Violation of Factorization Theorem in QCD and QED For Non-Light-Like Wilson Line

TL;DR

This paper demonstrates that the factorization theorem in QCD and QED holds for light-like Wilson lines but is violated for non-light-like Wilson lines, impacting high-energy collider calculations.

Contribution

It provides a rigorous proof using path integral formulation that factorization fails for non-light-like Wilson lines, clarifying previous misconceptions.

Findings

Factorization valid for light-like Wilson lines.

Factorization violated for non-light-like Wilson lines.

Implications for parton distribution and fragmentation functions.

Abstract

By using path integral formulation of QCD and QED we prove that the factorization theorem is valid for light-like Wilson line but is not valid for non-light-like Wilson line. This conclusion is shown to be consistent with Ward identity and Grammer-Yennie approximation. Hence we find that the factorization theorem is violated in all the previous studies which used the non-light-like Wilson line in the definition of the (transverse momentum dependent) parton distribution function and fragmentation function at high energy colliders.