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 $U{\left(1\right)}_{B-L}$ extension of the standard model with an additional $Z^{\prime }$ boson at future $e^{+}{e}^{-}$ linear colliders with center-of-mass energies of $\sqrt{s}=500\text{–}3000\text{ GeV}$ and integrated luminosities of $L=500-2000{fb}^{-1}$. The study includes the processes $e^{+}{e}^{-}\to (Z,Z^{\prime })\to Zh$ and $e^{+}{e}^{-}\to (Z,Z^{\prime })\to ZH$, 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 $Z^{\prime }$ 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 $e^{+}{e}^{-}\to (Z,Z^{\prime })\to Zh$ and $e^{+}{e}^{-}\to (Z,Z^{\prime })\to ZH$. (paper)