Leading and next-to-leading order gluon polarization in the nucleon and longitudinal double spin asymmetries from open charm muoproduction

The gluon polarisation in the nucleon was measured using open charmproduction by scattering 160 GeV/c polarised muons off longitudinally polarisedprotons or deuterons. The data were taken by the COMPASS collaboration between2002 and 2007. A detailed account is given of the analysis method that includesthe application of neural networks. Several decay channels of D^0 mesons areinvestigated. Longitudinal spin asymmetries of the D meson productioncross-sections are extracted in bins of D^0 transverse momentum and energy. Atleading 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 ~13(GeV/c)^2 and an average gluon momentum fraction ~ 0.11. For the first time,the average gluon polarisation is also obtained at next-to-leading order QCDaccuracy as (Delta g/G)^NLO = -0.13 +/- 0.15 (stat.) +/- 0.15 (syst.) at thescale ~ 13 (\GeV/c)^2 and ~ 0.20.