Exploring HVV amplitudes with CP violation using decomposition and the on-shell scattering amplitude method* *Supported by the National Natural Science Foundation of China ( 11847168), the Fundamental Research Funds for the Central Universities of China (GK202003018) and the Natural Science Foundation of Shannxi Province, China (2019JM-431, 2019JQ-739)

Abstract

violation may play an important role in baryogenesis in the early universe and should be examined comprehensively at colliders. We study the properties of vertexes between Higgs and gauge boson pairs by defining a violation phase angle ξ, which indicates the mixture of -even and -odd Higgs states in in new physics. A series of amplitudes, , and , with a phase angle are studied systematically to explicitly explain why violation can only be probed independently in the process. We obtain a novel amplitude decomposition relation that illustrates that if two preconditions (multilinear momentum dependent vertexes, and the current of is formally proportional to a photon's polarization vector) are satisfied, a higher-point amplitude can be decomposed into a summation of a series of lower-point amplitudes. As a practical example, the amplitude of the and processes can be decomposed into a summation of many amplitudes. We calculate these amplitudes in the framework of the on-shell scattering amplitude method, considering both massless and massive vector gauge bosons with the violation phase angle. The above two approaches provide consistent results and clearly reveal the violation ξ dependence in the amplitudes.