On the use of the KMR unintegrated parton distribution functions

TL;DR

This paper examines the Kimber-Martin-Ryskin (KMR) unintegrated parton distribution functions, highlighting issues with the differential definition at high transverse momenta and proposing the integral definition as a reliable alternative for phenomenology.

Contribution

It clarifies the proper use of KMR UPDFs by identifying errors in the differential approach and advocates for the integral definition in practical applications.

Findings

Differential UPDFs give erroneous results at large transverse momenta.

The use of ordinary PDFs in the integral definition is appropriate for phenomenology.

Identifies the cause of discrepancies as the use of cutoff dependent distributions.

Abstract

We discuss the unintegrated parton distribution functions (UPDFs) introduced by Kimber, Martin and Ryskin (KMR), which are frequently used in phenomenological analyses of hard processes with transverse momenta of partons taken into account. We demonstrate numerically that the commonly used differential definition of the UPDFs leads to erroneous results for large transverse momenta. We identify the reason for that, being the use of the ordinary PDFs instead of the cutoff dependent distribution functions. We show that in phenomenological applications, the integral definition of the UPDFs with the ordinary PDFs can be used.