High precision determination of the $Q^2$ evolution of the Bjorken sum

We present a significantly improved determination of the Bjorken sum for $0.6\le Q^2\le 4.8{\mathrm{GeV}}^2$ using precise new $g_1^p$ and $g_1^d$ data taken with the CLAS detector at Jefferson Lab. A higher-twist analysis of the $Q^2$ dependence of the Bjorken sum yields the twist-4 coefficient $f_2^{p-n}=-0.064\pm 0.009{\pm }_{0.036}^{0.032}$. This leads to the color polarizabilities ${\chi }_E^{p-n}=-0.032\pm 0.024$ and ${\chi }_B^{p-n}=0.032\pm 0.013$. The strong force coupling is determined to be ${\alpha }_s^{\overline{\mathrm{MS}}}(M_Z^2)=0.1123\pm 0.0061$, which has an uncertainty a factor of 1.5 smaller than earlier estimates using polarized deep inelastic scattering (DIS) data. This improvement makes the comparison between ${\alpha }_s$ extracted from polarized DIS and other techniques a valuable test of QCD.

Figure 1

The Bjorken sum ${\mathrm{\Gamma }}_1^{p-n}$. The solid blue circles give our results. The blue band is the systematic uncertainty. Other symbols show the world data. For those, the inner error bar indicates the statistical uncertainty and the outer error bar the quadratic sum of the statistic and systematic uncertainties. The gray band represents the leading-twist NNLO pQCD calculation in the $\overline{\mathrm{MS}}$ scheme.

Figure 2

The Bjorken sum ${\mathrm{\Gamma }}_1^{p-n}$ from EG1-DVCS (solid blue circles) compared with the phenomenological models described in the main text.

Figure 3

Three-parameter fit result for $f_2^{p-n}$ from the present study (square) and Refs. [11] (triangle) and [9] (circle). The inner error bar represents the point-to-point uncorrelated uncertainty and the outer error bar is the quadratic sum of the point-to-point correlated and uncorrelated uncertainties. Theoretical calculations [41, 42, 43, 44] are shown on the right.