The aim of the present work is to study the phenomenological behavior of unitegrated parton distribution functions (UPDF) by using the Kimber-Martin-Ryskin (KMR) and Martin-Ryskin-Watt (MRW) formalisms. In the first method, the leading order (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. While in the second scheme, the next-to-leading order (NLO) UPDF of the (MRW) procedure is generated through the set of MSTW2008-NLO PDFas the inputs. The different aspects of the UPDF in the two approaches, as well as the input PDF are discussed. Then, the deep inelastic proton structure functions, F 2 ðx; Q 2 Þ, are calculated from the above UPDF in the two schemes, and compared with the data, which are extracted from the ZEUS, NMC, and H1 þ ZEUS experimental measurements. In general, it is shown that the calculated structure functions 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 proton structure functions, which are extracted from the KMR prescription, have better agreement to the data with respect to that of MRW. Although the MRW formalism is in more compliance with the Dokshitzer-Bribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equation requisites, but it seems in the KMR case, the angular ordering constraint spreads the UPDF to the whole transverse momentum region, and makes the results to sum up the leading DGLAP and Balitski-Fadin-Kuraev-Lipatov (BFKL) Logarithms. This point is under study by the authors.

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To overcome the complexity of generalized two hard scale (k t ,µ) evolution equation, well known as the Ciaf aloni, Catani, F iorani and M archsini (CCF M ) evolution equations, and calculate the unintegrated parton distribution functions (U P DF ), Kimber, M artin and Ryskin (KM R) proposed a procedure based on (i) the inclusion of single-scale (µ) only at the last step of evolution and (ii) the angular ordering constraint (AOC) on the DGLAP terms (the DGLAP collinear approximation), to bring the second scale, k t into the U P DF evolution equations. In this work we intend to use the M ST W 2008 (Martin et al) parton distribution functions (PDF) and try to calculate U P DF for various values of x (the longitudinal fraction of parton momentum), µ(the probe scale) and k t (the parton transverse momentum) to see the general behavior of three dimensional U P DF at the N LO level up to the LHC working energy scales (µ 2 ). It is shown that there exits some pronounced peaks for the three dimensional U P DF (f a (x, k t )) with respect to the two variables x and k t at various energies (µ). These peaks get larger and move to larger values of k t , as the energy (µ) is increased. We hope these peaks could be detected in the LHC experiments at CERN and other laboratories in the less exclusive processes.

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