  The cross section for the nuclear diffractive dissociation in proton-lead
collisions at the LHC is estimated. Based on the current theoretical
uncertainties for the single (target) diffactive cross section in hadron-hadron
reactions one obtains sigma_SD(5.02 TeV) = 19.67 \pm 5.41 mb and sigma_SD(8.8
TeV) = 18.76 \pm 5.77 mb, respectively. The invariant mass M_X for the reaction
pPb -> pX is also analyzed. Discussion is performed on the main theoretical
uncertainties associated to the calculations.
