Twistor Particle Programme Rebooted: A "zig-z̄ag" Theory of Massive Spinning Particles

Recently, the Newman-Janis shift has been revisited from the angle of scattering amplitudes in terms of the so-called "massive spinor-helicity variables," tracing back to Penrose and Perjés in the 70s. However, well-established results are limited in the same-helicity (self-dual) sector, while a puzzle of spurious poles arises in mixed-helicity sectors. This talk will outline how massive twistor theory can reproduce the same-helicity results while offering a possible solution to the spurious pole puzzle. Firstly, the Newman-Janis shift in the same-helicity sector is derived from a complexified version of the equivalence principle. Secondly, the massive twistor particle is coupled to background fields from bottom-up and top-down perspectives. The former is based on perturbations of symplectic structures in massive twistor space. The latter provides a generalization of Newman-Janis shift in generic backgrounds, which also leads to "curved massive twistor space" and its deformed massive incidence relation. Lastly, the Feynman rules of the first-quantized massive twistor particle and their physical interpretation are briefly discussed. Overall, a significant emphasis is put on the Kähler geometry ("zig-z̄ag structure") of massive twistor space, which eventually connects to a worldsheet structure of the Kerr solution.