A phenomenological investigation of the integral and the differential versions of the Kimber-Martin-Ryskin unintegrated parton distribution functions using two different constraints and the MMHT2014 PDF

We previously investigated the compatibility of the Kimber–Martin–Ryskin (KMR) unintegrated parton distribution functions (UPDF) with the experimental data on the proton (longitudinal) structure functions (PSF (PLSF)). Recently Golec-Biernat and Stasto (GBS) demonstrated that the differential version of KMR prescription and the implementations of angular (strong) ordering (AOC (SOC)) constraints, cause the negative-discontinuous UPDF with the ordinary parton distribution functions (PDF) as the input, which leads to a sizable effect on the calculation of PSF. In the present work, we use the new MMHT2014-LO-PDF as the input and focus on the UPDF behaviors as was raised by GBS. The resulting PSF and PLSF are compared with the MSTW2008-LO-PDF and MRST99-PDF and the 2014 data given by the ZEUS and H1 collaborations. The calculated PSF and PLSF based on the integral prescription of the KMR-UPDF with the AOC and the ordinary PDF as the input are reasonably consistent with the experimental data. Therefore, they are approximately independent to the PDF (no need to impose cutoff on the PDF). At very small x regions because of the excess of gluons in the MMHT2014-LO-PDF and MSTW2008-LO-PDF, an increase in PSF and PLSF is achieved. Finally, according to the GBS report the differential version by using the cutoff independent PDF produces results far from the experimental data.