Measuring Trilinear Higgs Coupling in $WHH$ and $ZHH$ Productions at the HL-LHC

Determination of trilinear Higgs coupling ($\lambda_{HHH}=\kappa\lambda_{HHH}^{\rm SM}$) through Higgs pair productions is a major motivation for the LHC high luminosity phase. We perform a detailed collider simulation to explore the potential of measuring $\lambda_{HHH}$ in the $VHH$ ($V=W,Z$) production at the HL-LHC. We find that the trilinear Higgs coupling in the SM ($\lambda_{HHH}^{\rm SM}$) could be measured at the level of $1.3\sigma$. Combining with the gluon fusion, vector boson fusion and $t\bar{t}HH$ channels, $\lambda_{HHH}^{\rm SM}$ is expected to be measured at the level of $3.13\sigma$. If no evidence of Higgs pair productions were observed, the $VHH$ production, together with the gluon fusion channel, would impose a bound of $0.5\leq \kappa \leq 2.2$ at the 95\% confidence level.