Double Higgs production at the 14 TeV LHC and the 100 TeV pp-collider

We consider effective Higgs boson couplings, including both the CP-even and CP-odd couplings, that affect Higgs boson pair production in this study. Through the partial wave analysis, we find that the process $gg\to hh$ is dominated by the $s$-wave component even at a 100~TeV $pp$-collider. Making use of the $s$-wave kinematics, we propose a cut efficiency function to mimic the collider simulation and obtain the potential of measuring Higgs effective couplings at the 14~TeV LHC with an integrated luminosity of $3000~{\rm fb}^{-1}$ and at a 100 TeV $pp$-collider. Analytical expressions of the $2\sigma$ exclusion limits at the LHC and the $5\sigma$ discovery bands at the 100 TeV machine are given.