QCD radiative and power corrections and generalized Gerasimov-Drell-Hearn sum rules

We extend the earlier suggested QCD-motivated model for the $Q^2$ dependence of the generalized Gerasimov-Drell-Hearn (GDH) sum rule which assumes the smooth dependence of the structure function $g_T$, while the sharp dependence is due to the $g_2$ contribution and is described by the elastic part of the Burkhardt-Cottingham sum rule. The model successfully predicts the low crossing point for the proton GDH integral, but is at variance with the recent very accurate JLAB data. We show that, at this level of accuracy, one should include the previously neglected radiative and power QCD corrections, as boundary values for the model. We stress that the GDH integral, when measured with such a high accuracy achieved by the recent JLAB data, is very sensitive to QCD power corrections. We estimate the value of these power corrections from the JLAB data at $Q^2\sim 1{\mathrm{G}\mathrm{e}\mathrm{V}}^2$. The inclusion of all QCD corrections leads to a good description of proton, neutron, and deuteron data at all $Q^2$.

Figure 1

Our description of ${\Gamma }_1^p(Q^2)$ versus $Q^2$. The thick line is the new analysis to be compared with the thin line, which represents our previous approach without corrections.

Figure 2

Our prediction for ${\Gamma }_1^{p-n}(Q^2)$ versus $Q^2$. The thick line is the new analysis to be compared with the thin line, which represents our previous approach without corrections.

Figure 3

Our prediction for ${\Gamma }_1^n(Q^2)$ versus $Q^2$. The thick line is the new analysis to be compared with the thin line, which represents our previous approach without corrections.

Figure 4

Our prediction for ${\Gamma }_1^d(Q^2)$ versus $Q^2$. The thick line is the new analysis to be compared with the thin line, which represents our previous approach without corrections.