A study of the b-quark fragmentation function with the DELPHI detector at LEP I and an averaged distribution obtained at the Z Pole

The nature of b-quark jet hadronisation has been investigated using data taken at the Z peak by the DELPHI detector at LEP. Two complementary methods are used to reconstruct the energy of weakly decaying b-hadrons, EBʷᵉᵃᵏ . The average value of xʷᵉᵃᵏB = EBʷᵉᵃᵏ/Ebeam is measured to be 0.699±0.011. The resulting xʷᵉᵃᵏB distribution is then analysed in the framework of two choices for the perturbative contribution (parton shower and Next to Leading Log QCD calculation) in order to extract measurements of the non-perturbative contribution to be used in studies of b-hadron production in other experimental environments than LEP. In the parton shower framework, data favour the Lund model ansatz and corresponding values of its parameters have been determined within PYTHIA 6.156 from DELPHI data: a= 1.84+0.23-0.21 b=0.642+0.073-0.063~GeV⁻², with a correlation factor ρ=92.2%. Combining the data on the b-quark fragmentation distributions with those obtained at the Z peak by ALEPH, OPAL and SLD, the average value of xʷᵉᵃᵏB is found to be 0.7092±0.0025 and the non-perturbative fragmentation component is extracted. Using the combined distribution, a better determination of the Lund parameters is also obtained: a= 1.48+0.11-0.10 b=0.509+0.024-0.023~GeV⁻², with a correlation factor ρ=92.6%.