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

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A 6-dimensional grand unified theory with the compact space having the topology of a real projective plane, i.e., a 2-sphere with opposite points identified, is considered. The space is locally flat except for two conical singularities where the curvature is concentrated. One supersymmetry is preserved in the effective 4d theory. The unified gauge symmetry, for example SU(5) , is broken only by the non-trivial global topology. In contrast to the Hosotani mechanism, no adjoint Wilson-line modulus associated with this breaking appears. Since, locally, SU(5) remains a good symmetry everywhere, no UV-sensitive threshold corrections arise and SU(5)-violating local operators are forbidden. Doublettriplet splitting can be addressed in the context of a 6d N = 2 super Yang-Mills theory with gauge group SU(6). If this symmetry is first broken to SU(5) at a fixed point and then further reduced to the standard model group in the above non-local way, the two light Higgs doublets of the MSSM are predicted by the group-theoretical and geometrical structure of the model.

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