The Diffractive Contribution to Deep Inelastic Lepton-Proton Scattering: Implications for QCD Momentum Sum Rules and Parton Distributions

Abstract

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.