Final COMPASS results on the deuteron spin-dependent structure function $g_1^{\rm d}$ and the Bjorken sum rule

Final results are presented from the inclusive measurement of deep-inelastic polarised-muon scattering on longitudinally polarised deuterons using a 6 LiD target. The data were taken at 160 GeV beam energy and the results are shown for the kinematic range 1(GeV/c)2<Q2<100(GeV/c)2 in photon virtuality, 0.004<x<0.7 in the Bjorken scaling variable and W>4GeV/c2 in the mass of the hadronic final state. The deuteron double-spin asymmetry A1d and the deuteron longitudinal-spin structure function g1d are presented in bins of x and Q2 . Towards lowest accessible values of x , g1d decreases and becomes consistent with zero within uncertainties. The presented final g1d values together with the recently published final g1p values of COMPASS are used to again evaluate the Bjorken sum rule and perform the QCD fit to the g1 world data at next-to-leading order of the strong coupling constant. In both cases, changes in central values of the resulting numbers are well within statistical uncertainties. The flavour-singlet axial charge a0 , which is identified in the MS‾ renormalisation scheme with the total contribution of quark helicities to the nucleon spin, is extracted at next-to-leading order accuracy from only the COMPASS deuteron data: a0(Q2=3(GeV/c)2)=0.32±0.02stat±0.04syst±0.05evol . Together with the recent results on the proton spin structure function g1p , the results on g1d constitute the COMPASS legacy on the measurements of g1 through inclusive spin-dependent deep inelastic scattering.