Can a Lagrangian in QFT be Renormalizable?

[Giuseppe Lacagnina]

Possibly very silly question in QFT. Consider the Lagrangian for a scalar field theory.
A term like

g/φ^2

should be renormalizable on power counting arguments. The mass dimension of g should be

2 (D-1)

where D is the number of space-time dimensions.Does this make sense?

 

[DuckAmuck]

Isn't there a rule where if the mass dimension is greater than 5, the term is non-renormalizable?
2(D-1)=6, if D=4.

 

[Giuseppe Lacagnina]

As far as I know, a lagrangian term is not perturbatively renormalizable if it involves a coupling with negative mass dimension.
Like it happens for gravity or the Fermi model of weak interactions, which works as an effective theory with an energy cutoff.