  The anomalous dimension $\gamma_m =1$ in the infrared region near conformal
edge in the broken phase of the large $N_f$ QCD has been shown by the ladder
Schwinger-Dyson equation and also by the lattice simulation for $N_f=8$ for $
N_c=3$. Recently Zwicky claimed another independent
  argument (without referring to explicit dynamics) for the same result,
$\gamma_m =1$. We show that this is not justified by explicit evaluation of
each matrix element based on the ``dilaton chiral perturbation theory (dChPT)''
:
  $<\pi(p_2)| 2\cdot \sum^{N_f}_{i=1} m_f \bar \psi_i \psi_i |\pi(p_1)>=
  2M_\pi^2 + [(1-\gamma_m) M_\pi^2\cdot 2/(1+\gamma_m)]= 2 M_\pi^2 \cdot
2/(1+\gamma_m)
  \ne 2 M_\pi^2$
  in contradiction with his estimate, which is compared with
  $<\pi(p_2)| (1+\gamma_m) \cdot \sum^{N_f}_{i=1} m_f \bar \psi_i \psi_i
|\pi(p_1)> =(1+\gamma_m) M_\pi^2+ [(1-\gamma_m) M_\pi^2]=2 M_\pi^2$ (both up to
trace anomaly), where the terms in $[ \,\,]$ are from the $\sigma$
(pseudo-dilaton) pole contribution. Thus there is no constraint on $\gamma_m$
when the $\sigma$ pole
  contribution is treated consistently for both.
