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We present the production cross section of heavy quarks \sigma^{cc},\sigma^{bb} and {\sigma^{tt}} at the next-to-leading order in theelectron-proton interaction by using the quarks and gluon distributionfunctions at the initial scale Q^{2}_{0}. To do this, we use a fitted form ofthe heavy quark coefficient functions for deep-inelastic lepton-hadronscattering to obtain the structure functions of heavy quarks. Then, wecalculate the reduced cross section of heavy quarks by using the structurefunctions and subsequently present the single differential and the integratedcross section of heavy quarks at the center-of-mass energies of 319 GeV , 1.3TeV and 3.5 TeV in the electron-proton collision. The obtained numericalresults of the cross section of the charm and beauty quarks are compared withthe HERA data, which is a combination from the results of the H1 and ZEUSdetectors, and with the predictions from H1PDF, MSTW2008 and MSRT03.Furthermore, we present the production cross section of top quark as a directprediction from our calculations.

Production cross section of heavy quarks in ep interaction at the NLO approximation