  As a first step towards considering a chiral perturbation theory for overlap
fermions, we investigate whether there are any ambiguities in the expression
for the pion mass resulting from multiple chiral symmetries. The concern is
that, calculating the conserved current for Ginsparg Wilson chiral symmetries
in the usual way, different expressions of the chiral symmetries lead to
different currents. This implies an ambiguity in the definition of the pion and
pion decay constant for all Ginsparg-Wilson expressions of the Dirac operator,
including the overlap operator. We use a renormalisation group mapping
procedure to consider local chiral symmetry transformations for a continuum
Ginsparg-Wilson "Dirac-operator." We find that this naturally leads to an
expression for the conserved current that differs from the standard expression
by cut-off artefacts, but is independent of which of the Ginsparg-Wilson
symmetries is chosen. We recover the standard expressions for the massive Dirac
operator, propagator, and chiral condensate. With this in place, we proceed to
calculate the pion mass in the mapped theory as a function of the quark mass,
and discover a unique expression for $F_\pi$ and $m_\pi$, recovering the usual
Gell-Mann-Oakes-Renner relation, baring the substitution of the chiral
condensate with its modified value. We hypothesise that the argument can be
carried directly over to the lattice theory.
