Search for non-resonant Higgs boson pair production in the $2b + 2\ell + E_\mathrm{T}^\mathrm{miss}$ final state in $pp$ collisions at $\sqrt{s} = 13\,\mathrm{TeV}$ with the ATLAS detector

A search for non-resonant Higgs boson pair ($HH$) production is presented, in which one of the Higgs bosons decays to a b-quark pair ($b\bar b$) and the other decays to $WW^*$, or $ZZ^*$, or $\tau^+\tau^-$, with in each case a final state with $\ell^+\ell^- +$ neutrinos ($\ell = e, \mu$). Both gluon-gluon fusion and vector boson fusion are considered as production modes. Data recorded by the ATLAS detector in proton-proton collisions at a centre-of-mass energy of 13 TeV at the Large Hadron Collider, corresponding to an integrated luminosity of $140\,\mathrm{fb}^{-1}$, are used in this analysis. Events are selected to have exactly two $b$-tagged jets and two leptons with opposite electric charge and missing transverse momentum in the final state. These events are classified using multivariate analysis algorithms to separate the $HH$ events from other Standard Model processes. No evidence of the signal is found. The observed (expected) upper limit on the cross-section for non-resonant Higgs boson pair production is determined to be 9.6 (16.2) times the Standard Model prediction at 95% confidence level. Likelihood scans for the Higgs boson self-interaction coupling parameter $\kappa_\lambda$ and the quadrilinear coupling parameter $\kappa_{2V}$ are also performed in this analysis, constraining these parameters to be within the ranges ${[-6.2, 13.3]}$ and ${[-0.17, 2.4]}$, respectively, at 95% confidence level.