Measurement and interpretation of same-sign $W$ boson pair production in association with two jets in $pp$ collisions at $\sqrt{s} = 13$ TeV with the ATLAS detector

This paper presents the measurement of fiducial and differential cross sections for the electroweak and inclusive production of a same-sign $W$ boson pair in association with two jets ($W^\pm W^\pm jj$) using $139$ fb$^{-1}$ of proton-proton collision data recorded at a centre-of-mass energy of $\sqrt{s}=13$ TeV by the ATLAS detector at the Large Hadron Collider. The analysis is performed in the detector fiducial phase-space region defined by the presence of two same-charge leptons, electron or muon, and at least two jets with a large invariant mass and rapidity difference. The measured fiducial cross sections for electroweak $W^\pm W^\pm jj$ production and for inclusive $W^\pm W^\pm jj$ production are $2.88 \pm 0.22\, \text{(stat.)} \pm 0.19\, \text{(syst.)}$ fb and $3.35 \pm 0.22\, \text{(stat.)} \pm 0.20\, \text{(syst.)}$ fb, respectively, in agreement with the Standard Model predictions. The data collected are also used to constrain anomalous quartic gauge couplings by extracting confidence level intervals of 95\% on dimension-8 operators. A search for doubly charged Higgs bosons produced in vector boson fusion processes and decaying into two same-sign $W$ boson pairs is performed.