Spin structure of the proton from polarized inclusive deep-inelastic muon-proton scattering

We have measured the spin-dependent structure function ${g}_{1}^{p}$ in inclusive deep-inelastic scattering of polarized muons off polarized protons, in the kinematic range $0.003<x<0.7$ and $1{\mathrm{GeV}}^{2}<{Q}^{2}<60{\mathrm{GeV}}^{2}.$ A next-to-leading order QCD analysis is used to evolve the measured ${g}_{1}^{p}{(x,Q}^{2})$ to a fixed ${Q}_{0}^{2}.$ The first moment of ${g}_{1}^{p}$ at ${Q}_{0}^{2}=10{\mathrm{GeV}}^{2}$ is ${\ensuremath{\Gamma}}_{1}^{p}=0.136\ifmmode\pm\else\textpm\fi{}0.013$ (stat) $\ifmmode\pm\else\textpm\fi{}0.009$ (syst) $\ifmmode\pm\else\textpm\fi{}0.005$ (evol). This result is below the prediction of the Ellis-Jaffe sum rule by more than two standard deviations. The singlet axial charge ${a}_{0}$ is found to be $0.28\ifmmode\pm\else\textpm\fi{}0.16.$ In the Adler-Bardeen factorization scheme, $\ensuremath{\Delta}g\ensuremath{\simeq}2$ is required to bring \ensuremath{\Delta}\ensuremath{\Sigma} in agreement with the quark-parton model. A combined analysis of all available proton, deuteron, and ${}^{3}\mathrm{He}$ data confirms the Bjorken sum rule.