  In nuclear chiral perturbation theory (ChPT), an operator is defined in a
space with a cutoff which may be varied within a certain range. The operator
runs as a result of the variation of the cutoff [renormalization group (RG)
running]. In order for ChPT to be useful, the operator should run in a way
consistent with the counting rule; that is, the running of chiral counter terms
have to be of natural size. We vary the cutoff using the Wilsonian
renormalization group (WRG) equation, and examine this consistency. As an
example, we study the s-wave pion production operator for NN\to d pi, derived
in ChPT. We demonstrate that the WRG running does not generate any
chiral-symmetry-violating (CSV) interaction, provided that we start with an
operator which does not contain a CSV term. We analytically show how the
counter terms are generated in the WRG running in case of the infinitesimal
cutoff reduction. Based on the analytic result, we argue a range of the cutoff
variation for which the running of the counter terms is of natural size. Then,
we numerically confirm this.
