Exploring $HVV$ amplitudes with $CP$ violation by decomposition and on-shell scattering amplitude methods

Abstract

$CP$ violation may play an important role in Baryogenesis in early universe, and should be examined at colliders comprehensively. We study $CP$ properties of $HVV$ vertexes between Higgs and gauge boson pairs with defining a $CP$ violation phase angle $\xi$, which indicates the mixture of $CP$-even and $CP$-odd Higgs states in $HVV$ in new physics. A series of $HVV$ amplitudes $H\to \gamma \gamma ,H\to \gamma V\to \gamma \ell \ell$, and $H\to VV\to 4\ell$ with $CP$ phase angle are studied systematically, which explains explicitly why $CP$ violation could only be probed in $4\ell$ process independently. We get a novel amplitude decomposition relation which illustrates if two preconditions (multilinear momentum dependent vertexes and current $J_{\mu }$ of $V\to {\ell }^{+}{\ell }^{-}$ is formally proportional to a photon's polarization vector) are satisfied, an high-point amplitude can be decomposed into a summation of a series of low-point amplitudes. As a practical example, the amplitude of $H\to \gamma V\to \gamma \ell \ell$, and $H\to VV\to 4\ell$ processes can be decomposed into summation of many $H\to \gamma \gamma$ amplitudes. Meanwhile, we calculate these amplitudes in the framework of on-shell scattering amplitude method, with considering both massless and massive vector gauge bosons with $CP$ violation phase angle. The above two approaches provides consistent results and exhibit clearly the $CP$ violation $\xi$ dependence in the amplitudes.

33 pages, 11 figures

References in corpus (6)

• Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC
• Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC
• Constraints on the Higgs boson width from off-shell production and decay to Z-boson pairs
• Measurements of the Higgs boson width and anomalous HVV couplings from on-shell and off-shell production in the four-lepton final state
• Measurement of the Higgs boson width and evidence of its off-shell contributions to ZZ production
• Massive On-shell Recursion Relations for n-point Amplitudes

Cited by in corpus (2)

• Study on the sensitivity of the Higgs boson couplings in photon-photon collision at CLIC and muon collider
• $H\to Z\gamma$ decay and $CP$ violation