无鬼双度规理论树级 $2\to 2$ 散射振幅的完整集合
Complete set of tree-level $2\to 2$ scattering amplitudes of ghost-free bimetric theory
- Stockholm University（斯德哥尔摩大学）
- The Oskar Klein Centre, Stockholm University（斯德哥尔摩大学奥斯卡·克莱因中心）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文计算了无鬼双度规理论在比例闵可夫斯基背景下的全部199个树级2→2散射振幅，发现振幅层级结构，且最大能量增长为E^6，对应Λ3标度。
AI中文摘要：
双度规理论是广义相对论的扩展，它微扰地描述了一个无质量和一个有质量的引力子。该理论允许观测上可行的宇宙学，通过局部引力测试，并为动态暗能量和自旋-2暗物质提供候选者。散射振幅通过解析性、幺正性和因果性等性质，为其一致性提供了互补的探测手段。虽然密切相关的大质量引力理论的树级 $2\to 2$ 振幅此前已被计算和分析，但双度规理论更丰富的振幅结构大多仅针对特定过程和螺旋度扇区进行了研究。我们给出了无鬼双度规理论在比例闵可夫斯基背景周围树级 $2\to 2$ 散射振幅的完整集合。我们将作用量展开到质量本征态的四阶，并使用计算机代数工作流程计算所有 $199$ 个对称不等价的螺旋度振幅。我们发现了一个清晰的层级结构：具有单个有质量外部态的振幅为零，恰好具有两个有质量外部态的振幅与非线性双度规参数无关，而非线性无鬼参数依赖性首次出现在具有三个有质量外部态的情况中。取大质量引力极限可得到完整的树级 $2\to 2$ 大质量引力振幅集合，与先前结果完全一致。最后，所有振幅随能量的增长最多为 $E^6$，对应于特征性的 $\Lambda_3$ 强耦合标度，且这种最大增长无法通过任何非平凡的理论参数选择来消除。
英文摘要：
Bimetric theory is an extension of general relativity that perturbatively describes one massless and one massive graviton. It admits observationally viable cosmologies, passes local tests of gravity, and provides candidates for dynamical dark energy and spin-2 dark matter. Scattering amplitudes provide a complementary probe of its consistency, e.g. through analyticity, unitarity, and causality. While the tree-level $2\to2$ amplitudes of the closely related theory of massive gravity have previously been computed and analysed, the richer amplitude structure of bimetric theory has mostly been studied for selected processes and helicity sectors. We present the complete set of tree-level $2\to2$ scattering amplitudes of ghost-free bimetric theory around proportional Minkowski backgrounds. We expand the action through quartic order in the mass eigenstates and use a computer-algebra workflow to compute all of the $199$ symmetry-inequivalent helicity amplitudes. We find a clear hierarchy: amplitudes with a single massive external state vanish, those with exactly two are independent of the nonlinear bimetric parameters, and nonlinear ghost-free parameter dependence first appears with three massive external states. Taking the massive-gravity limit yields the complete set of tree-level $2\to2$ massive gravity amplitudes, which agree exactly with previous results. Finally, all amplitudes grow with energy at most as $E^6$, corresponding to the characteristic $Λ_3$ strong-coupling scale, and this maximal growth cannot be eliminated by any nontrivial choice of the theory parameters.
