  The cross section for deep inelastic lepton-proton scattering (DIS) $\ell p
\to \ell' X$ includes a diffractive deep inelastic (DDIS) contribution $\ell p
\to \ell' p' X$, in which the proton remains intact with a large longitudinal
momentum fraction $x_F$ greater than 0.9 and small transverse momentum. The
DDIS events, which can be identified with Pomeron exchange in the $t$-channel,
account for approximately $10\%$ of all of the DIS events. Thus, when one
measures DIS, one automatically includes the leading-twist Bjorken-scaling DDIS
events as a contribution to the DIS cross section, whether or not the
final-state proton $p'$ is detected. In such events, the missing momentum
fraction $x_{p'} \sim 0.9$ carried by the final-state proton $p'$ in the DDIS
events could be misidentified with the light-front momentum fraction carried by
sea quarks or gluons in the protons' Fock structure. As we shall show in this
article, the underlying QCD Pomeron-exchange amplitude which produces the DDIS
events does not obey the operator product expansion nor satisfy momentum sum
rules. Thus we conclude that the quark and gluon distributions measured in DIS
experiments will be misidentified, unless the measurements explicitly exclude
the DDIS events and that a correct determination of the parton distribution
functions (PDFs) derived from the DIS data requires the explicit subtraction of
the DDIS contribution from the full DIS cross section.
