Constraints on ∆L = 2 vector bosons with tree couplings to SM particles

Abstract

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 l_i → l_jγ. Strong constraints are obtained from $l_{\alpha }^{-}\to l_{\beta }^{+}{l}_{\rho }^{-}{l}_{\sigma }^{-}$ with |$Y_{\mathit{ee}}{Y}_{\mathit{\mu e}}^{\ast }$| < 3.29 × 10⁻¹¹ (m_V/GeV)²,$\mid Y_{\mathit{ee}}{Y}_{\mathit{\mu e}}^{\ast }\mid$< 3.29 × 10⁻¹¹ (m_V/GeV)² and from l_i → l_jγ with $\mid Y_{\mathit{\tau e}}{Y}_{\mathit{\mu \tau }}^{\ast }\mid$< 3.46 × 10⁻¹²(m_V/GeV)²,$\mid Y_{\mathit{e\tau }}{Y}_{\mathit{\tau \mu }}^{\ast }\mid$< 3.46 × 10⁻¹² (m_V/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.