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.
Highlights
In recent years, the extraction of unintegrated parton distribution functions (UPDFs) have become very important, since there exist plenty of experimental data on the various events, such as the exclusive and semi-inclusive processes in the high energy collisions in LHC, which indicate the necessity for a computation of these kt -dependent parton distribution functions.The UPDF, fa(x, kt2, μ2), are the two-scale dependent functions, i.e., kt2 and μ2, which satisfy the Ciafaloni–Catani–Fiorani–Marchesini (CCFM) equations [1,2,3,4,5], where x, kt, and μ are the longitudinal momentum fraction, the transverse momentum, and the factorization scale, respectively
To obtain the UPDF, Kimber, Martin and Ryskin (KMR) [18,19] proposed a different procedure based on the standard Dokshitzer–Gribov–Lipatov– Altarelli–Parisi (DGLAP) equations in the leading order (LO) approximation, along with a modification due to the angular ordering condition, which is the key dynamical property of the CCFM formalism
They are based on the DGLAP equations along with some modifications due to the separation of virtual and real parts of the evolutions, and the choice of the splitting functions at leading order (LO) and the next-to-leading order (NLO) levels, respectively: (i) In the KMR formalism [18,19], the UPDFs, fa(x, kt2, μ2) (a = q and g), are defined in terms of the quarks and the gluons PDF, i.e., fq (x, kt2, μ2)
Summary
The extraction of unintegrated parton distribution functions (UPDFs) have become very important, since there exist plenty of experimental data on the various events, such as the exclusive and semi-inclusive processes in the high energy collisions in LHC, which indicate the necessity for a computation of these kt -dependent parton distribution functions. Golec-Biernat and Stasto [45,46] (GS) have used the kt and collinear factorizations [39,40,41,42,43] as well as the dipole approach to generate the longitudinal structure function, but by using the DGLAP/BFKL re-summation method, developed by Kwiecinski, Martin and Stasto (KMS) [47], for a calculation of the unintegrated gluon density at small x They have parameterized the input non-perturbative gluon distribution so that they could get the best fit to the experimental proton structure function data [47].
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