Double Higgs boson production and decay in Randall-Sundrum model at hadron colliders

We investigate the double Higgs production and decay at the $14~ {\rm TeV}$ LHC and $33~ {\rm TeV}$ HE-LHC in both the standard model and Randall-Sundrum (RS) model. In our calculation we consider reasonably only the contribution of the lightest two Kaluza-Klein (KK) gravitons. We present the integrated cross sections and some kinematic distributions in both models. Our results show that the RS effect in the vicinities of $M_{HH} \sim M_{1}$, $M_{2}$ (the masses of the lightest two KK gravitons) or in the central Higgs rapidity region is quite significant, and can be extracted from the heavy SM background by imposing proper kinematic cuts on final particles. We also study the dependence of the cross section on the RS model parameters, the first KK graviton mass $M_1$ and the effective coupling $c_0$, and find that the RS effect is reduced obviously with the increment of $M_1$ or decrement of $c_0$.