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Leading and Next-to-Leading Order Gluon Polarisation in the Nucleon and Longitudinal Double Spin Asymmetries from Open Charm Muoproduction

The gluon polarisation in the nucleon was measured using open charm production by scattering 160 GeV/c polarised muons off longitudinally polarised protons or deuterons. The data were taken by the COMPASS collaboration between 2002 and 2007. A detailed account is given of the analysis method that includes the application of neural networks. Several decay channels of D^0 mesons are investigated. Longitudinal spin asymmetries of the D meson production cross-sections are extracted in bins of D^0 transverse momentum and energy. At leading order QCD accuracy the average gluon polarisation is determined as (Delta g/G)^LO=-0.06 +/- 0.21 (stat.) +/- 0.08 (syst.) at the scale <mu^2> ~13 (GeV/c)^2 and an average gluon momentum fraction <x>~ 0.11. For the first time, the average gluon polarisation is also obtained at next-to-leading order QCD accuracy as (Delta g/G)^NLO = -0.13 +/- 0.15 (stat.) +/- 0.15 (syst.) at the scale <mu^2> ~ 13 (\GeV/c)^2 and <x> ~ 0.20.