We discuss the dRGT massive gravity interacting with spin-0, spin-1/2, or spin-1 matter. The effective theory of a massive spin-2 particle coupled to matter particles is constructed directly at the amplitude level. In this setting we calculate the gravitational Compton scattering amplitudes and study their UV properties. While the Compton am- plitudes generically grow with energy as O ( E 6 ), we identify regions of the parameter space where they are softened to O ( E 4 ) or even O ( E 3 ), which allows for a larger validity range of the effective theory. In these regions, both positivity and beyond-positivity of the forward Compton amplitudes are fulfilled, and the equivalence principle automatically emerges.

中文翻译：

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大重力中的物质耦合

我们讨论了 dRGT 大重力与自旋 0、自旋 1/2 或自旋 1 物质相互作用。与物质粒子耦合的大质量自旋 2 粒子的有效理论是直接在振幅水平上构建的。在此设置中，我们计算引力康普顿散射幅度并研究它们的 UV 特性。虽然康普顿振幅通常随能量增长为 O ( E 6 )，但我们确定了参数空间的区域，其中它们被软化为 O ( E 4 ) 甚至 O ( E 3 )，这允许更大的有效性范围有效理论。在这些区域，前向康普顿振幅的正性和超正性都得到满足，等效原理自动出现。