Updating the proton heavy quark content analysis in the k-factorization formalism using the KMR and MRW approaches

The beauty structure function ( F 2 b b ‾ ( x , Q 2 ) ) and the reduced beauty cross section ( σ r e d b b ‾ ( x , Q 2 ) ) are calculated in the k t -factorization formalism by using the unintegrated parton distribution functions ( UPDF ) which are generated through the integral form of the Kimber et al ( KMR ) and Martin et al ( MRW ) approaches with the angular ordering constraint ( AOC ) at leading order of QCD running coupling with λ Q C D = 200 M e V and n F = 5 . The MMHT 2014 PDF set is used as the input PDF for the corresponding UPDF . By comparing the resulted F 2 b b ‾ and σ r e d b b ‾ with the experimental data and the theoretical predictions, we encounter an overestimation of the experimental data and the theoretical predictions that, according to our recent reports on the beauty content of a proton, cannot be due to different choices of the upper limit of the transverse momentum k max . By considering the same value of the QCD coupling constant, α s ( M z 2 ) as used in fitting the input PDF to the K M R − U P D F and M R W − U P D F , i.e. α s , L O ( M z 2 ) = 0.135 and α s , N L O ( M z 2 ) = 0.118 , respectively, the overestimation is eliminated. Given the importance of the topic, in this paper, we present an updated analysis of the charm content of the proton and demonstrate that despite the calculated charm structure functions based on the above two UPDF approaches are consistent to the experimental data and others theoretical predictions, the results obtained from the KMR approach are in much better agreement with the experimental data.