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Physics

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    $\begingroup$ Your answer given to your own question is correct, explaining at the same time the reason for preferring the compact notation used in your first formula. $\endgroup$
    – Hyperon
    Commented Apr 8 at 6:47
  • $\begingroup$ @Hyperon gave you as close to the perfect answer as it comes. Beyond that, however, and conceptually completely independently, your dimensional analysis is egregiously wrong in your crude schematic interpolating field expression: the l.h.s. has energy dimension 1, but the r.h.s. has energy dimension 3. You need to match those with two powers of $f_\pi$. $\endgroup$
    – Cosmas Zachos
    Commented Apr 8 at 19:43