Probing Trilinear Higgs Self-coupling at the HL-LHC via Multivariate Analysis

We perform a multivariate analysis of Higgs-pair production in $HH \to b\bar b \gamma\gamma$ channel at the HL-LHC to probe the trilinear Higgs self--coupling $\lambda_{3H}$, which takes the value of 1 in the SM. We consider all the known background processes. Also, for the signal we are the first to adopt the most recent event generator of POWHEG-BOX-V2 to exploit the NLO distributions for Toolkit for Multivariate Data Analysis (TMVA), taking account of the full top--quark mass dependence. Through Boosted Decision Tree (BDT) analysis trained for $\lambda_{3H}=1$, we find that the significance can reach up to 1.95 with about $9$ signal and $18$ background events. In addition, the Higgs boson self-coupling can be constrained to $1.00 < \lambda_{3H} < 6.22$ at 95\% confidence level (CL). We also perform a likelihood fitting of $M_{\gamma\gamma bb}$ distribution and find the $1\sigma$ confidence interval (CI) of $0.1 < \lambda_{3H} < 2.2\, \cup\,5.4 < \lambda_{3H} < 6.6$ for the $\lambda_{3H}=1$ nominal set. On the other hand, using BDTs trained for each value of $\lambda_{3H}$, we find a bulk region of $0.5 <\sim \lambda_{3H} <\sim~ 4.5$, for which it is hard to pin down the trilinear coupling.