  We propose a dimensional regularization scheme to deal with the divergences
caused by colliding supercurrents inserted at the interaction points, in the
light-cone gauge NSR superstring field theory. We formulate the theory in $d$
dimensions and define the amplitudes as analytic functions of $d$. With an
appropriately chosen three-string interaction term and large negative $d$, the
tree level amplitudes for the (NS,NS) closed strings can be recast into a BRST
invariant form, using the superconformal field theory proposed in
Ref.[arXiv:0911.3704]. We show that in the limit $d \to 10$ they coincide with
the results of the first quantized theory. Therefore we obtain the desired
results without adding any contact interaction terms to the action.
