The production of charmed and beauty hadrons in proton-proton collisions at high energies are analyzed within the modified quark-gluon string model (QGSM) including the internal motion of quarks in colliding hadrons. We present some predictions for the future experiments on the beauty baryon production in $pp$ collisions at LHC energies. This analysis allows us to find interesting information on the Regge trajectories of the heavy (b{bar b}) mesons and the sea beauty quark distributions in the proton.
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