Evidence for Longitudinally Polarized $ W$ Bosons in the Electroweak Production of Same-Sign $ W$ Boson Pairs in Association with Two Jets in $ pp$ Collisions at $ \sqrt{s}=13\text{}\text{}\mathrm{TeV}$ with the ATLAS Detector

This Letter reports the first evidence of electroweak production of same-sign $ W$ boson pairs where at least one of the $ W$ bosons is longitudinally polarized and the most stringent constraint to date for the production of two longitudinally polarized same-sign $ W$ bosons. The dataset used corresponds to an integrated luminosity of $ 140\text{}\text{}{\mathrm{fb}}^{-1}$ of proton-proton collisions at a center-of-mass energy of 13 TeV, collected with the ATLAS detector during run 2 of the Large Hadron Collider. The study is performed in final states including two same-sign leptons (electrons or muons), missing transverse momentum, and at least two jets with a large invariant mass and a large rapidity difference. Two independent fits are performed targeting the production of same-sign $ W$ bosons with at least one, or two longitudinally polarized $ W$ bosons. The observed (expected) significance of the production with at least one longitudinally polarized $ W$ boson is 3.3 (4.0) standard deviations. An observed (expected) 95% confidence level upper limit of 0.45 (0.70) fb is reported on the fiducial production cross section of two longitudinally polarized same-sign $ W$ bosons.