  Dynamical breaking of chiral symmetry in effective models of QCD is studied.
Introducing a cut-off function or a non-local interaction, the Noether current
must be modified and thus the Ward-Takahashi identity and the PCAC relation are
modified accordingly. We point out that the pion decay constant must be defined
consistently with the Noether current so that the low-energy relations are
satisfied. We define the proxy of the Noether current for general effective
models, which is consistent with loop expansion of the
Cornwall-Jackiw-Tomboulis effective action. A general formula for the pion
decay constant in terms of the Bethe-Salpeter amplitude is derived.
  The effective Pagels-Stokar formula is proposed which is useful to estimate
the decay constant without solving the Bethe-Salpeter equation.
