Exploring HVV amplitudes with CP violation using decomposition and the on-shell scattering amplitude method

CP violation may play an important role in baryogenesis in the early universe and should be examined comprehensively at colliders.We study the CP properties of HVV vertexes between Higgs and gauge boson pairs by defining a CP violation phase angle,which indicates the mixture of CP-even and CP-odd Higgs states in HVV in new physics.A series of HVV amplitudes,H→γγ,H-→V→γtt,and H→VV-→4f,with a CP phase angle are studied systematically to explicitly explain why CP violation can only be probed independently in the 4t pro-cess.We obtain a novel amplitude decomposition relation that illustrates that if two preconditions(multilinear mo-mentum dependent vertexes,and the current J_(μ) of V→l^(+)l^(-)is formally proportional to a photon's polarization vec-tor)are satisfied,a higher-point amplitude can be decomposed into a summation of a series of lower-point amp-litudes.As a practical example,the amplitude of the H→γV-→γtt and H→VV→4t processes can be decom-posed into a summation of many H→γγ 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 CP viola-tion phase angle.The above two approaches provide consistent results and clearly reveal the CP violation ξ depend-ence in the amplitudes.