标题： 关于磁单极子催化理论的EFT 显示英文标题

标题： On the EFT of Dyon-Monopole Catalysis

摘要： 单极子-费米子（以及磁单极子-费米子）相互作用提供了一个著名的例子，在这个例子中，从一个紧凑物体的散射会产生远大于物体几何尺寸的截面。 这构成了单极子催化违反重子数现象的基础，因为在存在单极子的情况下反应速率比不存在时大得多。 有时声称它违反了短距离物理通常与长距离可观测量解耦的普遍要求——这一性质支撑了有效场论（EFT）方法的广泛应用。 在这种背景下，解耦最简单地可以用点粒子有效场论（PPEFT）来表达，这些理论旨在系统地捕获当仅在远大于其尺寸的尺度上探测时，小但质量大的物体如何影响其周围环境。 这些理论已在普通和π介子原子的核性质对原子能级的影响的精确计算中得到验证。 我们采用PPEFT形式主义来描述低能$S$波磁单极子-费米子散射，以了解是否大的催化截面违反了解耦（并说明为何它们没有）。 我们还探讨了与此相关但独立的问题，即在外围极化磁单极子费米子真空的长距离复杂性，并展示了在某些情况下PPEFT方法如何简化低能费米子-磁单极子散射的计算。 我们提出了一个有效的哈密顿量，用时变的真空角度来描述磁单极子激发对费米子散射的响应，并概述了其微观推导中仍存在的开放问题。 显示英文摘要

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.