\begin{document}${U}(1)_{\rm{{B-L}}}$\end{document} extension of the Standard Model (B-L-SM) offers an explanation for neutrino mass generation via a seesaw mechanism; it also offers two new physics states, namely an extra Higgs boson and a new \begin{document}$ Z' $\end{document} gauge boson. The emergence of a second Higgs particle as well as a new \begin{document}$ Z^\prime $\end{document} gauge boson, both linked to the breaking of a local \begin{document}${U}(1)_{\rm{{B-L}}}$\end{document} symmetry, makes the B-L-SM rather constrained by direct searches in Large Hadron Collider (LHC) experiments. We investigate the phenomenological status of the B-L-SM by confronting the new physics predictions with the LHC and electroweak precision data. Taking into account the current bounds from direct LHC searches, we demonstrate that the prediction for the muon \begin{document}$ \left(g-2\right)_\mu $\end{document} anomaly in the B-L-SM yields at most a contribution of approximately \begin{document}$ 8.9 \times 10^{-12} $\end{document} , which represents a tension of \begin{document}$ 3.28 $\end{document} standard deviations, with the current \begin{document}$ 1\sigma $\end{document} uncertainty, by means of a \begin{document}$ Z^\prime $\end{document} boson if its mass is in the range of \begin{document}$ 6.3 $\end{document} to \begin{document}$ 6.5\; {\rm{TeV}} $\end{document}, within the reach of future LHC runs. This means that the B-L-SM, with heavy yet allowed \begin{document}$ Z^\prime $\end{document} boson mass range, in practice, does not resolve the tension between the observed anomaly in the muon \begin{document}$ \left(g-2\right)_\mu $\end{document} and the theoretical prediction in the Standard Model. Such a heavy \begin{document}$ Z^\prime $\end{document} boson also implies that the minimal value for the new Higgs mass is of the order of 400 GeV."> What can a heavy <inline-formula><tex-math id="M1-3">\begin{document}${{U(1)}_{\bf B-L} \; {Z^\prime}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/ff387a55-a82b-4a37-b9b4-b02b3fdd21c0/CPC-2020-0355_M1-3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/ff387a55-a82b-4a37-b9b4-b02b3fdd21c0/CPC-2020-0355_M1-3.png"/></alternatives></inline-formula> boson do to the muon <inline-formula><tex-math id="M2">\begin{document}${{(g-2)}_{\mu}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/ff387a55-a82b-4a37-b9b4-b02b3fdd21c0/CPC-2020-0355_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/ff387a55-a82b-4a37-b9b4-b02b3fdd21c0/CPC-2020-0355_M2.png"/></alternatives></inline-formula> anomaly and to a new Higgs boson mass? -
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