Measuring Higgs pair production ($HH$) will provide information about the Higgs self coupling, which is key to determine the shape of the Higgs potential at higher order. The leading $HH$ production mode at the Large Hadron Collider is gluon gluon fusion and the sub-leading production mode is vector boson fusion. Given the small cross section, Higgs pair production has not yet been observed. However, competitive upper limits on the $HH$ production cross section and Higgs self coupling modifier $ \kappa_{\lambda}$ are set by the ATLAS and CMS Collaborations.
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Searches for $HH$ production in a final state where one Higgs boson decays to a pair of $b$ quarks, and the other Higgs boson decays either to two photons, two $b$ quarks or four leptons, with the full Run 2 proton-proton collision data set at $\sqrt{s}$ = 13 TeV from the ATLAS and CMS experiments, are presented. Combinations of $HH$ searches and Higgs self coupling measurements with partial Run 2 data are also presented.
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Competitive upper limits on the $HH$ cross section are obtained by the ATLAS and CMS $HH$ searches in the $b\bar{b}\gamma \gamma$ final state. However, the CMS $HH$ search in the $b\bar{b}b\bar{b}$ final state sets the current most stringent observed upper limit on the $HH$ production cross section of 3.6 times the Standard Model expectation at 95\% confidence level. The current most stringent limits on $ \kappa_{\lambda}$ are obtained by the ATLAS $HH$ search in the $b\bar{b}\gamma \gamma$ final state, which sets observed (expected) limits of $-1.5 ~(-2.4) < \kappa_{\lambda}< 6.7 ~ (7.7)$ at 95% confidence level.