Collinear factorization for deep inelastic scattering structure functions at large Bjorken xB

TL;DR

The paper addresses the reliability of perturbative QCD factorization for DIS structure functions at large $x_B$ by formulating target mass corrections (TMC) in momentum space within collinear factorization, expressing them entirely in terms of PDFs to avoid unphysical regions and enabling cleaner extractions of large-$x$ PDFs. It extends the framework by incorporating final-state jet mass corrections (JMC) through a jet spectral function, linking hadronization effects to the partonic hard scattering and PDFs. A central result is the factorized, physically consistent expressions for structure functions that include TMC and, where applicable, JMC, highlighting their potential size at low to moderate $Q^2$ and large $x_B$. The work also discusses connections to lattice QCD via the jet propagator and outlines practical paths for implementing these corrections in global PDF fits, as well as extensions to polarized DIS, semi-inclusive processes, and nuclear targets.

Abstract

We examine the uncertainty of perturbative QCD factorization for hadron structure functions in deep inelastic scattering at a large value of the Bjorken variable xB. We analyze the target mass correction to the structure functions by using the collinear factorization approach in the momentum space. We express the long distance physics of structure functions and the leading target mass corrections in terms of parton distribution functions with the standard operator definition. We compare our result with existing work on the target mass correction. We also discuss the impact of a final-state jet function on the extraction of parton distributions at large fractional momentum x.

Figures (10)

• Figure 1: Collinear factorization of the hadronic tensor in the impulse approximation. The top blob represents the interaction of a virtual boson with a parton computed in pQCD at any order in $\alpha_s$.
• Figure 2: DIS in the impulse approximation, for the special case of an internal on-shell light parton, $k^2 = 0$, relevant to collinear factorization. The current jet has momentum $p_j$ and the target jet has momentum $p_Y$. The net baryon number is only shown to flow in the target jet (lower part of the graph).
• Figure 3: Comparison of prescriptions for NLO target mass corrections to the $F_2$ structure function. The ratio $F_2/F_2^{(0)}$ is plotted as a function of $x_B$ and $Q^2$. The structure functions have been computed using MRST2002 parton distributions Martin:2002aw.
• Figure 4: Comparison of prescriptions for NLO target mass corrections to the ratio of the longitudinal and transverse cross sections, $R=\sigma_L/\sigma_T= F_L/F_1$. The ratio $R/R^{(0)}$ is plotted as a function of $x_B$ and $Q^2$. The structure functions have been computed using MRST2002 parton distributions Martin:2002aw.
• Figure 5: DIS handbag diagram at leading order in $\alpha_s$.