Higgs Pair Production in the $H(\rightarrow \tau\tau)H(\rightarrow b\bar{b})$ channel at the High-Luminosity LHC

Prospects studies are presented for the observation of double Higgs production in the channel $H(\rightarrow b \overline{b})H(\rightarrow \tau \tau)$ for a total integrated luminosity of 3000~fb$ ^{-1}$ of $\sqrt{s}=$14~TeV proton-proton collisions at the HL-LHC. A cut-based analysis strategy using MC data and a parametrisation of the ATLAS detector provide assessment to the measurement prospects performed under different assumptions for the trilinear Higgs couplings values. Assuming SM background and SM signal, we expect to set an upper limit of the cross section for the di-Higgs production of $4.3 \times \sigma(HH \rightarrow b\bar{b}\tau^+\tau^-)$ at 95\% Confidence Level. Using an effective Lagrangian for the Higgs potential, and allowing its trilinear coupling to vary, we can project an exclusion of $\lambda_{HHH}/\lambda_{SM} \leq -4$ and $\lambda_{HHH}/\lambda_{SM} \geq 12$.