We compute the tree-level four-point scattering amplitudes in string models
where matter fields live on D-brane intersections. Extracting the contribu
tion of massless modes, we are left with dimension-six four-fermion operato
rs which in general receive contributions from three different sources: exc
hange of massive Kaluza-Klein excitations, winding modes and string oscilla
tor states. We compute their coefficients and extract new bounds on the str
ing scale in the brane-world scenario. This is contrasted with the situatio
n where matter fields arise from open strings with both ends confined on th
e same collection of D-branes, in which case the exchange of massive string
modes leads to dimension-eight operators that have been studied in the pas
t. When matter fields live on brane intersections, the presence of dimensio
n-six operators increases the lower bound on the string scale to 2-3 TeV, i
ndependently of the number of large extra dimensions.