The new $Z^{\mathrm{\prime }}$ boson of the Bestest Little Higgs Model as a portal to signatures of Higgs bosons $h_0$ and $H_0$ at the future muon collider

We study the new $Z^{\mathrm{\prime }}$ boson as a portal for the production of Higgs bosons $h_0$ and $H_0$ predicted by the Bestest Little Higgs Model through the Higgs-strahlung processes ${\mu }^{+}{\mu }^{-}\to (Z,Z^{\mathrm{\prime }})\to Z{h}_0,Z{H}_0$. We focus on the resonance and non-resonance effects of the $Z{h}_0,Z{H}_0$ signals. In our analysis, we consider the center-of-mass energies of $\sqrt{s}=3,4,6,10,30$ TeV and integrated luminosities of $\mathcal{L}=2,4,6,10,30$ $\mathrm{a}{\mathrm{b}}^{-1}$ projected for a future muon collider. The possibility of performing precision measurements for the Higgs bosons $h_0$ and $H_0$ is very promising at the future muon collider. Furthermore, our results may be helpful to the High Energy Physics community. Complementarily, we generate and provide the Feynman rules necessary for studying the processes ${\mu }^{+}{\mu }^{-}\to (Z,Z^{\mathrm{\prime }})\to Z{h}_0,Z{H}_0$.