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

TL;DR

This paper evaluates the validity of various PDF sets and their corresponding KMR UPDFs in describing proton structure functions using $k_t$-factorization, comparing results with experimental data and analyzing the transverse momentum distributions.

Contribution

It provides a comprehensive comparison of different PDF and UPDF sets, assesses their agreement with experimental data, and introduces a Gaussian fit method to estimate average transverse momentum in proton structure functions.

Findings

Minimal differences between input PDF sets and their UPDF ratios.

Reasonable agreement of structure functions with experimental data across different PDFs.

Estimated average transverse momentum $<k_t^2>$ aligns with other predictions.

Abstract

In this work, we discuss: (i) The ratios of different parton distribution functions (PDFs), i.e., MMHT2014, CJ15, CTEQ6l1, 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 $90$ $GeV^2$, 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 $Q^2=2.4-1.44\times10^4$ $GeV^2$, which is in agreement with the other groups predictions, $0.25-0.44$ $GeV^2$ at $Q^2=2.4$ $GeV^2$. (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.