Using a novel analysis technique, the gluon polarisation in the nucleon is re-evaluated using the longitudinal double-spin asymmetry measured in the cross section of semi-inclusive single-hadron muoproduction with photon virtuality $Q^2>1~({rm GeV}/c)^2$. The data were obtained by the COMPASS experiment at CERN using a 160 GeV/$c$ polarised muon beam impinging on a polarised $^6$LiD target. By analysing the full range in hadron transverse momentum $p_{rm T}$, the different $p_{rm T}$-dependences of the underlying processes are separated using a neural-network approach. In the absence of pQCD calculations at next-to-leading order in the selected kinematic domain, the gluon polarisation $Delta g/g$ is evaluated at leading order in pQCD at a hard scale of $mu^2= langle Q^2 rangle = 3 ({rm GeV}/c)^2$. It is determined in three intervals of the nucleon momentum fraction carried by gluons, $x_{rm g}$, covering the range $0.04 !<! x_{ rm g}! <! 0.28$~ and does not exhibit a significant dependence on $x_{rm g}$. The average over the three intervals, $langle Delta g/g rangle = 0.113 pm 0.038_{rm (stat.)}pm 0.036_{rm (syst.)}$ at $langle x_{rm g} rangle approx 0.10$, suggests that the gluon polarisation is positive in the measured $x_{rm g}$ range.
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