is highly sensitive to errors in signs and factors. We have also checked that if only the $s$-channel results are taken our numerical results are in close agreement with those of Ref.[@Eboli], and this, of course, implies that the $t$-channel contributions can be easily checked using crossing symmetry.

In our numerical analysis of this problem, we have also considered diagrams mediated by gravitons in place of $\gamma,Z$. Such diagrams, in fact, are of the same order in perturbation theory after summation over the graviton propagators, but it turns out that the contributions are very small — typically less than 1% for experimentally-allowed values of $M_S$ — due to the smallness of the effective graviton coupling after summation.

It is also worth mentioning that contributions due to graviscalars in the ADD model can also be neglected. It can be shown[@HLZ] that diagrams with graviscalars coupling to external fermion legs and vertices undergo large cancellations and the final contribution is proportional to the electron mass. This leaves only the diagrams with graviscalars emitted from the massive $Z$-propagator, which is again suppressed at high energies by a factor of $M_Z^2/s$ compared to the gravitensor contributions, the latter being jacked up by derivative couplings.

