  The structure of an anomalous Lagrangian of the pi-rho-omega-a_1 system is
investigated within the hidden local SU(2)_R x SU(2)_L symmetry approach. The
interaction of the external electromagnetic and weak vector and axial-vector
fields with the above hadron system is included.
  The Lagrangian of interest contains the anomalous Wess-Zumino term following
from the well known Wess-Zumino-Witten action and six independent homogenous
terms. It is characterized by four constants that are to be determined from a
fit to the data on various elementary reactions. Present data allows one to
extract the constants with a good accuracy.
  The homogenous part of the Lagrangian has been applied in the study of
anomalous processes that could enhance the high energy tail of the spectrum of
photons, produced in the radiative muon capture in hydrogen. It should be noted
that recently, an intensive search for such enhancement processes has been
carried in the literature, in an attempt to resolve the so called "g_P puzzle":
an about 50 % difference between the theoretical prediction of the value of the
induced pseudoscalar constant g_P and its value extracted from the high energy
tail of the photon spectrum, measured in the precision TRIUMF experiment.
  Here, more details on the studied material are presented and new results,
obtained by using the Wess-Zumino term, are provided.
