Observation of the $K^{+}\rightarrow\pi^{+}\nu\bar{\nu}$ decay and measurement of its branching ratio

A measurement of the $K^{+}\rightarrow\pi^{+}\nu\bar{\nu}$ decay by the NA62 experiment at the CERN SPS is presented, using data collected in 2021 and 2022. This dataset was recorded, after modifications to the beamline and detectors, at a higher instantaneous beam intensity with respect to the 2016--2018 data taking. Combining NA62 data collected in 2016--2022, a measurement of $B(K^{+}\rightarrow\pi^{+}\nu\bar{\nu}) = \left( 13.0^{+ 3.3}_{- 3.0} \right)\times10^{-11}$ is reported. With $51$ signal candidates observed and an expected background of $18^{+3}_{-2}$ events, $B(K^{+}\rightarrow\pi^{+}\nu\bar{\nu})$ becomes the smallest branching ratio measured with a signal significance above $5\,\sigma$.