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Muon anomalous magnetic moment in a $SU(4) \otimes U(1)_N$ model without exotic electric charges

We study an electroweak gauge extension of the standard model, so called 3-4-1 model, which does not contain exotic electric charges and it is anomaly free. We discuss phenomenological constraints of the model and compute all the corrections to the muon magnetic moment. Mainly, we discuss different mass regimes and their impact on this correction, deriving for the first time direct limits on the masses of the neutral fermions and charged vector bosons. Interestingly, the model could address the reported muon anomalous magnetic moment excess, however it would demands a rather low scale of symmetry breaking, far below the current electroweak constraints on the model. Thus, if this excess is confirmed in the foreseeable future by the g-2 experiment at FERMILAB, this 3-4-1 model can be decisively ruled out since the model cannot reproduce a sizeable and positive contribution to the muon anomalous magnetic moment consistent with current electroweak limits.