Three-Loop Gravitational Ladder Diagrams in Twistor-EBIKK-β Theory

This work presents the first complete analysis of 3-loop gravitational ladder diagrams in UV-finite quantum gravity using twistor-regularizationmethods. We demonstrate the automatic finiteness of ladder-type amplitudes through κ-dependent propagators and entropic terms, extendingprevious 2-loop results. The calculation reveals a characteristic κ3ln(µ2/κ) dependence in the effective action, with implications for Planck-scalephenomenology. The mechanism guarantees finiteness for all loop orders, resolving key challenges in quantum gravity.本工作首次采用扭量正则化方法（twistor-regularization methods），针对紫外有限量子引力（UV-finite quantum gravity）中的三圈引力梯级图（3-loop gravitational ladder diagrams）开展完整分析。我们借助依赖κ的传播子与熵项，证明了梯级型振幅的自动有限性，拓展了此前的两圈研究成果。本次计算揭示了有效作用量中存在特征性的κ³ln(µ²/κ)依赖关系，该结论对普朗克尺度现象学具有重要启示。该机制可保证任意圈阶下的理论有限性，解决了量子引力领域的关键科学难题。