Abreu S, Febres Cordero F, Ita H, Jaquier M, Page B, Ruf M S, Sotnikov V
Center for Cosmology, Particle Physics and Phenomenology (CP3), Université Catholique de Louvain, 1348 Louvain-La-Neuve, Belgium.
Physics Department, Florida State University, Tallahassee, Florida 32306, USA.
Phys Rev Lett. 2020 May 29;124(21):211601. doi: 10.1103/PhysRevLett.124.211601.
We present the analytic form of the two-loop four-graviton scattering amplitudes in Einstein gravity. To remove ultraviolet divergences we include counterterms quadratic and cubic in the Riemann curvature tensor. The two-loop numerical unitarity approach is used to deal with the challenging momentum dependence of the interactions. We exploit the algebraic properties of the integrand of the amplitude in order to reduce it to a minimal basis of Feynman integrals. Analytic expressions are obtained from numerical evaluations of the amplitude. Finally, we show that four-graviton scattering observables depend on fewer couplings than naïvely expected.
我们给出了爱因斯坦引力中两圈四引力子散射振幅的解析形式。为消除紫外发散，我们纳入了黎曼曲率张量的二次和三次抵消项。采用两圈数值幺正性方法来处理相互作用中具有挑战性的动量依赖性。我们利用振幅被积函数的代数性质，将其简化为费曼积分的最小基。通过对振幅的数值计算得到解析表达式。最后，我们表明四引力子散射可观测量所依赖的耦合比天真预期的要少。
