Connecting Leptonic Unitarity Triangle to Neutrino Oscillation with CP
  Violation in Vacuum and in Matter
  Leptonic unitarity triangle (LUT) provides fundamental means to geometrically
describe CP violation in neutrino oscillation. In this work, we use LUT to
present a new geometrical interpretation of the vacuum oscillation probability,
and derive a compact new oscillation formula in terms of only 3 independent
parameters of the corresponding LUT. Then, we systematically study matter
effects in the geometrical formulation of neutrino oscillation with CP
violation. Including nontrivial matter effects, we derive a very compact new
oscillation formula by using the LUT formulation. We further demonstrate that
this geometrical formula holds well for applications to neutrino oscillations
in matter, including the long baseline experiments T2K, MINOS, NOvA, and DUNE.
