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arXiv 2409.09534hep-thhep-ph
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双标量 Sigma 模型的新软定理

New Soft Theorems for Two-Scalar Sigma Models

Karol Kampf, Jiri Novotny, Mikhail Shifman, Jaroslav Trnka

AI总结:

本文研究双标量 sigma 模型的软散射行为,证明 Goldstone 情形仅有 Adler 零点,并构造及推广不含振幅导数的非平凡软定理与求和规则。

摘要:

在本文中,我们研究具有两个标量的 sigma 模型的散射振幅和软定理。我们表明,如果粒子是 Goldstone 玻色子,那么必然得到 Adler 零点,不存在非平凡软定理的可能性。对于非 Goldstone 玻色子,软行为通常由 Cheung 等人研究的几何软定理刻画,其右端包含低点振幅的导数。受近期关于二维 sigma 模型工作的启发,我们研究一个特殊的双标量 sigma 模型,其中目标空间中对称性的存在转化为一个特殊但非平凡、且不含导数的软定理。我们进一步将该构造推广到两类更大的此类模型,并导出若干软定理求和规则,同样避免振幅的导数。我们的分析提供了一个有趣的双标量 sigma 模型与软定理层级,从 Goldstone 玻色子情形延伸到一般目标空间,并表明二者之间存在有趣的理论。

英文摘要:

In this paper, we study the scattering amplitudes and soft theorems for the sigma models with two scalars. We show that if the particles are Goldstone bosons, then you necessarily get Adler zero with no possibility for non-trivial soft theorems. For non-Goldstone bosons, the soft behavior is generically captured by the geometric soft theorem studied by Cheung et al., and the right-hand side contains derivatives of lower-point amplitudes. Inspired by the recent work on the 2D sigma models, we study one special two-scalar sigma model, where the presence of symmetries in the target space translates into a special but non-trivial soft theorem without derivatives. We further generalize the construction to two larger classes of such models and derive certain soft theorem sum rules, again avoiding the derivatives of amplitudes. Our analysis provides an interesting hierarchy of two-scalar sigma models and soft theorems, ranging from Goldstone boson case to a generic target space, and showing that there are interesting theories in between.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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