Constraints on $\Delta L=2$ 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, $\Delta L=2$. 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, $e^{-}{e}^{+}\to l^{-}{l}^{+}$, and also one-loop level processes such as the magnetic dipole moment of a charged lepton and $l_i\to l_j\gamma$. Strong constraints are obtained from $l_{\alpha }^{-}\to l_{\beta }^{+}{l}_{\rho }^{-}{l}_{\sigma }^{-}$ with $\left|Y_{ee}{Y}_{\mu e}^{\ast }\right|<3.29\times 10^{-11}{\left(m_V/\mathrm{GeV}\right)}^2,\left|Y_{ee}{Y}_{e\mu }^{\ast }\right|<3.29\times 10^{-11}{\left(m_V/\mathrm{GeV}\right)}^2$ and from $l_i\to l_j\gamma$ with $\left|Y_{\tau e}{Y}_{\mu \tau }^{\ast }\right|<3.46\times 10^{-12}(m_V/\mathrm{GeV}{)}^2,\left|Y_{e\tau }{Y}_{\tau \mu }^{\ast }\right|<3.46\times 10^{-12}{\left(m_V/\mathrm{GeV}\right)}^2$, 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.

Comments: 12 pages, 2 figures