A new phenomenological investigation of KMR and MRW unintegrated parton distribution functions

We address the longitudinal proton structure function, $$F_L(x,Q^2)$$FL(x,Q2), from the$$k_t$$kt-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 input. The different aspects of$$F_L(x,Q^2)$$FL(x,Q2) in the two approaches, as well as its perturbative and non-perturbative parts, are calculated. Then the comparison of$$F_L(x,Q^2)$$FL(x,Q2) is made with the data given by the ZEUS and H1 collaborations. It is demonstrated that the extracted$$F_L(x,Q^2)$$FL(x,Q2), based on the UPDF of two schemes, are consistent with the experimental data, and to a good approximation they are independent of the input PDF. But the one developed from the KMR prescription has better agreement with the data with respect to that of MRW. As 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.