Matching of Fracture Functions for SIDIS in Target Fragmentation Region

TL;DR

This paper investigates the factorization properties of fracture functions in semi-inclusive deep inelastic scattering, providing gauge-invariant results up to twist-3 and aiding in modeling and resummation techniques.

Contribution

It derives gauge-invariant factorization formulas for fracture functions up to twist-3, enhancing understanding of target fragmentation in SIDIS.

Findings

Factorization applies when transverse momentum is between _{QCD} and Q.

Derived gauge-invariant results up to twist-3 level.

Facilitates modeling and resummation of large logarithms.

Abstract

In the target fragmentation region of Semi-Inclusive Deep Inelastic Scattering, the diffractively produced hadron has small transverse momentum. If it is at order of $\Lambda_{QCD}$, it prevents to make predictions with the standard collinear factorization. However, in this case, differential cross-sections can be predicted by the factorization with fracture functions, diffractive parton distributions. If the transverse momentum is much larger than $\Lambda_{QCD}$ but much smaller than $Q$ which is the virtuality of the virtual photon, both factorizations apply. In this case, fracture functions can be factorized with collinear parton distributions and fragmentation functions. We study the factorization up to twist-3 level and obtain gauge invariant results. They will be helpful for modeling fracture functions and useful for resummation of large logarithm of the transverse momentum appearing in collinear factorization.