  Given the Dirac neutrino mass term, we explore the constraint conditions
which allow the corresponding mass matrix to be invariant under the \mu-\tau
reflection transformation, leading us to the phenomenologically favored
predictions \theta_{23} = \pi/4 and \delta = 3\pi/2 in the standard
parametrization of the 3\times 3 lepton flavor mixing matrix. If such a flavor
symmetry is realized at a superhigh energy scale \Lambda_{\mu\tau}, we
investigate how it is spontaneously broken via the one-loop
renormalization-group equations (RGEs) running from \Lambda_{\mu\tau} down to
the Fermi scale \Lambda_{\rm F}. Such quantum corrections to the neutrino
masses and flavor mixing parameters are derived, and an analytical link is
established between the Jarlskog invariants of CP violation at
\Lambda_{\mu\tau} and \Lambda_{\rm F}. Some numerical examples are also
presented in both the minimal supersymmetric standard model and the type-II
two-Higgs-doublet model, to illustrate how the octant of \theta_{23}, the
quadrant of \delta and the neutrino mass ordering are correlated with one
another as a result of the RGE-induced \mu-\tau reflection symmetry breaking
effects.
