One-loop contributions for $h\to \mathrm{\ell }\bar{\mathrm{\ell }}\gamma$ and $e^{-}{e}^{+}\to h\gamma$ in $U(1{)}_{B-L}$ extension of the standard model

We present one-loop contributing for $h\to \mathrm{\ell }\bar{\mathrm{\ell }}\gamma$ with $\mathrm{\ell }={\nu }_{e,\mu ,\tau },e,\mu$ and $e^{-}{e}^{+}\to h\gamma$ in $U(1{)}_{B-L}$ extension of the standard models. In phenomenological results, the signal strengths for $h\to \mathrm{\ell }\bar{\mathrm{\ell }}\gamma$ at Large Hadron Collider and for $e^{-}{e}^{+}\to h\gamma$ at future Lepton Colliders are analyzed in physical parameter space for both vector and chiral $B-L$ models. We find that the contributions from neutral gauge boson $Z^{\mathrm{\prime }}$ to the signal strengths are rather small. Consequently, the effects are hard to probe at future colliders. While the impacts of charged Higgs, CP-odd Higgs in the chiral $B-L$ model on the signal strengths are significant and can be measured with the help of the initial polarization beams at future lepton colliders.