arXiv 2407.016842024-07-17hep-phgr-qchep-th

具有膜局域曲率项的 Randall-Sundrum 模型中的散射振幅

Scattering amplitudes in the Randall-Sundrum model with brane-localized curvature terms

R. Sekhar Chivukula, Kirtimaan A. Mohan, Dipan Sengupta, Elizabeth H. Simmons, Xing Wang

备注：: 36 pages, 2 figures. Minor changes, new reference added
发表信息：: Phys.Rev.D 110 (2024) 9, 095034
DOI：: 10.1103/PhysRevD.110.095034

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AI总结：

研究含膜局域曲率项的 Randall-Sundrum 模型，揭示自旋2 KK态散射振幅呈 ${\cal O}(s^3)$ 增长，并将其归因于自旋0 Goldstone/Galileon 相互作用及微分同胚不变性结构。

摘要：

本文研究具有膜局域曲率项的 Randall-Sundrum 模型中自旋为2的 Kaluza-Klein（KK）态的散射振幅。我们表明，膜局域曲率相互作用的存在改变了度规的（4D）标量涨落的性质，导致有质量自旋2 KK态的散射振幅按 ${\cal O}(s^3)$ 而非 ${\cal O}(s)$ 增长。我们基于自旋2和自旋0度规涨落的 Sturm-Liouville 模系统的一致性，讨论了对膜局域曲率相互作用强度的约束。我们将散射振幅的性质与具有膜局域曲率相互作用的紧致化 KK 理论的微分同胚不变性联系起来。我们验证了涉及膜局域外源（物质）的散射振幅具有微分同胚不变性，但表明定域在体空间任意点处的物质的散射振幅则不然。我们证明，在 Feynman 规范中，对应于有质量自旋2 KK玻色子螺旋度0态的自旋0 Goldstone玻色子表现为一个 Galileons 塔，正是它们的相互作用产生了散射振幅的高能行为。我们还概述了我们的结果与 Dvali-Gabadadze-Porrati（DGP）模型中结果之间的对应关系。在附录中，我们讨论了额外维规范理论中的类似问题，并表明膜局域规范动能项的存在不会改变相应 KK 矢量玻色子散射振幅的高能行为。

英文摘要：

In this paper we investigate the scattering amplitudes of spin-2 Kaluza-Klein (KK) states in Randall-Sundrum models with brane-localized curvature terms. We show that the presence of brane-localized curvature interactions modifies the properties of (4D) scalar fluctuations of the metric, resulting in scattering amplitudes of the massive spin-2 KK states which grow as ${\cal O}(s^3)$ instead of ${\cal O}(s)$. We discuss the constraints on the size of the brane-localized curvature interactions based on the consistency of the Sturm-Liouville mode systems of the spin-2 and spin-0 metric fluctuations. We connect the properties of the scattering amplitudes to the diffeomorphism invariance of the compactified KK theory with brane-localized curvature interactions. We verify that the scattering amplitudes involving brane-localized external sources (matter) are diffeomorphism-invariant, but show that those for matter localized at an arbitrary point in the bulk are not. We demonstrate that, in Feynman gauge, the spin-0 Goldstone bosons corresponding to helicity-0 states of the massive spin-2 KK bosons behave as a tower of Galileons, and that it is their interactions that produce the high-energy behavior of the scattering amplitudes. We also outline the correspondence between our results and those in the Dvali-Gabadadze-Porrati (DGP) model. In an appendix we discuss the analogous issue in extra-dimensional gauge theory, and show that the presence of a brane-localized gauge kinetic-energy term does not change the high-energy behavior of corresponding KK vector boson scattering amplitudes.

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