  The method of searching for signals of heavy virtual particles is developed.
It is based on a renormalization group equation for the low energy effective
Lagrangian and the decoupling theorem. As an application, the model independent
search for Abelian Z' boson in four-fermion processes is analyzed. The basic
one-loop renormalization group relation for the parameters of the effective
Lagrangian is derived which gives possibility to reduce the problem to the
scattering of the Standard Model particles in the ``external field''
substituting heavy virtual Z' state. From the set of derived relations it is
determined that the absolute value of the Z' coupling to the axial currents has
to be the same for all fermions and is strongly correlated to the Z' coupling
to the scalar fields. The corresponding dependences between the parameters of
the effective Lagrangians are derived.
