关于双子–磁单极子催化的有效场论
On the EFT of Dyon-Monopole Catalysis
AI总结：
本文将PPEFT用于低能S波双子–费米子散射，证明大催化截面并不违反退耦，并处理真空极化及双子激发响应的有效描述。
摘要：
磁单极子–费米子（以及双子–费米子）相互作用提供了一个著名例子：从致密客体散射时，截面可以远大于该客体的几何尺寸。这构成了磁单极子催化重子数破坏现象的基础，因为存在磁单极子时的反应速率远高于不存在磁单极子时的反应速率。有时人们声称这违背了在其他情形下普遍成立的要求，即短程物理应与长程可观测量退耦——这一性质支撑着有效场论（EFT）方法的广泛适用性。在此语境下，退耦最简单的表述可借助点粒子有效场论（PPEFT）给出；这类理论旨在系统地刻画：当只在远大于客体尺寸的长度尺度上进行探测时，小而重的客体如何影响其周围环境。它们已在关于核性质如何影响普通原子和π原子能级的精密计算中得到检验。我们调整PPEFT形式体系，用以描述低能S波双子–费米子散射，以理解巨大的催化截面是否违背退耦，并说明为何它们并不违背。我们还探讨了一个相关但独立的问题：使双子外部的费米子真空极化所带来的长程复杂性，并展示在某些情况下，PPEFT方法如何能够在存在这些复杂性时简化低能费米子–双子散射的计算。我们以含时真空角的形式提出了一个有效哈密顿量，用于支配双子激发如何响应费米子散射，并概述了其微观推导中仍然存在的开放问题。
英文摘要：
Monopole-fermion (and dyon-fermion) interactions provide a famous example where scattering from a compact object gives a cross section much larger than the object's geometrical size. This underlies the phenomenon of monopole catalysis of baryon-number violation because the reaction rate is much larger in the presence of a monopole than in its absence. It is sometimes claimed to violate the otherwise generic requirement that short distance physics decouples from long-distance observables -- a property that underpins the general utility of effective field theory (EFT) methods. Decoupling in this context is most simply expressed using point-particle effective field theories (PPEFTs) designed to capture systematically how small but massive objects influence their surroundings when probed only on length scales large compared to their size. These have been tested in precision calculations of how nuclear properties affect atomic energy levels for both ordinary and pionic atoms. We adapt the PPEFT formalism to describe low-energy $S$-wave dyon-fermion scattering with a view to understanding whether large catalysis cross sections violate decoupling (and show why they do not). We also explore the related but separate issue of the long-distance complications associated with polarizing the fermion vacuum exterior to a dyon and show in some circumstances how PPEFT methods can simplify calculations of low-energy fermion-dyon scattering in their presence. We propose an effective Hamiltonian governing how dyon excitations respond to fermion scattering in terms of a time-dependent vacuum angle and outline open questions remaining in its microscopic derivation.
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