  We apply to the Random Field Ising Model at zero temperature (T= 0) the
perturbative loop expansion around the Bethe solution. A comparison with the
standard epsilon-expansion is made, highlighting the key differences that make
the new expansion much more appropriate to correctly describe strongly
disordered systems, especially those controlled by a T = 0 RG fixed point. This
new loop expansion produces an effective theory with cubic vertices. We compute
the one-loop corrections due to cubic vertices, finding new terms that are
absent in the epsilon-expansion. However, these new terms are subdominant with
respect to the standard, supersymmetric ones, therefore dimensional reduction
is still valid at this order of the loop expansion.
