  The current laws of physics do not explain the observed imbalance of matter
and antimatter in the universe. Sakharov proposed that an explanation would
require the violation of CP symmetry between matter and antimatter. The only CP
violation observed so far is in the weak interactions of quarks, and it is too
small to explain the matter-antimatter imbalance of the universe. It has been
shown that CP violation in the lepton sector could generate the
matter-antimatter disparity through the process called leptogenesis. The
quantum mixing of neutrinos, the neutral leptons in the Standard Model,
provides a potential source of CP violation through a complex phase dCP, which
may have consequences for theoretical models of leptogenesis. This CP violation
can be measured in muon neutrino to electron neutrino oscillations and the
corresponding antineutrino oscillations, which are experimentally accessible
with accelerator-produced beams as established by the T2K experiment. Until
now, the value of dCP has not been significantly constrained by neutrino
oscillation experiments. Here the T2K collaboration reports a measurement that
favors large enhancement of the neutrino oscillation probability, excluding
values of dCP which result in a large enhancement of the observed anti-neutrino
oscillation probability at three standard deviations (3 sigma). The 3 sigma
confidence level interval for dCP, which is cyclic and repeats every 2pi, is
[-3.41,-0.03] for the so-called normal mass ordering, and [-2.54,-0.32] for the
inverted mass ordering. Our results show an indication of CP violation in the
lepton sector. Herein we establish methods for sensitive searches for
matter-antimatter asymmetry in neutrino oscillations using accelerator-produced
neutrino beams. Future measurements with larger data samples will determine
whether the leptonic CP violation is larger than the quark sector CP violation.
