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 $0.003<x<\mathrm{}0.7\mathrm{}$ and $1{\mathrm{GeV}}^2<Q^2<60\mathrm{}{\mathrm{GeV}}^2.$ 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 $Q_0^2=10\mathrm{}{\mathrm{GeV}}^2$ is ${\Gamma }_1^p=0.136\mathrm{}\pm 0.013$ (stat) $\pm 0.009$ (syst) $\pm 0.005$ (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 $0.28\pm \mathrm{0.16.}$ In the Adler-Bardeen factorization scheme, $\Delta g\simeq 2$ is required to bring ΔΣ 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.