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Vector currents of integer-spin Majorana particles

A general and comprehensive analysis for the vector currents of two massive particles, $X_2$ and $X_1$, with arbitrary integer-spin values is given. Our special focus is on the case when two particles are charge self-conjugate, i.e. Majorana bosons. The general structure of their couplings to an on-shell or off-shell vector boson $V$ is described in a manifestly covariant way and then the constraints on the triple vertex due to discrete CP symmetry and the Majorana condition of two particles being Majorana are worked out. The validity of our full analytic investigation is checked by studying the two-body decay, $X_2\to V X_1$, with an on-shell or off-shell $V$ boson in the helicity formalism complementary to the covariant formulation. Threshold effects of the two-lepton invariant-mass and polar-angle correlations in the two sequential two-body decays, $X_2\to V X_1$ and $V\to \ell^-\ell^+$ with $\ell=e$ or $μ$, are derived analytically in a compact form by use of the Wick helicity rotation and they are investigated numerically in a few specific spin-combination scenarios for probing the spin and dynamical structure of the $X_2X_1V$ vertex.