Structure Functions are not Parton Probabilities

Abstract

The common view that structure functions measured in deep inelastic lepton scattering are determined by the probability of finding quarks and gluons in the target is not correct in gauge theory. We show that gluon exchange between the fast, outgoing partons and target spectators, which is usually assumed to be an irrelevant gauge artifact, affects the leading twist structure functions in a profound way. This observation removes the apparent contradiction between the projectile (eikonal) and target (parton model) views of diffractive and small x_{Bjorken} phenomena. The diffractive scattering of the fast outgoing quarks on spectators in the target causes shadowing in the DIS cross section. Thus the depletion of the nuclear structure functions is not intrinsic to the wave function of the nucleus, but is a coherent effect arising from the destructive interference of diffractive channels induced by final state interactions. This is consistent with the Glauber-Gribov interpretation of shadowing as a rescattering effect.

Figures (8)

• Figure 1: Two types of final state interactions. (a) Scattering of the antiquark ($p_2$ line), which in the aligned jet kinematics is part of the target dynamics. (b) Scattering of the current quark ($p_1$ line). For each LC time-ordered diagram, the potentially on-shell intermediate states corresponding to the denominators $D_a, D_b, D_c$ are denoted by dashed lines.
• Figure 2: Glauber-Gribov shadowing involves interference between rescattering amplitudes.
• Figure 3: Forward $\gamma^* T \to \gamma^* T$ amplitude. All attachments of the exchanged gluons to the upper scalar loop are included, as well as topologically distinct permutations of the lower vertices on the target line.
• Figure 4: Single gluon exchange diagrams in scalar abelian theory.
• Figure 5: Double gluon exchange diagrams. In Feynman gauge four more diagrams contribute at leading order, where one or both of the exchanged gluons attach to the quark ($p_1$) line.