A new phenomenological Investigation of $KMR$ and $MRW$ $unintegrated$ parton distribution functions

TL;DR

This paper investigates the proton structure function $F_L(x,Q^2)$ using unintegrated parton distribution functions generated by KMR and MRW methods, comparing theoretical predictions with experimental data to assess their accuracy.

Contribution

It introduces a comparative analysis of $F_L(x,Q^2)$ using UPDFs from KMR and MRW schemes, highlighting the better agreement of KMR with experimental data.

Findings

KMR-based $F_L(x,Q^2)$ aligns closely with ZEUS and H1 data.

Both schemes produce $F_L(x,Q^2)$ largely independent of input PDFs.

Lowering the factorization scale improves theoretical data agreement.

Abstract

The longitudinal proton structure function, $F_L(x,Q^2)$, from the $k_t$ factorization formalism by using the unintegrated parton distribution functions (UPDF) which are generated through the KMR and MRW procedures. The LO UPDF of the KMR prescription is extracted, by taking into account the PDF of Martin et al, i.e. MSTW2008-LO and MRST99-NLO and next, the NLO UPDF of the MRW scheme is generated through the set of MSTW2008-NLO PDF as the inputs. The different aspects of $F_L(x,Q^2)$ in the two approaches, as well as its perturbative and non-perturbative parts are calculated. Then the comparison of $F_L(x,Q^2)$ is made with the data given by the ZEUS and H1 collaborations. It is demonstrated that the extracted $F_L(x,Q^2)$ based on the UPDF of two schemes, are consistent to the experimental data, and by a good approximation, they are independent to the input PDF. But the one developed from the KMR prescription, have better agreement to the data with respect to that of MRW. As it has been suggested, by lowering the factorization scale or the Bjorken variable in the related experiments, it may be possible to analyze the present theoretical approaches more accurately.