Search for Higgs boson pair production with one associated vector boson in proton-proton collisions at $\sqrt{s}=13~\text{TeV}$

A search is presented for Higgs boson pair production ($\text{HH}$) associated with a vector boson $\text{V}$ ($\text{W}$ or $\text{Z}$ boson) with $138~\mathrm{fb}^{-1}$ of proton-proton ($\text{pp}$) collisions at a center-of-mass energy of 13 TeV with the CMS detector at the LHC at CERN. The processes in this search include $\text{pp}\to\text{ZHH}$ and $\text{pp}\to\text{WHH}$ production. All hadronic decays and leptonic decays of $\text{W}$ and $\text{Z}$ bosons involving electrons, muons, and neutrinos are utilized. The decay channel of the Higgs bosons is restricted to $\text{b}\bar{\text{b}}\text{b}\bar{\text{b}}$. An observed (expected) upper limit at $95\%$ confidence level ($\text{CL}$) is set at 294 (124) times the cross section from the standard model prediction of the $\text{pp}\to\text{VHH}$ process. Constraints are also set on the modifier of the Higgs boson trilinear self-coupling $\kappa_{\lambda}$, and on the coupling of two Higgs bosons with two vector bosons $\kappa_{\text{VV}}$. The observed (expected) allowed intervals of these coupling modifiers from this search at $95\%$ $\text{CL}$ are $-37.7<\kappa_{\lambda}<37.2$ ($-30.1<\kappa_{\lambda}<28.9$) and $-12.2<\kappa_{\text{VV}}<13.5$ ($-7.64<\kappa_{\text{VV}}<8.90$). In addition, a $95\%$ $\text{CL}$ upper limit is set at 43 (22) times the cross section of the $\text{pp}\to\text{VHH}$ process when $\kappa_{\lambda}=5.5$ and other couplings are set to standard model predictions. $$\textit{This document has been revised with respect to the version dated March 23, 2023.}$$