Parity-Odd Term in the Lagrangian I'm currently reading chapter 94 of Srednicki's book, where he calculates the pion contribution to the nEDM (neutron electric dipole moment), after Eq. 94.22 he writes the following

I'm having a hard time understanding what he says about performing an axial rotation to get rid of the first term of 94.22, can someone explain to me how we can do that?
 A: It looks like a generic chiral redefinition to simplify terms like this,
$$
-m_N \overline{\cal N}{\cal N} -im_2 \overline{\cal N}\gamma_5{\cal N}. \tag{1} 
$$
The pseudoscalar piece, the second one, may be redefined away by a chiral rotation,
$$
{\cal N}\longrightarrow e^{-i\alpha \gamma_5}  {\cal N}
$$
which leaves the kinetic terms, etc invariant, but maps (1) to
$$
-m_N \overline{\cal N}e^{-i2\alpha \gamma_5} {\cal N} -im_2 \overline{\cal N}e^{-i2\alpha \gamma_5} \gamma_5{\cal N}\\ =
-m_N \overline{\cal N}{\cal N} \left (\cos 2\alpha+ \frac{m_2}{m_N} \sin 2\alpha \right )-im_2 \overline{\cal N}  \gamma_5{\cal N}\left (\cos 2\alpha- \frac{m_N}{m_2} \sin 2\alpha\right ) . 
$$
You may then choose $m_2/m_N= \tan 2\alpha$ to eliminate the second term (pseudoscalar).
But, now, observe the first (scalar) term hasn't changed that much, since
$$
2\alpha = m_2/m_N + O((m_2/m_N)^3),
$$
so the  correction to the original mass coefficient in (1) reveals  a mere  leading correction $m_N\longrightarrow m_N + m_2^2/2m_N$.  As though by magic, for small $m_2/m_N$, the pseudoscalar term was redefined away!
