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

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.