Pathologies of the KMR prescriptions for unintegrated PDFs: Which prescription should be preferred?

TL;DR

This paper compares different KMR prescriptions for unintegrated PDFs, highlighting discrepancies and identifying the AO cut-off as problematic due to overestimation and ill-definition issues, recommending the SO cut-off for accuracy.

Contribution

The study critically evaluates KMR prescriptions, clarifies their issues, and advocates for the strong-ordering cut-off as the preferred method for unintegrated PDFs.

Findings

AO cut-off overestimates heavy-flavor cross sections by about a factor of 3.

SO cut-off provides results consistent with expected cross sections.

AO cut-off leads to ill-defined KMR uPDFs, unlike the SO cut-off.

Abstract

We discuss the different Kimber-Martin-Ryskin (KMR) prescriptions for unintegrated parton distribution functions (uPDFs). We show that the strong-ordering (SO) and the angular-ordering (AO) cut-offs lead to strong discrepancies between the obtained cross sections. While the result obtained with the AO cut-off overestimates the heavy-flavor cross section by about a factor 3, the SO cut-off gives the correct answer. We also solve the issue of the KMR uPDFs definitions mentioned by Golec-Biernat and Sta\'sto, and show that, in the case of the AO cut-off, the KMR uPDFs are ill-defined.