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

A bstract 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 $$ {l}_{\alpha}^{-}\to {l}_{\beta}^{+}{l}_{\rho}^{-}{l}_{\sigma}^{-} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>l</mml:mi> <mml:mi>α</mml:mi> <mml:mo>−</mml:mo> </mml:msubsup> <mml:mo>→</mml:mo> <mml:msubsup> <mml:mi>l</mml:mi> <mml:mi>β</mml:mi> <mml:mo>+</mml:mo> </mml:msubsup> <mml:msubsup> <mml:mi>l</mml:mi> <mml:mi>ρ</mml:mi> <mml:mo>−</mml:mo> </mml:msubsup> <mml:msubsup> <mml:mi>l</mml:mi> <mml:mi>σ</mml:mi> <mml:mo>−</mml:mo> </mml:msubsup> </mml:math> , 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 j γ . Strong constraints are obtained from $$ {l}_{\alpha}^{-}\to {l}_{\beta}^{+}{l}_{\rho}^{-}{l}_{\sigma}^{-} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>l</mml:mi> <mml:mi>α</mml:mi> <mml:mo>−</mml:mo> </mml:msubsup> <mml:mo>→</mml:mo> <mml:msubsup> <mml:mi>l</mml:mi> <mml:mi>β</mml:mi> <mml:mo>+</mml:mo> </mml:msubsup> <mml:msubsup> <mml:mi>l</mml:mi> <mml:mi>ρ</mml:mi> <mml:mo>−</mml:mo> </mml:msubsup> <mml:msubsup> <mml:mi>l</mml:mi> <mml:mi>σ</mml:mi> <mml:mo>−</mml:mo> </mml:msubsup> </mml:math> with | $$ {Y}_{ee}{Y}_{\mu e}^{\ast } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Y</mml:mi> <mml:mi>ee</mml:mi> </mml:msub> <mml:msubsup> <mml:mi>Y</mml:mi> <mml:mi>μe</mml:mi> <mml:mo>∗</mml:mo> </mml:msubsup> </mml:math> | &lt; 3 . 29 × 10 − 11 ( m V / GeV) 2 , $$ \mid {Y}_{ee}{Y}_{\mu e}^{\ast}\mid $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>∣</mml:mo> <mml:msub> <mml:mi>Y</mml:mi> <mml:mi>ee</mml:mi> </mml:msub> <mml:msubsup> <mml:mi>Y</mml:mi> <mml:mi>μe</mml:mi> <mml:mo>∗</mml:mo> </mml:msubsup> <mml:mo>∣</mml:mo> </mml:math> &lt; 3 . 29 × 10 − 11 ( m V / GeV) 2 and from l i → l j γ with $$ \mid {Y}_{\tau e}{Y}_{\mu \tau}^{\ast}\mid $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>∣</mml:mo> <mml:msub> <mml:mi>Y</mml:mi> <mml:mi>τe</mml:mi> </mml:msub> <mml:msubsup> <mml:mi>Y</mml:mi> <mml:mi>μτ</mml:mi> <mml:mo>∗</mml:mo> </mml:msubsup> <mml:mo>∣</mml:mo> </mml:math> &lt; 3 . 46 × 10 − 12 ( m V / GeV) 2 , $$ \mid {Y}_{e\tau}{Y}_{\tau \mu}^{\ast}\mid $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>∣</mml:mo> <mml:msub> <mml:mi>Y</mml:mi> <mml:mi>eτ</mml:mi> </mml:msub> <mml:msubsup> <mml:mi>Y</mml:mi> <mml:mi>τμ</mml:mi> <mml:mo>∗</mml:mo> </mml:msubsup> <mml:mo>∣</mml:mo> </mml:math> &lt; 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.