Higgs bosons production and decay at future e^+e^- linear colliders as a probe of the B-L model

We study the phenomenology of the light and heavy Higgs boson production and decay in the context of a $U(1)_{B-L}$ extension of the Standard Model with an additional $Z'$ boson at future $e^+e^-$ linear colliders with center-of-mass energies of $\sqrt{s}=500-3000\hspace{0.8mm}GeV$ and integrated luminosities of ${\cal L}=500-2000\hspace{0.8mm}fb^{-1}$. The study includes the processes $e^{+}e^{-}\rightarrow (Z, Z') \to Zh$ and $e^{+}e^{-}\rightarrow (Z, Z') \to ZH$, considering both the resonant and non-resonant effects. We find that the total number of expected $Zh$ and $ZH$ events can reach 909,124 and 97,487, respectively, which is a very optimistic scenario and thus it would be possible to perform precision measurements for both Higgs bosons $h$ and $H$, as well as for the $Z'$ boson in future high-energy and high-luminosity $e^+e^-$ colliders experiments. Our study complements other studies on the B-L model and on the Higgs-strahlung processes $e^{+}e^{-}\rightarrow (Z, Z') \to Zh$ and $e^{+}e^{-}\rightarrow (Z, Z') \to ZH$.