On validity of different PDFs sets using the proton kt -factorization structure functions and the Gaussian kt-dependence of KMR UPDFs

In this work, we discuss: (i) The ratios of different parton distribution functions (PDFs), i.e., MMHT2014, CJ15, CTEQ611, HERAPDF15, MSTW2008, HERAPDF20 and MSHT20, and the corresponding Kimber-Martin-Ryskin (KMR) unintegrated parton distribution functions (UPDFs) sets versus the hard scale Q(2), to find out the sensibility of the KMR UPDFs with respect to the input PDFs sets. It is shown that there is not much difference between the different input-PDFs or corresponding UPDFs sets ratios. (ii) Then, the dependence of proton k(t)-factorization structure functions on the different UPDFs sets which can use the above PDFs sets as input, are presented. The results are compared with the experimental data of ZEUS, NMC and H1+ZEUS at the hard scale Q(2) = 27 and 90 GeV2, and a reasonable agreement is found, considering different input PDFs sets. (iii) Furthermore, by fitting a Gaussian function, which depends on the transverse momentum k(t), to the KMR UPDFs and averaging over x (the fractional parton momentum), we obtain the average transverse momentum, < k(t)(2)>, in the scale range Q(2) = 2.4-1.44 x 10(4) GeV2, which is in agreement with the other groups predictions, 0.25-0.44 GeV2 at Q(2) = 2.4 GeV2. (iv) Finally we explore the average transverse momentum for which, the results of proton structure function with the KMR UPDFs and that of the Gaussian k(t)-dependent, are consistent to each other. Through the above report, at each step the parton branching (PB) UPDFs, i.e., the transverse momentum dependent PDFs (PB TMDPDFs) are considered for comparisons with the corresponding KMR UPDFs output.

Automated summary

In this work, we discuss the ratios of different parton distribution functions (PDFs) and corresponding unintegrated parton distribution functions (UPDFs) sets, and their impact on proton k(t)-factorization structure functions. The results show that there is not much difference between the different input-PDFs or corresponding UPDFs sets ratios. By comparing with experimental data, reasonable agreement is found considering different input PDFs sets. The average transverse momentum is obtained by fitting a Gaussian function, which is consistent with predictions from other research groups. Finally, we explore the average transverse momentum that is consistent between the results of the proton structure function with KMR UPDFs and the Gaussian k(t)-dependent.