Determining the Higgs boson self-coupling at hadron colliders

Inclusive standard model Higgs boson pair production at hadron colliders has the capability to determine the Higgs boson self-coupling $\lambda .$ We present a detailed analysis of the $g\overrightarrow{g}H\overrightarrow{H}{(W}^{+}{W}^{-}{\left)\right(W}^{+}{W}^{-})\to (jj{\mathcal{l}}^{\pm }\nu \left)\right(jj{\mathcal{l}}^{\prime \pm }\nu )$ and $g\overrightarrow{g}H\overrightarrow{H}{(W}^{+}{W}^{-}{\left)\right(W}^{+}{W}^{-})\to (jj{\mathcal{l}}^{\pm }\nu \left)\right({\mathcal{l}}^{\prime \pm }\nu {\mathcal{l}}^{″\mp }\nu )$ $(\mathcal{l},{\mathcal{l}}^{\prime },{\mathcal{l}}^{″}=e,\mu )$ signal channels, and the relevant background processes, for the CERN Large Hadron Collider, and a future Very Large Hadron Collider operating at a center-of-mass energy of 200 TeV. We also derive quantitative sensitivity limits for $\lambda .$ We find that it should be possible at the LHC with design luminosity to establish that the standard model Higgs boson has a nonzero self-coupling and that $\lambda /{\lambda }_{\mathrm{SM}}$ can be restricted to a range of 0–3.8 at $95\%$ confidence level (C.L.) if its mass is between 150 and 200 GeV. At a 200 TeV collider with an integrated luminosity of $300{\mathrm{fb}}^{-1},$ $\lambda$ can be determined with an accuracy of 8–25 % at $95\%$ C.L. in the same mass range.