A Proof of Factorization Theorem of Drell-Yan Process at Operator Level

TL;DR

This paper provides an operator-level proof of the Drell-Yan factorization theorem, demonstrating the cancellation of final state interactions and soft gluons through unitarity and field redefinitions, enabling eikonal approximations.

Contribution

It offers a novel operator-level proof of factorization for Drell-Yan processes, emphasizing unitarity and decoupling of soft gluons via new collinear fields.

Findings

Final state interactions cancel at operator level due to unitarity.

Soft gluons decouple from collinear jets through new field definitions.

Eikonal line approximation is justified after integral path deformation.

Abstract

An alternative proof of factorization theorem for Drell-Yan process that works at operator level is given in the article. Final state interactions for such inclusive processes are proved to be cancel out at operator level according to the unitarity of time evolution operator. After this cancellation, one can always deform the integral path so that eikonal line approximation works while calculating the time evolution of electromagnetic currants. Decoupling of soft gluons from collinear jets is realized by defining new collinear fields that decouple from soft gluons. Cancelation of soft gluons is attribute to unitarity of time evolution operator and light-like Wilson lines of soft gluons.