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We previously investigated the compatibility of the$Kimber$-$Martin$-$Ryskin$ ($KMR$) $unintegrated$ parton distribution functions($UPDF$) with the experimental data on the proton (longitudinal) structurefunctions ($PSF$ ($PLSF$)). Recently $Golec-Biernat$ and $Stasto$ ($GBS$)demonstrated that the differential version of $KMR$ prescription and theimplementations of angular (strong) ordering ($AOC$ ($SOC$)) constraints, causethe negative-discontinuous $UPDF$ with the ordinary parton distributionfunctions ($PDF$) as the input, which leads to a sizable effect on thecalculation 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 integralprescription of the $KMR$-$UPDF$ with the $AOC$ and the ordinary $PDF$ as theinput are reasonably consistent with the experimental data. Therefore, they areapproximately 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 differentialversion by using the cutoff independent $PDF$ produces results far from theexperimental data.

european physical journal. c, particles and fields

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