We investigate phenomenological implications of vector bosons V transforming as (1, 2, -3/2) under the standard model (SM) product gauge group SU(3)C, SU(2)L and U(1)Y. These vector bosons can couple to two SM leptons at tree-level forming dimension-4 operators. These operators dictate V to have two units of global lepton number, ∆L = 2. The operators generated conserve the global lepton number but can violate generational lepton numbers. We study constraints on the couplings Y of V to SM particles using tree-level processes such as \( {l}_{\alpha}^{-}\to {l}_{\beta}^{+}{l}_{\rho}^{-}{l}_{\sigma}^{-} \) , muonium and antimuonium oscillation, neutrino trident scattering, inverse muon decay, e−e+ → l−l+, and also one-loop level processes such as the magnetic dipole moment of a charged lepton and li → ljγ. Strong constraints are obtained from \( {l}_{\alpha}^{-}\to {l}_{\beta}^{+}{l}_{\rho}^{-}{l}_{\sigma}^{-} \) with | \( {Y}_{ee}{Y}_{\mu e}^{\ast } \) | < 3.29 × 10−11 (mV/GeV)2, \( \mid {Y}_{ee}{Y}_{\mu e}^{\ast}\mid \) < 3.29 × 10−11 (mV/GeV)2 and from li → ljγ with \( \mid {Y}_{\tau e}{Y}_{\mu \tau}^{\ast}\mid \) < 3.46 × 10−12(mV/GeV)2, \( \mid {Y}_{e\tau}{Y}_{\tau \mu}^{\ast}\mid \) < 3.46 × 10−12 (mV/GeV)2, respectively. Interestingly, the imaginary part of the coupling constant in our model induces CP violation, which is constrained by experimental limits on the electric dipole moment.
