Search for Higgs boson pair production in association with a vector boson in $pp$ collisions at $\sqrt{s}=$ 13 TeV with the ATLAS detector

This paper reports a search for Higgs boson pair ($hh$) production inassociation with a vector boson ($W$ or $Z$) using 139 $fb^{-1}$ ofproton-proton collision data at $\sqrt{s}=$ 13 TeV recorded with the ATLASdetector at the Large Hadron Collider. The search is performed in final statesin which the vector boson decays leptonically ($W\to\ell\nu,Z\to\ell\ell,\nu\nu$ with $\ell=e, \mu$) and the Higgs bosons each decay into apair of $b$-quarks. It targets $Vhh$ signals from both non-resonant $hh$production, present in the Standard Model (SM), and resonant $hh$ production,as predicted in some SM extensions. A 95% confidence-level upper limit of 183(87) times the SM cross-section is observed (expected) for non-resonant $Vhh$production when assuming the kinematics are as expected in the SM. Constraintsare also placed on Higgs boson coupling modifiers. For the resonant search,upper limits on the production cross-sections are derived for two specificmodels: one is the production of a vector boson along with a neutral heavyscalar resonance $H$, in the mass range 260-1000 GeV, that decays into $hh$,and the other is the production of a heavier neutral pseudoscalar resonance $A$that decays into a $Z$ boson and $H$ boson, where the $A$ boson mass is 360-800GeV and the $H$ boson mass is 260-400 GeV. Constraints are also derived in theparameter space of two-Higgs-doublet models.