Deep Inelastic Scattering from off-Shell Nucleons

TL;DR

This work develops a covariant framework for deep-inelastic scattering from off-shell nucleons, deriving the full hadronic tensor and identifying that only three transverse structure functions survive in the Bjorken limit, with gauge invariance and the Callan-Gross relation preserved. It demonstrates that the conventional convolution model is not generally derivable within this formalism due to antiparticle degrees of freedom and off-shell effects, and it applies the framework to the deuteron, nuclear matter, and dressed nucleons. The results reveal sizable off-shell corrections in bound systems and emphasize the need for fully covariant treatments when interpreting nuclear DIS data. Overall, the paper clarifies the limitations of traditional convolution approaches and provides a pathway to consistently incorporate off-shell dynamics into nuclear structure function calculations.

Abstract

We derive the general structure of the hadronic tensor required to describe deep-inelastic scattering from an off-shell nucleon within a covariant formalism. Of the large number of possible off-shell structure functions we find that only three contribute in the Bjorken limit. In our approach the usual ambiguities encountered when discussing problems related to off-shellness in deep-inelastic scattering are not present. The formulation therefore provides a clear framework within which one can discuss the various approximations and assumptions which have been used in earlier work. As examples, we investigate scattering from the deuteron, nuclear matter and dressed nucleons. The results of the full calculation are compared with those where various aspects of the off-shell structure are neglected, as well as with those of the convolution model.

Figures (9)

• Figure 1: The truncated nucleon tensor $\chi_{\mu\nu}$.
• Figure 2: Scattering from an off-shell nucleon in a composite target. The functions $A_i$ describe the nucleon--composite target interaction.
• Figure 3: Leading twist contribution to the off-shell tensor $\chi_{\mu\nu}$. The function $H(p,k)$ describes the soft, non-perturbative physics.
• Figure 4: Valence $u_V+d_V$ quark distribution in the nucleon, evolved from $Q_0^2 = 0.15$ GeV$^2$ (dashed curve) to $Q^2 = 4$ GeV$^2$ (solid curve), and compared against parameterisations (dotted curves) of world data DATAFIT.
• Figure 5: Valence $d_V/u_V$ ratio, evolved from $Q_0^2 = 0.15$ GeV$^2$ (dashed curve) to $Q^2 = 4$ GeV$^2$ (solid curve), and compared against parameterisations (dotted curves) of world data DATAFIT.