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In this work, we study the structure of the leading order Martin-Ryskin-Watt(MRW) unintegrated parton distribution function (UPDF) and explain in detailwhy there exists discrepancy between the two different definitions of this UPDFmodel, i.e., the integral (I-MRW) and differential (D-MRW) MRW UPDFs. Weperform this investigation with both angular and strong ordering cutoffs. Thederivation footsteps of obtaining the I-MRW UPDF from the D-MRW ones arenumerically performed, and the reason of such non-equivalency between the twoforms is clearly explained. We show and find out that both methods suggested inthe papers by Golec-Biernat and Stasto as well as that of Guiot haveshortcomings, and only the combination of their prescriptions can give us thesame UPDF structure from both of these two different versions of the MRW UPDF,namely I-MRW and the D-MRW UPDFs.

On the ambiguity between differential and integral forms of the Martin-Ryskin-Watt unintegrated parton distribution function model