# Fracture Functions in Different Kinematic Regions and Their Factorizations

## TL;DR

This paper investigates fracture functions in various kinematic regions, demonstrating their factorization properties and deriving evolution equations through one-loop calculations, which are crucial for understanding diffractive processes in QCD.

## Contribution

It provides a detailed analysis of fracture functions' factorization and evolution in different kinematic regimes, including explicit one-loop calculations for processes involving real photons.

## Key findings

- Fracture functions can be factorized into twist-2 PDFs and fragmentation functions in high-energy regimes.
- Derived evolution equations for fracture functions align with theoretical expectations.
- Explicit one-loop calculations confirm the factorization and evolution properties.

## Abstract

Fracture functions are parton distributions of an initial hadron in the presence of an almost collinear particle observed in the final state. They are important ingredients in QCD factorization for processes where a particle is produced diffractively. There are different fracture functions for a process in different kinematic regions. We take the production of a lepton pair combined with a diffractively produced particle in hadron collisions to discuss this. Those fracture functions can be factorized further if there are large energy scales involved. They can be factorized with twist-2 parton distribution functions and fragmentation functions. We perform one-loop calculations to illustrate the factorization in the case with the diffractively produced particle as a real photon. Evolution equations of different fracture functions are derived from our explicit calculations. They agree with expectations. These equations can be used for re-summations of large log terms in perturbative expansions.