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arXiv 2106.04568hep-thgr-qchep-ph
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从引力等价定理和双拷贝理论看Kaluza-Klein引力子散射振幅的结构

Structure of Kaluza-Klein Graviton Scattering Amplitudes from Gravitational Equivalence Theorem and Double-Copy

Yan-Feng Hang, Hong-Jian He

摘要:

本文研究了紧致化5d广义相对论中Kaluza-Klein(KK)引力子和KKGoldstone玻色子的散射振幅结构。我们在一般的$R_ξ$规范固定下分析了紧致化下KK引力子质量产生的几何“Higgs”机制,该规范固定不受vDVZ不连续性的影响.然后,我们建立了引力等效定理(GRET),将纵向KK引力子振幅与KK Goldstone振幅联系起来,这是几何Higgs机制在$S$ -矩阵水平上的一种表现。在高能极限下,我们直接计算了与纵向KK引力子振幅相等的三能级KK Goldstone振幅。我们进一步推广了色运动学对偶的双拷贝方法,从紧致化的5d Yang-Mills(YM)理论中的KK纵向规范玻色子(Goldstone)振幅在高能展开下重建了质量为KK的纵向引力子(Goldstone)振幅.从这些,我们重建的KK纵向引力子(戈德斯通)振幅在5d GR从KK纵向规范玻色子(戈德斯通)振幅在5d YM理论的GRET。无论是使用GRET还是双拷贝重建,我们都提供了一个理论机制,表明高能四纵向KK引力子振幅中所有能量-功率项之和[直到$O(E^{10})$ ]必须抵消到$O(E^2)$,这是通过匹配相应KK Goldstone振幅的能量-功率依赖性或通过匹配KK YM理论的双拷贝振幅来实现的。利用双拷贝方法,我们建立了5d KK YM理论中的$E^4 \to E^0$和5d KK GR理论中的$E^{10} \to E^2$这两个能量抵消之间的新的对应关系.我们进一步分析了GRET中剩余项的结构,发现了一种新的能量抵消机制。

英文摘要:

We study the structure of scattering amplitudes of the Kaluza-Klein (KK) gravitons and of the gravitational KK Goldstone bosons in the compactified 5d General Relativity (GR). We analyze the geometric "Higgs" mechanism for mass-generation of KK gravitons under compactification with a general $R_ξ$ gauge-fixing, which is free from the vDVZ discontinuity. Then, we formulate the Gravitational Equivalence Theorem (GRET) to connect the longitudinal KK graviton amplitudes to the KK Goldstone amplitudes, which is a manifestation of the geometric Higgs mechanism at $S$-matrix level. We directly compute the tree-level KK Goldstone amplitudes which equal the longitudinal KK graviton amplitudes in the high energy limit. We further extend the double-copy method with color-kinematics duality to reconstruct the massive KK longitudinal graviton (Goldstone) amplitudes from the KK longitudinal gauge boson (Goldstone) amplitudes in the compactified 5d Yang-Mills (YM) theory under high energy expansion. From these, we reconstruct the GRET of the KK longitudinal graviton (Goldstone) amplitudes in the 5d GR from the KK longitudinal gauge boson (Goldstone) amplitudes in the 5d YM theory. Using either the GRET or the double-copy reconstruction, we provide a theoretical mechanism showing that the sum of all the energy-power terms [up to $O(E^{10})$] in the high-energy four longitudinal KK graviton amplitudes must cancel down to $O(E^2)$ as enforced by matching the energy-power dependence of the corresponding KK Goldstone amplitudes or by matching that of the double-copy amplitudes from the KK YM theory. With the double-copy approach, we establish a new correspondence between the two energy-cancellations: $E^4 \to E^0$ in the 5d KK YM theory and $E^{10} \to E^2$ in the 5d KK GR theory. We further analyze the structure of the residual terms in the GRET and uncover a new energy-cancellation mechanism therein.

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