Definition and Calculation of Bottom Quark Cross-Sections in Deep-inelastic Scattering at HERA and Determinat ion of their Uncertainties

The uncertainties involved in the calculation of bottom quark cross-sections in deep-inelastic scattering at HERA are studied in different phase space regions. Besides the inclusive bottom quark cross-section, definitions closer to the detector acceptance requiring at least one high energetic muon from the semi-leptonic \bquark decay or a jet with high transverse energy are investigated. For each case the uncertainties due to the choice of the renormalisation and factorisation scale as well as the \bquark mass are estimated in the perturbative NLO QCD calculation and furthermore uncertainties in the fragmenation of the bottom quark to a B-meson and in its semi-leptonic decay are discussed.