Parton distributions in the presence of target mass corrections

TL;DR

This paper examines the impact of target mass corrections on parton distribution functions at low Q^2, proposing an order-by-order expansion to improve physical consistency and analyzing its convergence.

Contribution

It introduces a new expansion method for target mass corrections that avoids unphysical regions and assesses its numerical convergence.

Findings

Proposed an order-by-order expansion for TMCs

Achieved closed-form expressions for unpolarized structure functions

Analyzed the convergence properties of the expansion

Abstract

We study the consistency of parton distribution functions in the presence of target mass corrections (TMCs) at low Q^2. We review the standard operator product expansion derivation of TMCs in both x and moment space, and present the results in closed form for all unpolarized structure functions and their moments. To avoid the unphysical region at x > 1 in the standard TMC analysis, we propose an expansion of the target mass corrected structure functions order by order in M^2/Q^2, and assess the convergence properties of the resulting forms numerically.