  Accelerated muon beams have been considered for next-generation studies of
high-energy lepton-antilepton collisions and neutrino oscillations. However,
high-brightness muon beams have not yet been produced. The main challenge for
muon acceleration and storage stems from the large phase-space volume occupied
by the beam, derived from the muon production mechanism through the decay of
pions from proton collisions. Ionization cooling is the technique proposed to
decrease the muon beam phase-space volume. Here we demonstrate a clear signal
of ionization cooling through the observation of transverse emittance reduction
in beams that traverse lithium hydride or liquid hydrogen absorbers in the Muon
Ionization Cooling Experiment (MICE). The measurement is well reproduced by the
simulation of the experiment and the theoretical model. The results shown here
represent a substantial advance towards the realization of muon-based
facilities that could operate at the energy and intensity frontiers.
