Constraints on the Higgs boson self-coupling from ttH+tH, H to gamma gamma differential measurements at the HL-LHC

This note details a study of prospects for ttH+tH, $\mathrm{H}\rightarrow\gamma\gamma$ differential cross section measurements at the HL-LHC with the CMS Phase-2 detector. The study is performed using simulated proton-proton collisions at a centre-of-mass energy of $\sqrt{s}=14$ TeV, corresponding to 3 $\mathrm{ab}^{-1}$ of data. The expected performance of the upgraded CMS detector is used to model the object reconstruction efficiencies under HL-LHC conditions. The results are interpreted in terms of the expected sensitivity to deviations of the Higgs boson self-coupling, $\kappa_\lambda$, from beyond standard model effects. Using the HL-LHC data, the precision expected in ttH+tH, $\mathrm{H}\rightarrow\gamma\gamma$ differential cross section measurements will constrain $\kappa_\lambda$ within the range $\mathrm{-4.1}<\kappa_\lambda<\mathrm{14.1}$, at the $95\%$ confidence level, assuming all other Higgs boson couplings are fixed to standard model predictions. Moreover, it is possible to disentangle the effects of a modified Higgs boson self coupling from the presence of other anomalous couplings by using the differences in the shape of the measured spectrum. This separation is unique to differential cross section measurements. The ultimate sensitivity to the Higgs boson self coupling, achievable using differential cross section measurements, will result from a combination across Higgs boson production modes and decay channels. $$\textit{This document has been revised with respect to the version dated November 19, 2018.}$$