Combined analysis of double Higgs production via gluon fusion at the HL-LHC in the effective field theory approach

We perform the combined analysis of the double Higgs production via gluon fusion in the $b\bar{b} \gamma\gamma$ and $b\bar{b}\tau^+\tau^-$ decay channels at the High-Luminosity LHC (HL-LHC). To validate our analysis, we reproduce the ATLAS result of the $b\bar{b} \gamma\gamma$ process including all contributions from fakes. For the $b\bar{b}\tau^+\tau^-$ decay channel, we perform the similar analysis to the CMS one. As an improvement, we also perform the multivariate analysis employing the Boosted Decision Tree algorithm. Then, we derive 68% probability contours on anomalous Higgs couplings in the Effective Field Theory (EFT) approach for various analyses. We find that the $b\bar{b}\tau^+\tau^-$ process outperforms the $b\bar{b}\gamma\gamma$ for measurement of energy-growing operators, while adding the $b\bar{b}\tau^+\tau^-$ process is least beneficial for improving the precision of the Higgs self coupling (mainly set by the $b\bar{b}\gamma\gamma$ process). We illustrate that the double Higgs production alone can be comparable to the single Higgs process in constraining the modification of the top Yukawa coupling in the positive direction. Focusing on the Higgs self coupling as a special interest, we derive the precision as a function of various improvable parameters such as tag and mis-tag rates of tau-leptons, heavy flavor jets, photon identification and di-photon mass resolution to take into account future phenomenological studies. As an optimistic benchmark scenario, we illustrate that 68% and 95% probability intervals of the Higgs self coupling, $\lambda_3/\lambda_{3}^{SM}$, at the HL-LHC can reach $[0.04,\, 2.7] \cup [5.5,\, 5.6]$ and $[-0.1,\, 6.4]$ respectively where the correlation among the EFT coefficients is taken into account