理解近阈值强子共振。

摘要:

由于在两粒子阈值附近存在左支割线,历史悠久的有效力程展开的适用范围可能非常有限。这种左支割线出现在两粒子相互作用中,涉及交换一个质量小于或略大于两粒子质量差的轻粒子,这被认定为一种长程力,在广泛的系统中都会遇到。这会妨碍对低能散射观测量和共振极点的精确提取。为了解决这一问题,我们提出了一种新的低能散射振幅参数化方法,该方法考虑了左支割线。该参数化类似于Padé近似,但包含来自左支割线的非解析项,可视为有效力程展开的一种推广。这种参数化方法具有通用性,适用于广泛的具有Yukawa型相互作用的系统——包括粒子、强子、核、冷原子和量子气体系统。特别是,它在理解各种近阈值强子共振方面应具有重要价值。作为附带成果,我们还表明该参数化方法可用于提取被交换粒子与散射粒子之间的耦合常数,并推导出由短程和长程相互作用共同导致的振幅零点表达式。

英文摘要:

The validity range of the time-honored effective range expansion can be very limited due to the presence of a left-hand cut close to the two-particle threshold. Such a left-hand cut arises in the two-particle interaction involving a light particle exchange with a mass small or slightly heavier than the mass difference of the two particles, identified as a long-range force, a scenario encountered in a broad range of systems. This can hinder a precise extraction of low-energy scattering observables and resonance poles. To address this issue, we propose a new parameterization for the low-energy scattering amplitude that accounts for the left-hand cut. The parameterization is like a Padé approximation but with nonanalytic terms from the left-hand cut and can be regarded as an extension of the effective range expansion. This parameterization is versatile and applicable to a broad range of systems with Yukawa-type interactions -- including particle, hadronic, nuclear, cold atom and quantum gas systems. In particular, it should be invaluable in understanding various near-threshold hadron resonances. As byproducts, we also show that the parameterization can be used to extract the couplings of the exchanged particle to the scattering particles, and derive expressions for amplitude zeros caused by the interplay between the short- and long-range interactions.

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